diff --git a/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb b/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb
index f184de74e..f44a3fc0f 100644
--- a/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb
+++ b/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb
@@ -2689,9 +2689,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 3,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'                                                                                                                         \\nThis is taken from the data file of the mass 2016 evaluation.                                                               \\nAll files are 3436 lines long with 124 character per line.                                                                  \\n       Headers are 39 lines long.                                                                                           \\n   col 1     :  Fortran character control: 1 = page feed  0 = line feed                                                     \\n   format    :  a1,i3,i5,i5,i5,1x,a3,a4,1x,f13.5,f11.5,f11.3,f9.3,1x,a2,f11.3,f9.3,1x,i3,1x,f12.5,f11.5                     \\n   These formats are reflected in the pandas widths variable below, see the statement                                       \\n   widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1),                                                            \\n   Pandas has also a variable header, with length 39 in this case.                                                          \\n'"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "\"\"\"                                                                                                                         \n",
     "This is taken from the data file of the mass 2016 evaluation.                                                               \n",
@@ -2717,7 +2728,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2759,28 +2770,26 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "            N    Z    A Element  Ebinding\n",
-      "A                                        \n",
-      "1   0       0    1    1       H  0.000000\n",
-      "2   1       1    1    2       H  1.112283\n",
-      "3   2       2    1    3       H  2.827265\n",
-      "4   6       2    2    4      He  7.073915\n",
-      "5   9       3    2    5      He  5.512132\n",
-      "...       ...  ...  ...     ...       ...\n",
-      "264 3304  156  108  264      Hs  7.298375\n",
-      "265 3310  157  108  265      Hs  7.296247\n",
-      "266 3317  158  108  266      Hs  7.298273\n",
-      "269 3338  159  110  269      Ds  7.250154\n",
-      "270 3344  160  110  270      Ds  7.253775\n",
-      "\n",
-      "[267 rows x 5 columns]\n"
+      "A        \n",
+      "1    0         1\n",
+      "2    1         2\n",
+      "3    2         3\n",
+      "4    6         4\n",
+      "5    9         5\n",
+      "            ... \n",
+      "264  3304    264\n",
+      "265  3310    265\n",
+      "266  3317    266\n",
+      "269  3338    269\n",
+      "270  3344    270\n",
+      "Name: A, Length: 267, dtype: int64\n"
      ]
     }
    ],
@@ -2790,7 +2799,9 @@
     "N = Masses['N']\n",
     "Element = Masses['Element']\n",
     "Energies = Masses['Ebinding']\n",
-    "print(Masses)"
+    "#print(Masses)\n",
+    "xx = A\n",
+    "print(xx)"
    ]
   },
   {
diff --git a/doc/pub/week38/html/._week38-bs000.html b/doc/pub/week38/html/._week38-bs000.html
index 0d1b2580c..dc41103ec 100644
--- a/doc/pub/week38/html/._week38-bs000.html
+++ b/doc/pub/week38/html/._week38-bs000.html
@@ -1,11 +1,11 @@
 <!--
 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
 -->
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
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-              ('Ridge and LASSO Regression, reminder',
-               2,
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+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
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+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
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-              ('Still thinking', 2, None, 'still-thinking'),
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+              ('More thinking', 2, None, '___sec8'),
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                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
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-              ('Linear regression', 2, None, 'linear-regression'),
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-               None,
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-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
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-               None,
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-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
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-               None,
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-              ('Basics', 2, None, 'basics'),
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-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
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-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
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-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
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-<h2 id="plans-for-week-38" class="anchor">Plans for week 38 </h2>
+<h2 id="___sec0" class="anchor">Plans for week 38 </h2>
 
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 <li> Thursday: Summary of regression methods and discussion of project 1.  Start Logistic Regression</li>
@@ -449,7 +356,7 @@ MathJax.Hub.Config({
 
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+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
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-               None,
-               'conjugate-gradient-method'),
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-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0002"></a>
 <!-- !split -->
 
-<h2 id="thursday-september-23" class="anchor">Thursday September 23 </h2>
+<h2 id="___sec1" class="anchor">Thursday September 23 </h2>
 
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 <p>
@@ -446,7 +353,7 @@ MathJax.Hub.Config({
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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diff --git a/doc/pub/week38/html/._week38-bs003.html b/doc/pub/week38/html/._week38-bs003.html
index df89ceb8e..d642a66eb 100644
--- a/doc/pub/week38/html/._week38-bs003.html
+++ b/doc/pub/week38/html/._week38-bs003.html
@@ -1,11 +1,11 @@
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-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
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                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
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-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
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-               None,
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-               None,
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-               None,
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-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
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-               None,
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-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
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-              ('The ideal', 2, None, 'the-ideal'),
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+              ('The equations', 2, None, '___sec51'),
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+              ('Steepest descent', 2, None, '___sec54'),
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-               2,
-               None,
-               'standard-steepest-descent'),
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-               None,
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-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
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-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
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                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
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@@ -311,94 +218,94 @@ MathJax.Hub.Config({
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         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0003"></a>
 <!-- !split -->
 
-<h2 id="ridge-and-lasso-regression-reminder" class="anchor">Ridge and LASSO Regression, reminder </h2>
+<h2 id="___sec2" class="anchor">Ridge and LASSO Regression, reminder </h2>
 
 <p>
 The expression for the standard Mean Squared Error (MSE) which we used to define our cost function and the equations for the ordinary least squares (OLS) method, that is 
@@ -500,7 +407,7 @@ $$
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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diff --git a/doc/pub/week38/html/._week38-bs004.html b/doc/pub/week38/html/._week38-bs004.html
index 20753a5ea..33f6020a8 100644
--- a/doc/pub/week38/html/._week38-bs004.html
+++ b/doc/pub/week38/html/._week38-bs004.html
@@ -1,11 +1,11 @@
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+(https://github.com/hplgit/doconce/)
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 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
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 {'highest level': 2,
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-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
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-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
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-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
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-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
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                2,
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-               None,
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-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
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-               None,
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-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
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-               None,
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-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
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-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
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-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
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-               None,
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-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
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-              ('The derivative of the cost/loss function',
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-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
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                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
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-<h2 id="various-steps-in-cross-validation" class="anchor">Various steps in cross-validation </h2>
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@@ -464,7 +371,7 @@ cross-validation (LOOCV).
 
 <!-- Bootstrap footer
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+<a href="http://..."><img width="250" align=right src="http://..."></a>
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+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
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 <!-- !split  -->
 
-<h2 id="how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" class="anchor">How to set up the cross-validation for Ridge and/or Lasso </h2>
+<h2 id="___sec4" class="anchor">How to set up the cross-validation for Ridge and/or Lasso </h2>
 
 <ul>
 <li> Define a range of interest for the penalty parameter.</li>
@@ -476,7 +383,7 @@ $$
 
 <!-- Bootstrap footer
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+<a href="http://..."><img width="250" align=right src="http://..."></a>
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-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0006"></a>
 <!-- !split -->
 
-<h2 id="cross-validation-in-brief" class="anchor">Cross-validation in brief </h2>
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 <p>
 For the various values of \( k \)
@@ -467,7 +374,7 @@ For the various values of \( k \)
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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diff --git a/doc/pub/week38/html/._week38-bs007.html b/doc/pub/week38/html/._week38-bs007.html
index 0729c7279..ed8bcc88a 100644
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+++ b/doc/pub/week38/html/._week38-bs007.html
@@ -1,11 +1,11 @@
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-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
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                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
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                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
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-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
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-              ('Including more classes', 2, None, 'including-more-classes'),
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-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
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-               None,
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-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
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-              ('The ideal', 2, None, 'the-ideal'),
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+              ('The equations', 2, None, '___sec51'),
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-               None,
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-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
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-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
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                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
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-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
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         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,14 +321,14 @@ MathJax.Hub.Config({
 <a name="part0007"></a>
 <!-- !split -->
 
-<h2 id="code-example-for-cross-validation-and-k-fold-cross-validation" class="anchor">Code Example for Cross-validation and \( k \)-fold Cross-validation </h2>
+<h2 id="___sec6" class="anchor">Code Example for Cross-validation and \( k \)-fold Cross-validation </h2>
 
 <p>
 The code here uses Ridge regression with cross-validation (CV)  resampling and \( k \)-fold CV in order to fit a specific polynomial. 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> KFold
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> Ridge
@@ -546,7 +453,7 @@ plt<span style="color: #666666">.</span>show()
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs008.html b/doc/pub/week38/html/._week38-bs008.html
index 91739634e..6e08f6a7d 100644
--- a/doc/pub/week38/html/._week38-bs008.html
+++ b/doc/pub/week38/html/._week38-bs008.html
@@ -1,11 +1,11 @@
 <!--
 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
 -->
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
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-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
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-               None,
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-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
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-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
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-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
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 <p>
 When you are comparing your own code with for example <b>Scikit-Learn</b>'s
@@ -433,7 +340,7 @@ Thus, if we cannot assume that the expected outputs/targets are zero
 when all predictors are zero (the columns in the design matrix), it
 may be a bad idea to implement a model which penalizes the intercept.
 Furthermore, in for example Ridge and Lasso regression, the solutions
-(when not shrinking $$\beta_0$$) for the unknown parameters
+(when not shrinking \( \beta_0 \)) for the unknown parameters
 \( \boldsymbol{\beta} \) are derived&#160;under the assumption that both \( \boldsymbol{y} \) and
 \( \boldsymbol{X} \) are zero centered, that is we subtract the mean values.
 
@@ -473,7 +380,7 @@ Furthermore, in for example Ridge and Lasso regression, the solutions
 
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+<a href="http://..."><img width="250" align=right src="http://..."></a>
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+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
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+               '___sec11'),
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               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
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-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
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-               2,
-               None,
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-              ('Basics', 2, None, 'basics'),
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-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
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-               None,
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-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
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-              ('Simple geometric interpretation',
-               2,
-               None,
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-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
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-               None,
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-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
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-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
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-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
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+<a href="http://..."><img width="250" align=right src="http://..."></a>
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               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0010"></a>
 <!-- !split -->
 
-<h2 id="still-thinking" class="anchor">Still thinking </h2>
+<h2 id="___sec9" class="anchor">Still thinking </h2>
 
 <p>
 Keep in mind that when you transform your data set before training a model, the same transformation needs to be done
@@ -423,7 +330,7 @@ on your eventual new data set  before making a prediction. If we translate this
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #408080; font-style: italic">#Model training, we compute the mean value of y and X</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic">#Model training, we compute the mean value of y and X</span>
 y_train_mean <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean(y_train)
 X_train_mean <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean(X_train,axis<span style="color: #666666">=0</span>)
 X_train <span style="color: #666666">=</span> X_train <span style="color: #666666">-</span> X_train_mean
@@ -476,7 +383,7 @@ y_pred <span style="color: #666666">=</span> y_pred <span style="color: #666666"
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs011.html b/doc/pub/week38/html/._week38-bs011.html
index 130fb0677..eb852aa0d 100644
--- a/doc/pub/week38/html/._week38-bs011.html
+++ b/doc/pub/week38/html/._week38-bs011.html
@@ -1,11 +1,11 @@
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-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
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 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
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                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
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-               None,
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-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
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-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
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+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
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-              ('Some simple problems', 2, None, 'some-simple-problems'),
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-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
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-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
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-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
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-               None,
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-              ('Conjugate gradient method',
-               2,
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-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
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-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0011"></a>
 <!-- !split -->
 
-<h2 id="linear-regression-code-intercept-handling-first" class="anchor">Linear Regression code, Intercept handling first </h2>
+<h2 id="___sec10" class="anchor">Linear Regression code, Intercept handling first </h2>
 
 <p>
 This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (<em>code example thanks to  &#216;yvind Sigmundson Sch&#248;yen</em>). Here our scaling of the data is done by subtracting the mean values only.
@@ -422,7 +329,7 @@ This code shows a simple first-order fit to a data set using the above transform
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LinearRegression
@@ -531,7 +438,7 @@ plt<span style="color: #666666">.</span>show()
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs012.html b/doc/pub/week38/html/._week38-bs012.html
index 1bb7caa48..453862089 100644
--- a/doc/pub/week38/html/._week38-bs012.html
+++ b/doc/pub/week38/html/._week38-bs012.html
@@ -1,11 +1,11 @@
 <!--
 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
 -->
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
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-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0012"></a>
 <!-- !split -->
 
-<h2 id="what-does-centering-subtracting-the-mean-values-mean-mathematically" class="anchor">What does centering (subtracting the mean values) mean mathematically? </h2>
+<h2 id="___sec11" class="anchor">What does centering (subtracting the mean values) mean mathematically? </h2>
 
 <p>
 Let us try to understand what this may imply mathematically when we subtract the mean values, also known as <em>zero centering</em>. To catch many birds with just one stone, we will focus on Ridge regression.
@@ -451,7 +358,7 @@ If we assume that every column of \( \boldsymbol{X} \) is centered, which we can
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>X <span style="color: #666666">=</span> X <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(X,axis<span style="color: #666666">=0</span>)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>X <span style="color: #666666">=</span> X <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(X,axis<span style="color: #666666">=0</span>)
 </pre></div>
 <p>
 the sum \( \sum_{i=0}^{n-1} X_{ij} \)
@@ -530,7 +437,7 @@ and \( \tilde{X}_{ij} = X_{ij} - \frac{1}{n}\sum_{k=1}^{n-1}X_{kj} \).
 
 <!-- Bootstrap footer
 <footer>
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+<a href="http://..."><img width="250" align=right src="http://..."></a>
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diff --git a/doc/pub/week38/html/._week38-bs013.html b/doc/pub/week38/html/._week38-bs013.html
index 659ea337e..741d9ab3f 100644
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@@ -1,11 +1,11 @@
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-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
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-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0013"></a>
 <!-- !split -->
 
-<h2 id="code-examples" class="anchor">Code Examples </h2>
+<h2 id="___sec12" class="anchor">Code Examples </h2>
 
 <p>
 Armed with this wisdom, we attempt first simply set the intercept eqault to <b>False</b> in our implementation of Ridge regression for a vanilla data set.
@@ -422,7 +329,7 @@ Armed with this wisdom, we attempt first simply set the intercept eqault to <b>F
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
@@ -534,7 +441,7 @@ Let us see how we can change this code by zero centering.
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs014.html b/doc/pub/week38/html/._week38-bs014.html
index 01b0c6c01..03f7e06c4 100644
--- a/doc/pub/week38/html/._week38-bs014.html
+++ b/doc/pub/week38/html/._week38-bs014.html
@@ -1,11 +1,11 @@
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+(https://github.com/hplgit/doconce/)
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 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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-              ('Ridge and LASSO Regression, reminder',
-               2,
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+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
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-              ('LASSO regression', 2, None, 'lasso-regression'),
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+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
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-               None,
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-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
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-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
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-              ('Plotting the mean value for each group',
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-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,11 +321,11 @@ MathJax.Hub.Config({
 <a name="part0014"></a>
 <!-- !split -->
 
-<h2 id="taking-out-the-mean" class="anchor">Taking out the mean </h2>
+<h2 id="___sec13" class="anchor">Taking out the mean </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
@@ -542,7 +449,7 @@ plt<span style="color: #666666">.</span>show()
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs015.html b/doc/pub/week38/html/._week38-bs015.html
index cfdf84010..d05dd42d7 100644
--- a/doc/pub/week38/html/._week38-bs015.html
+++ b/doc/pub/week38/html/._week38-bs015.html
@@ -1,11 +1,11 @@
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-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
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 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
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-               'ridge-and-lasso-regression-reminder'),
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+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
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-              ('LASSO regression', 2, None, 'lasso-regression'),
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+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
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                None,
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-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
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-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
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+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
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                None,
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-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
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-              ('The ideal', 2, None, 'the-ideal'),
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-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0015"></a>
 <!-- !split -->
 
-<h2 id="more-complicated-example-the-ising-model" class="anchor">More complicated Example: The Ising model </h2>
+<h2 id="___sec14" class="anchor">More complicated Example: The Ising model </h2>
 
 <p>
 The one-dimensional Ising model with nearest neighbor interaction, no
@@ -440,7 +347,7 @@ with their respective energies.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">mpl_toolkits.axes_grid1</span> <span style="color: #008000; font-weight: bold">import</span> make_axes_locatable
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">seaborn</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sns</span>
@@ -506,7 +413,7 @@ the coupling constant to achieve this.
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs016.html b/doc/pub/week38/html/._week38-bs016.html
index 4d84de842..03af90f3b 100644
--- a/doc/pub/week38/html/._week38-bs016.html
+++ b/doc/pub/week38/html/._week38-bs016.html
@@ -1,11 +1,11 @@
 <!--
 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
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 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
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                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
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-              ('A more compact expression',
-               2,
-               None,
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-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
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                None,
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-               None,
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-              ('Extending to more than one variable',
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-               None,
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-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
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-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
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-               2,
-               None,
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-              ('Gradient method', 2, None, 'gradient-method'),
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-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
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-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0016"></a>
 <!-- !split -->
 
-<h2 id="reformulating-the-problem-to-suit-regression" class="anchor">Reformulating the problem to suit regression </h2>
+<h2 id="___sec15" class="anchor">Reformulating the problem to suit regression </h2>
 
 <p>
 A more general form for the one-dimensional Ising model is
@@ -455,7 +362,7 @@ We split the data in training and test data as discussed in the previous example
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((n, L <span style="color: #666666">**</span> <span style="color: #666666">2</span>))
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((n, L <span style="color: #666666">**</span> <span style="color: #666666">2</span>))
 <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(n):
     X[i] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>outer(spins[i], spins[i])<span style="color: #666666">.</span>ravel()
 y <span style="color: #666666">=</span> energies
@@ -499,7 +406,7 @@ X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_tes
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs017.html b/doc/pub/week38/html/._week38-bs017.html
index 715f834c9..429af35b8 100644
--- a/doc/pub/week38/html/._week38-bs017.html
+++ b/doc/pub/week38/html/._week38-bs017.html
@@ -1,11 +1,11 @@
 <!--
 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
 -->
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0017"></a>
 <!-- !split -->
 
-<h2 id="linear-regression" class="anchor">Linear regression </h2>
+<h2 id="___sec16" class="anchor">Linear regression </h2>
 
 <p>
 In the ordinary least squares method we choose the cost function
@@ -443,7 +350,7 @@ first column of \( \boldsymbol{X} \) consists of \( 1 \). We do this here
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>X_train_own <span style="color: #666666">=</span> np<span style="color: #666666">.</span>concatenate(
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>X_train_own <span style="color: #666666">=</span> np<span style="color: #666666">.</span>concatenate(
     (np<span style="color: #666666">.</span>ones(<span style="color: #008000">len</span>(X_train))[:, np<span style="color: #666666">.</span>newaxis], X_train),
     axis<span style="color: #666666">=1</span>
 )
@@ -455,7 +362,7 @@ X_test_own <span style="color: #666666">=</span> np<span style="color: #666666">
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">ols_inv</span>(x: np<span style="color: #666666">.</span>ndarray, y: np<span style="color: #666666">.</span>ndarray) <span style="color: #666666">-&gt;</span> np<span style="color: #666666">.</span>ndarray:
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">ols_inv</span>(x: np<span style="color: #666666">.</span>ndarray, y: np<span style="color: #666666">.</span>ndarray) <span style="color: #666666">-&gt;</span> np<span style="color: #666666">.</span>ndarray:
     <span style="color: #008000; font-weight: bold">return</span> scl<span style="color: #666666">.</span>inv(x<span style="color: #666666">.</span>T <span style="color: #666666">@</span> x) <span style="color: #666666">@</span> (x<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y)
 beta <span style="color: #666666">=</span> ols_inv(X_train_own, y_train)
 </pre></div>
@@ -497,7 +404,7 @@ beta <span style="color: #666666">=</span> ols_inv(X_train_own, y_train)
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs018.html b/doc/pub/week38/html/._week38-bs018.html
index 8cd02d15c..442896c45 100644
--- a/doc/pub/week38/html/._week38-bs018.html
+++ b/doc/pub/week38/html/._week38-bs018.html
@@ -1,11 +1,11 @@
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 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0018"></a>
 <!-- !split -->
 
-<h2 id="singular-value-decomposition" class="anchor">Singular Value decomposition </h2>
+<h2 id="___sec17" class="anchor">Singular Value decomposition </h2>
 
 <p>
 Doing the inversion directly turns out to be a bad idea since the matrix
@@ -456,14 +363,14 @@ linear system as an equation would reduce this down to
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">ols_svd</span>(x: np<span style="color: #666666">.</span>ndarray, y: np<span style="color: #666666">.</span>ndarray) <span style="color: #666666">-&gt;</span> np<span style="color: #666666">.</span>ndarray:
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">ols_svd</span>(x: np<span style="color: #666666">.</span>ndarray, y: np<span style="color: #666666">.</span>ndarray) <span style="color: #666666">-&gt;</span> np<span style="color: #666666">.</span>ndarray:
     u, s, v <span style="color: #666666">=</span> scl<span style="color: #666666">.</span>svd(x)
     <span style="color: #008000; font-weight: bold">return</span> v<span style="color: #666666">.</span>T <span style="color: #666666">@</span> scl<span style="color: #666666">.</span>pinv(scl<span style="color: #666666">.</span>diagsvd(s, u<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>], v<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>])) <span style="color: #666666">@</span> u<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y
 </pre></div>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>beta <span style="color: #666666">=</span> ols_svd(X_train_own,y_train)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>beta <span style="color: #666666">=</span> ols_svd(X_train_own,y_train)
 </pre></div>
 <p>
 When extracting the \( J \)-matrix  we need to make sure that we remove the intercept, as is done here
@@ -471,7 +378,7 @@ When extracting the \( J \)-matrix  we need to make sure that we remove the inte
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>J <span style="color: #666666">=</span> beta[<span style="color: #666666">1</span>:]<span style="color: #666666">.</span>reshape(L, L)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>J <span style="color: #666666">=</span> beta[<span style="color: #666666">1</span>:]<span style="color: #666666">.</span>reshape(L, L)
 </pre></div>
 <p>
 A way of looking at the coefficients in \( J \) is to plot the matrices as images.
@@ -479,7 +386,7 @@ A way of looking at the coefficients in \( J \) is to plot the matrices as image
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
 im <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>imshow(J, <span style="color: #666666">**</span>cmap_args)
 plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;OLS&quot;</span>, fontsize<span style="color: #666666">=18</span>)
 plt<span style="color: #666666">.</span>xticks(fontsize<span style="color: #666666">=18</span>)
@@ -536,7 +443,7 @@ In this case our matrix inversion was actually possible. The obvious question no
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs019.html b/doc/pub/week38/html/._week38-bs019.html
index 697fe8fac..629b20061 100644
--- a/doc/pub/week38/html/._week38-bs019.html
+++ b/doc/pub/week38/html/._week38-bs019.html
@@ -1,11 +1,11 @@
 <!--
 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
 -->
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
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-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
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-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
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+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
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-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
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-               2,
-               None,
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-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0019"></a>
 <!-- !split -->
 
-<h2 id="the-one-dimensional-ising-model" class="anchor">The one-dimensional Ising model </h2>
+<h2 id="___sec18" class="anchor">The one-dimensional Ising model </h2>
 
 <p>
 Let us bring back the Ising model again, but now with an additional
@@ -439,7 +346,7 @@ We will look at a system of \( L = 40 \) spins with a coupling constant of \( J
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">mpl_toolkits.axes_grid1</span> <span style="color: #008000; font-weight: bold">import</span> make_axes_locatable
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">seaborn</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sns</span>
@@ -497,7 +404,7 @@ We organize the data as we did above
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((n, L <span style="color: #666666">**</span> <span style="color: #666666">2</span>))
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((n, L <span style="color: #666666">**</span> <span style="color: #666666">2</span>))
 <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(n):
     X[i] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>outer(spins[i], spins[i])<span style="color: #666666">.</span>ravel()
 y <span style="color: #666666">=</span> energies
@@ -519,21 +426,21 @@ We will do all fitting with <b>Scikit-Learn</b>,
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>clf <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>LinearRegression()<span style="color: #666666">.</span>fit(X_train, y_train)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>clf <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>LinearRegression()<span style="color: #666666">.</span>fit(X_train, y_train)
 </pre></div>
 <p>
 When  extracting the \( J \)-matrix we make sure to remove the intercept
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>J_sk <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>coef_<span style="color: #666666">.</span>reshape(L, L)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>J_sk <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>coef_<span style="color: #666666">.</span>reshape(L, L)
 </pre></div>
 <p>
 And then we plot the results
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
 im <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>imshow(J_sk, <span style="color: #666666">**</span>cmap_args)
 plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;LinearRegression from Scikit-learn&quot;</span>, fontsize<span style="color: #666666">=18</span>)
 plt<span style="color: #666666">.</span>xticks(fontsize<span style="color: #666666">=18</span>)
@@ -583,7 +490,7 @@ The results perfectly with our previous discussion where we used our own code.
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs020.html b/doc/pub/week38/html/._week38-bs020.html
index e3cf5f3ed..d1215662d 100644
--- a/doc/pub/week38/html/._week38-bs020.html
+++ b/doc/pub/week38/html/._week38-bs020.html
@@ -1,11 +1,11 @@
 <!--
 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
 -->
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
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- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
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-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0020"></a>
 <!-- !split -->
 
-<h2 id="ridge-regression" class="anchor">Ridge regression </h2>
+<h2 id="___sec19" class="anchor">Ridge regression </h2>
 
 <p>
 Having explored the ordinary least squares we move on to ridge
@@ -433,7 +340,7 @@ $$
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>_lambda <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>_lambda <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
 clf_ridge <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>Ridge(alpha<span style="color: #666666">=</span>_lambda)<span style="color: #666666">.</span>fit(X_train, y_train)
 J_ridge_sk <span style="color: #666666">=</span> clf_ridge<span style="color: #666666">.</span>coef_<span style="color: #666666">.</span>reshape(L, L)
 fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
@@ -484,7 +391,7 @@ plt<span style="color: #666666">.</span>show()
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs021.html b/doc/pub/week38/html/._week38-bs021.html
index 92c18e7cd..d6711e37b 100644
--- a/doc/pub/week38/html/._week38-bs021.html
+++ b/doc/pub/week38/html/._week38-bs021.html
@@ -1,11 +1,11 @@
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-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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-              ('Ridge and LASSO Regression, reminder',
-               2,
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-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
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+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
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+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
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-               'more-complicated-example-the-ising-model'),
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-              ('LASSO regression', 2, None, 'lasso-regression'),
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+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
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-               None,
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-              ('Classification problems', 2, None, 'classification-problems'),
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-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
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-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
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-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
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+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
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               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
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               ('Optimization, the central part of any Machine Learning '
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-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
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-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
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+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0021"></a>
 <!-- !split -->
 
-<h2 id="lasso-regression" class="anchor">LASSO regression </h2>
+<h2 id="___sec20" class="anchor">LASSO regression </h2>
 
 <p>
 In the <b>Least Absolute Shrinkage and Selection Operator</b> (LASSO)-method we get a third cost function.
@@ -432,7 +339,7 @@ Finding the extremal point of this cost function is not so straight-forward as i
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>clf_lasso <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>Lasso(alpha<span style="color: #666666">=</span>_lambda)<span style="color: #666666">.</span>fit(X_train, y_train)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>clf_lasso <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>Lasso(alpha<span style="color: #666666">=</span>_lambda)<span style="color: #666666">.</span>fit(X_train, y_train)
 J_lasso_sk <span style="color: #666666">=</span> clf_lasso<span style="color: #666666">.</span>coef_<span style="color: #666666">.</span>reshape(L, L)
 fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
 im <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>imshow(J_lasso_sk, <span style="color: #666666">**</span>cmap_args)
@@ -487,7 +394,7 @@ constant as opposed to ridge and OLS. We get a sparse solution with
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs022.html b/doc/pub/week38/html/._week38-bs022.html
index d7a5cdefd..66dfaf391 100644
--- a/doc/pub/week38/html/._week38-bs022.html
+++ b/doc/pub/week38/html/._week38-bs022.html
@@ -1,11 +1,11 @@
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-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
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+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
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-              ('LASSO regression', 2, None, 'lasso-regression'),
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+              ('The one-dimensional Ising model', 2, None, '___sec18'),
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+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
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-               None,
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-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
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                2,
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-              ('Discussing the correlation data',
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+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
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               ('Other measures in classification studies: Cancer Data  again',
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                None,
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-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
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+               '___sec78'),
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+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
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                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0022"></a>
 <!-- !split -->
 
-<h2 id="performance-as-function-of-the-regularization-parameter" class="anchor">Performance as  function of the regularization parameter </h2>
+<h2 id="___sec21" class="anchor">Performance as  function of the regularization parameter </h2>
 
 <p>
 We see how the different models perform for a different set of values for \( \lambda \).
@@ -422,7 +329,7 @@ We see how the different models perform for a different set of values for \( \la
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">5</span>, <span style="color: #666666">10</span>)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">5</span>, <span style="color: #666666">10</span>)
 
 train_errors <span style="color: #666666">=</span> {
     <span style="color: #BA2121">&quot;ols_sk&quot;</span>: np<span style="color: #666666">.</span>zeros(lambdas<span style="color: #666666">.</span>size),
@@ -503,7 +410,7 @@ much. Ridge is more stable over a larger range of values for
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs023.html b/doc/pub/week38/html/._week38-bs023.html
index d2cc08158..5ae0757da 100644
--- a/doc/pub/week38/html/._week38-bs023.html
+++ b/doc/pub/week38/html/._week38-bs023.html
@@ -1,11 +1,11 @@
 <!--
 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
 -->
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0023"></a>
 <!-- !split -->
 
-<h2 id="finding-the-optimal-value-of-lambda" class="anchor">Finding the optimal value of \( \lambda \) </h2>
+<h2 id="___sec22" class="anchor">Finding the optimal value of \( \lambda \) </h2>
 
 <p>
 To determine which value of \( \lambda \) is best we plot the accuracy of
@@ -427,7 +334,7 @@ testing set that is close to the accuracy of the training set.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
 
 colors <span style="color: #666666">=</span> {
     <span style="color: #BA2121">&quot;ols_sk&quot;</span>: <span style="color: #BA2121">&quot;r&quot;</span>,
@@ -501,7 +408,7 @@ other models for all values of \( \lambda \).
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
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diff --git a/doc/pub/week38/html/._week38-bs024.html b/doc/pub/week38/html/._week38-bs024.html
index 47dadc10d..78c22aef5 100644
--- a/doc/pub/week38/html/._week38-bs024.html
+++ b/doc/pub/week38/html/._week38-bs024.html
@@ -1,11 +1,11 @@
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 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
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-<h2 id="logistic-regression" class="anchor">Logistic Regression </h2>
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 In linear regression our main interest was centered on learning the
@@ -467,7 +374,7 @@ simple recipe for fitting our data.
 
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+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
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+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
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-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
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+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
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-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
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-<h2 id="classification-problems" class="anchor">Classification problems </h2>
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 Classification problems, however, are concerned with outcomes taking
@@ -472,7 +379,7 @@ failure etc.
 
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+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0026"></a>
 <!-- !split -->
 
-<h2 id="optimization-and-deep-learning" class="anchor">Optimization and Deep learning </h2>
+<h2 id="___sec25" class="anchor">Optimization and Deep learning </h2>
 
 <p>
 Logistic regression will also serve as our stepping stone towards
@@ -470,7 +377,7 @@ models, as we will see later.
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs027.html b/doc/pub/week38/html/._week38-bs027.html
index 74f3d678f..e8c3825eb 100644
--- a/doc/pub/week38/html/._week38-bs027.html
+++ b/doc/pub/week38/html/._week38-bs027.html
@@ -1,11 +1,11 @@
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+(https://github.com/hplgit/doconce/)
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 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
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-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
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                None,
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-               2,
-               None,
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-              ('Extending to more than one variable',
-               2,
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-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
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+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
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               ('The sensitiveness of the gradient descent',
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                None,
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-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
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-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
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-              ('Conjugate gradient method',
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-              ('Conjugate gradient method',
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-               None,
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-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
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-              ('The derivative of the cost/loss function',
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-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
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+              ('Cross-validation in brief', 2, None, '___sec5'),
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                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
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 <p>
 Before moving to the logistic model, let us try to use our linear
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 <!-- Bootstrap footer
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-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
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+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
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               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0029"></a>
 <!-- !split -->
 
-<h2 id="some-selected-properties" class="anchor">Some selected properties </h2>
+<h2 id="___sec28" class="anchor">Some selected properties </h2>
 
 <p>
 The main problem with our function is that it takes values on the
@@ -471,7 +378,7 @@ the probability of a given category. This leads us to the logistic function.
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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diff --git a/doc/pub/week38/html/._week38-bs030.html b/doc/pub/week38/html/._week38-bs030.html
index 0af859c11..7226ce297 100644
--- a/doc/pub/week38/html/._week38-bs030.html
+++ b/doc/pub/week38/html/._week38-bs030.html
@@ -1,11 +1,11 @@
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-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
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                None,
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+              ('Cross-validation in brief', 2, None, '___sec5'),
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-              ('Still thinking', 2, None, 'still-thinking'),
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+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
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-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
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                2,
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-               'more-complicated-example-the-ising-model'),
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-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
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-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
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-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
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+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
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                None,
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+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
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+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
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+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
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+              ('The Hessian matrix', 2, None, '___sec81'),
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               ('Program example for gradient descent with Ridge Regression',
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@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0030"></a>
 <!-- !split -->
 
-<h2 id="simple-example" class="anchor">Simple example </h2>
+<h2 id="___sec29" class="anchor">Simple example </h2>
 
 <p>
 The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput  is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful.
@@ -422,7 +329,7 @@ The following example on data for coronary heart disease (CHD) as function of ag
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #408080; font-style: italic"># Common imports</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># Common imports</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">os</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
@@ -515,7 +422,7 @@ plt<span style="color: #666666">.</span>show()
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/._week38-bs031.html b/doc/pub/week38/html/._week38-bs031.html
index ab192b242..7df2d5473 100644
--- a/doc/pub/week38/html/._week38-bs031.html
+++ b/doc/pub/week38/html/._week38-bs031.html
@@ -1,11 +1,11 @@
 <!--
 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
 -->
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0031"></a>
 <!-- !split -->
 
-<h2 id="plotting-the-mean-value-for-each-group" class="anchor">Plotting the mean value for each group </h2>
+<h2 id="___sec30" class="anchor">Plotting the mean value for each group </h2>
 
 <p>
 What we could attempt however is to plot the mean value for each group.
@@ -422,7 +329,7 @@ What we could attempt however is to plot the mean value for each group.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>agegroupmean <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">0.1</span>, <span style="color: #666666">0.133</span>, <span style="color: #666666">0.250</span>, <span style="color: #666666">0.333</span>, <span style="color: #666666">0.462</span>, <span style="color: #666666">0.625</span>, <span style="color: #666666">0.765</span>, <span style="color: #666666">0.800</span>])
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>agegroupmean <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">0.1</span>, <span style="color: #666666">0.133</span>, <span style="color: #666666">0.250</span>, <span style="color: #666666">0.333</span>, <span style="color: #666666">0.462</span>, <span style="color: #666666">0.625</span>, <span style="color: #666666">0.765</span>, <span style="color: #666666">0.800</span>])
 group <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">1</span>, <span style="color: #666666">2</span>, <span style="color: #666666">3</span>, <span style="color: #666666">4</span>, <span style="color: #666666">5</span>, <span style="color: #666666">6</span>, <span style="color: #666666">7</span>, <span style="color: #666666">8</span>])
 plt<span style="color: #666666">.</span>plot(group, agegroupmean, <span style="color: #BA2121">&quot;r-&quot;</span>)
 plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0</span>,<span style="color: #666666">9</span>,<span style="color: #666666">0</span>, <span style="color: #666666">1.0</span>])
@@ -488,7 +395,7 @@ representing the probability for finding a value of \( y_i \) with a given
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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diff --git a/doc/pub/week38/html/._week38-bs032.html b/doc/pub/week38/html/._week38-bs032.html
index dc81f68e5..836d0c52d 100644
--- a/doc/pub/week38/html/._week38-bs032.html
+++ b/doc/pub/week38/html/._week38-bs032.html
@@ -1,11 +1,11 @@
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 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
 -->
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0032"></a>
 <!-- !split -->
 
-<h2 id="the-logistic-function" class="anchor">The logistic function </h2>
+<h2 id="___sec31" class="anchor">The logistic function </h2>
 
 <p>
 Another widely studied model, is the so-called 
@@ -472,7 +379,7 @@ Note that \( 1-p(t)= p(-t) \).
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
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+              ('More thinking', 2, None, '___sec8'),
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+              ('Code Examples', 2, None, '___sec12'),
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+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
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-              ('Classification problems', 2, None, 'classification-problems'),
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-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
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-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0033"></a>
 <!-- !split -->
 
-<h2 id="examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" class="anchor">Examples of likelihood functions used in logistic regression and nueral networks </h2>
+<h2 id="___sec32" class="anchor">Examples of likelihood functions used in logistic regression and nueral networks </h2>
 
 <p>
 The following code plots the logistic function, the step function and other functions we will encounter from here and on.
@@ -422,7 +329,7 @@ The following code plots the logistic function, the step function and other func
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;The sigmoid function (or the logistic curve) is a</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;The sigmoid function (or the logistic curve) is a</span>
 <span style="color: #BA2121; font-style: italic">function that takes any real number, z, and outputs a number (0,1).</span>
 <span style="color: #BA2121; font-style: italic">It is useful in neural networks for assigning weights on a relative scale.</span>
 <span style="color: #BA2121; font-style: italic">The value z is the weighted sum of parameters involved in the learning algorithm.&quot;&quot;&quot;</span>
@@ -515,7 +422,7 @@ plt<span style="color: #666666">.</span>show()
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
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diff --git a/doc/pub/week38/html/._week38-bs034.html b/doc/pub/week38/html/._week38-bs034.html
index 2a027a1ff..78d3299ab 100644
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+++ b/doc/pub/week38/html/._week38-bs034.html
@@ -1,11 +1,11 @@
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-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
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+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0034"></a>
 <!-- !split -->
 
-<h2 id="two-parameters" class="anchor">Two parameters </h2>
+<h2 id="___sec33" class="anchor">Two parameters </h2>
 
 <p>
 We assume now that we have two classes with \( y_i \) either \( 0 \) or \( 1 \). Furthermore we assume also that we have only two parameters \( \beta \) in our fitting of the Sigmoid function, that is we define probabilities 
@@ -471,7 +378,7 @@ $$
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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diff --git a/doc/pub/week38/html/._week38-bs035.html b/doc/pub/week38/html/._week38-bs035.html
index fa33d4425..9201cdd2f 100644
--- a/doc/pub/week38/html/._week38-bs035.html
+++ b/doc/pub/week38/html/._week38-bs035.html
@@ -1,11 +1,11 @@
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+(https://github.com/hplgit/doconce/)
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 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
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-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
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                None,
-               'brief-reminder-on-newton-raphson-s-method'),
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-               None,
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-               2,
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-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
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-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
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-              ('Conjugate gradient method',
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-              ('Conjugate gradient method',
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-               None,
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-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
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-              ('The derivative of the cost/loss function',
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-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
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-<h2 id="maximum-likelihood" class="anchor">Maximum likelihood </h2>
+<h2 id="___sec34" class="anchor">Maximum likelihood </h2>
 
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 In order to define the total likelihood for all possible outcomes from a  
@@ -472,7 +379,7 @@ $$
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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index 3ce3951cb..d73ff8a15 100644
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- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
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 <!-- !split -->
 
-<h2 id="the-cost-function-rewritten" class="anchor">The cost function rewritten </h2>
+<h2 id="___sec35" class="anchor">The cost function rewritten </h2>
 
 <p>
 Reordering the logarithms, we can rewrite the <b>cost/loss</b> function as
@@ -470,7 +377,7 @@ in practice we often supplement the cross-entropy with additional regularization
 
 <!-- Bootstrap footer
 <footer>
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+<a href="http://..."><img width="250" align=right src="http://..."></a>
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+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
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+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
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-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
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+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
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+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
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+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0037"></a>
 <!-- !split -->
 
-<h2 id="minimizing-the-cross-entropy" class="anchor">Minimizing the cross entropy </h2>
+<h2 id="___sec36" class="anchor">Minimizing the cross entropy </h2>
 
 <p>
 The cross entropy is a convex function of the weights \( \boldsymbol{\beta} \) and,
@@ -471,7 +378,7 @@ $$
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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index 75f6a1403..98b3bc77f 100644
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-              ('The logistic function', 2, None, 'the-logistic-function'),
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+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
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+              ('The logistic function', 2, None, '___sec31'),
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                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0038"></a>
 <!-- !split -->
 
-<h2 id="a-more-compact-expression" class="anchor">A more compact expression </h2>
+<h2 id="___sec37" class="anchor">A more compact expression </h2>
 
 <p>
 Let us now define a vector \( \boldsymbol{y} \) with \( n \) elements \( y_i \), an
@@ -472,7 +379,7 @@ $$
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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diff --git a/doc/pub/week38/html/._week38-bs039.html b/doc/pub/week38/html/._week38-bs039.html
index 52ed8b393..02db2ee2a 100644
--- a/doc/pub/week38/html/._week38-bs039.html
+++ b/doc/pub/week38/html/._week38-bs039.html
@@ -1,11 +1,11 @@
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-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
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-               None,
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-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
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-               None,
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-              ('Extending to more than one variable',
-               2,
-               None,
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-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
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-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
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-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
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-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
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-               None,
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-              ('Conjugate gradient method and iterations',
-               2,
-               None,
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-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
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-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
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 <!-- !split -->
 
-<h2 id="extending-to-more-predictors" class="anchor">Extending to more predictors </h2>
+<h2 id="___sec38" class="anchor">Extending to more predictors </h2>
 
 <p>
 Within a binary classification problem, we can easily expand our model to include multiple predictors. Our ratio between likelihoods is then with \( p \) predictors
@@ -465,7 +372,7 @@ $$
 
 <!-- Bootstrap footer
 <footer>
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+<a href="http://..."><img width="250" align=right src="http://..."></a>
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-               2,
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+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
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-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
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-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
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 <!-- !split -->
 
-<h2 id="including-more-classes" class="anchor">Including more classes </h2>
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 <p>
 Till now we have mainly focused on two classes, the so-called binary
@@ -477,7 +384,7 @@ and the model is specified in term of \( K-1 \) so-called log-odds or
 
 <!-- Bootstrap footer
 <footer>
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+<a href="http://..."><img width="250" align=right src="http://..."></a>
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index efa2cd448..aab36316a 100644
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-               None,
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+              ('Including more classes', 2, None, '___sec39'),
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-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
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-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0041"></a>
 <!-- !split -->
 
-<h2 id="more-classes" class="anchor">More classes </h2>
+<h2 id="___sec40" class="anchor">More classes </h2>
 
 <p>
 In our discussion of neural networks we will encounter the above again
@@ -489,7 +396,7 @@ methods</a>.
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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diff --git a/doc/pub/week38/html/._week38-bs042.html b/doc/pub/week38/html/._week38-bs042.html
index 2ca873953..3c4b29a00 100644
--- a/doc/pub/week38/html/._week38-bs042.html
+++ b/doc/pub/week38/html/._week38-bs042.html
@@ -1,11 +1,11 @@
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-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
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                None,
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-              ('Cross-validation in brief',
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-               None,
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+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
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-               2,
-               None,
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-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
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+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
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                2,
                None,
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               ('What does centering (subtracting the mean values) mean '
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-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
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-              ('Linear regression', 2, None, 'linear-regression'),
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-               None,
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-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
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-              ('Finding the optimal value of $\\lambda$',
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-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
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-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
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+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
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               ('Other measures in classification studies: Cancer Data  again',
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                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
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+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
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+               '___sec57'),
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+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
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+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
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+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
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-              ('Simple program', 2, None, 'simple-program'),
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+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
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               ('Program example for gradient descent with Ridge Regression',
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               ('Using gradient descent methods, limitations',
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@@ -311,94 +218,94 @@ MathJax.Hub.Config({
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-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -414,7 +321,7 @@ MathJax.Hub.Config({
 <a name="part0042"></a>
 <!-- !split -->
 
-<h2 id="friday-september-24" class="anchor">Friday September 24 </h2>
+<h2 id="___sec41" class="anchor">Friday September 24 </h2>
 
 <p>
 <p>
@@ -454,7 +361,7 @@ MathJax.Hub.Config({
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
 </footer>
 -->
 
diff --git a/doc/pub/week38/html/week38-bs.html b/doc/pub/week38/html/week38-bs.html
index 0d1b2580c..dc41103ec 100644
--- a/doc/pub/week38/html/week38-bs.html
+++ b/doc/pub/week38/html/week38-bs.html
@@ -1,11 +1,11 @@
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-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
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 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -41,239 +41,146 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
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-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
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-               None,
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-              ('Minimizing the cross entropy',
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-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
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-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -311,94 +218,94 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38" style="font-size: 80%;">Plans for week 38</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs002.html#thursday-september-23" style="font-size: 80%;">Thursday September 23</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs003.html#ridge-and-lasso-regression-reminder" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs004.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs005.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs006.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs007.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs008.html#to-think-about-first-part" style="font-size: 80%;">To think about, first part</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs009.html#more-thinking" style="font-size: 80%;">More thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs010.html#still-thinking" style="font-size: 80%;">Still thinking</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs011.html#linear-regression-code-intercept-handling-first" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs012.html#what-does-centering-subtracting-the-mean-values-mean-mathematically" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs013.html#code-examples" style="font-size: 80%;">Code Examples</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs014.html#taking-out-the-mean" style="font-size: 80%;">Taking out the mean</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs015.html#more-complicated-example-the-ising-model" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs016.html#reformulating-the-problem-to-suit-regression" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs017.html#linear-regression" style="font-size: 80%;">Linear regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs018.html#singular-value-decomposition" style="font-size: 80%;">Singular Value decomposition</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs019.html#the-one-dimensional-ising-model" style="font-size: 80%;">The one-dimensional Ising model</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs020.html#ridge-regression" style="font-size: 80%;">Ridge regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs021.html#lasso-regression" style="font-size: 80%;">LASSO regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs022.html#performance-as-function-of-the-regularization-parameter" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs023.html#finding-the-optimal-value-of-lambda" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs024.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs025.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs026.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs027.html#basics" style="font-size: 80%;">Basics</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs028.html#linear-classifier" style="font-size: 80%;">Linear classifier</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs029.html#some-selected-properties" style="font-size: 80%;">Some selected properties</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs030.html#simple-example" style="font-size: 80%;">Simple example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs031.html#plotting-the-mean-value-for-each-group" style="font-size: 80%;">Plotting the mean value for each group</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs032.html#the-logistic-function" style="font-size: 80%;">The logistic function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs033.html#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs034.html#two-parameters" style="font-size: 80%;">Two parameters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs035.html#maximum-likelihood" style="font-size: 80%;">Maximum likelihood</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs036.html#the-cost-function-rewritten" style="font-size: 80%;">The cost function rewritten</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs037.html#minimizing-the-cross-entropy" style="font-size: 80%;">Minimizing the cross entropy</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs038.html#a-more-compact-expression" style="font-size: 80%;">A more compact expression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs039.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs040.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs041.html#more-classes" style="font-size: 80%;">More classes</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs042.html#friday-september-24" style="font-size: 80%;">Friday September 24</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs043.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs044.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs045.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs046.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs047.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs049.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs050.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs051.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs052.html#the-equations" style="font-size: 80%;">The equations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs053.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs054.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs055.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs056.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs057.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs058.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs059.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs060.html#convex-function" style="font-size: 80%;">Convex function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs061.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs062.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs063.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs064.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs065.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs066.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs068.html#steepest-descent-method" style="font-size: 80%;">Steepest descent  method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs069.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs070.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs075.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs078.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs079.html#revisiting-some-of-our-first-linear-regression-encounters" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs081.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs082.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs083.html#simple-program" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs084.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs085.html#and-a-corresponding-example-using-_scikit-learn_" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs086.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs087.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week38-bs088.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 23</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">To think about, first part</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">More thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Still thinking</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">Linear Regression code, Intercept handling first</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">What does centering (subtracting the mean values) mean mathematically?</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Code Examples</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Taking out the mean</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">More complicated Example: The Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">Linear regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Singular Value decomposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">The one-dimensional Ising model</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Ridge regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">LASSO regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Performance as  function of the regularization parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Logistic Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Classification problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Optimization and Deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Basics</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Linear classifier</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">Some selected properties</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Simple example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Plotting the mean value for each group</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">The logistic function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs033.html#___sec32" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs034.html#___sec33" style="font-size: 80%;">Two parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs035.html#___sec34" style="font-size: 80%;">Maximum likelihood</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">The cost function rewritten</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs037.html#___sec36" style="font-size: 80%;">Minimizing the cross entropy</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs038.html#___sec37" style="font-size: 80%;">A more compact expression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Extending to more predictors</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Including more classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs041.html#___sec40" style="font-size: 80%;">More classes</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Friday September 24</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs043.html#___sec42" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs044.html#___sec43" style="font-size: 80%;">Using the correlation matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs045.html#___sec44" style="font-size: 80%;">Discussing the correlation data</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs046.html#___sec45" style="font-size: 80%;">Other measures in classification studies: Cancer Data  again</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs047.html#___sec46" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs048.html#___sec47" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs049.html#___sec48" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs050.html#___sec49" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs051.html#___sec50" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs052.html#___sec51" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs053.html#___sec52" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs054.html#___sec53" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs055.html#___sec54" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs056.html#___sec55" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs057.html#___sec56" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs058.html#___sec57" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs059.html#___sec58" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs060.html#___sec59" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs061.html#___sec60" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs062.html#___sec61" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs063.html#___sec62" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs064.html#___sec63" style="font-size: 80%;">Friday September 25</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs065.html#___sec64" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs066.html#___sec65" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs067.html#___sec66" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs068.html#___sec67" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs069.html#___sec68" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs070.html#___sec69" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs071.html#___sec70" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs072.html#___sec71" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs073.html#___sec72" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs074.html#___sec73" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs075.html#___sec74" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs076.html#___sec75" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs077.html#___sec76" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs078.html#___sec77" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs079.html#___sec78" style="font-size: 80%;">Revisiting some of our first Linear Regression Encounters</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs080.html#___sec79" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs081.html#___sec80" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs082.html#___sec81" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs083.html#___sec82" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs084.html#___sec83" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs085.html#___sec84" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs086.html#___sec85" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs087.html#___sec86" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week38-bs088.html#___sec87" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
 
         </ul>
       </li>
@@ -469,7 +376,7 @@ MathJax.Hub.Config({
 
 <!-- Bootstrap footer
 <footer>
-<a href="https://..."><img width="250" align=right src="https://..."></a>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
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diff --git a/doc/pub/week38/html/week38-reveal.html b/doc/pub/week38/html/week38-reveal.html
index 82b585c31..a01f0bb1b 100644
--- a/doc/pub/week38/html/week38-reveal.html
+++ b/doc/pub/week38/html/week38-reveal.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -13,7 +13,7 @@
 
 
 
-<!-- reveal.js: https://lab.hakim.se/reveal-js/ -->
+<!-- reveal.js: http://lab.hakim.se/reveal-js/ -->
 
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@@ -76,10 +76,10 @@ document.getElementsByTagName( 'head' )[0].appendChild( link );
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+     /*.reveal .alert-notice { background-image: url(http://hplgit.github.io/doconce/bundled/html_images/small_gray_notice.png); }
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+     .reveal .alert-warning { background-image: url(http://hplgit.github.io/doconce/bundled/html_images/small_gray_warning.png); }
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@@ -159,7 +159,7 @@ MathJax.Hub.Config({
 
 
 <section>
-<h2 id="plans-for-week-38">Plans for week 38 </h2>
+<h2 id="___sec0">Plans for week 38 </h2>
 
 <ul>
 <p><li> Thursday: Summary of regression methods and discussion of project 1.  Start Logistic Regression</li>
@@ -169,12 +169,12 @@ MathJax.Hub.Config({
 
 
 <section>
-<h2 id="thursday-september-23">Thursday September 23 </h2>
+<h2 id="___sec1">Thursday September 23 </h2>
 </section>
 
 
 <section>
-<h2 id="ridge-and-lasso-regression-reminder">Ridge and LASSO Regression, reminder </h2>
+<h2 id="___sec2">Ridge and LASSO Regression, reminder </h2>
 
 <p>
 The expression for the standard Mean Squared Error (MSE) which we used to define our cost function and the equations for the ordinary least squares (OLS) method, that is 
@@ -246,7 +246,7 @@ $$
 
 
 <section>
-<h2 id="various-steps-in-cross-validation">Various steps in cross-validation </h2>
+<h2 id="___sec3">Various steps in cross-validation </h2>
 
 <p>
 When the repetitive splitting of the data set is done randomly,
@@ -267,7 +267,7 @@ cross-validation (LOOCV).
 
 
 <section>
-<h2 id="how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">How to set up the cross-validation for Ridge and/or Lasso </h2>
+<h2 id="___sec4">How to set up the cross-validation for Ridge and/or Lasso </h2>
 
 <ul>
 <p><li> Define a range of interest for the penalty parameter.</li>
@@ -301,7 +301,7 @@ $$
 
 
 <section>
-<h2 id="cross-validation-in-brief">Cross-validation in brief </h2>
+<h2 id="___sec5">Cross-validation in brief </h2>
 
 <p>
 For the various values of \( k \)
@@ -323,14 +323,14 @@ For the various values of \( k \)
 
 
 <section>
-<h2 id="code-example-for-cross-validation-and-k-fold-cross-validation">Code Example for Cross-validation and \( k \)-fold Cross-validation </h2>
+<h2 id="___sec6">Code Example for Cross-validation and \( k \)-fold Cross-validation </h2>
 
 <p>
 The code here uses Ridge regression with cross-validation (CV)  resampling and \( k \)-fold CV in order to fit a specific polynomial. 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> KFold
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> Ridge
@@ -424,7 +424,7 @@ plt.show()
 
 
 <section>
-<h2 id="to-think-about-first-part">To think about, first part </h2>
+<h2 id="___sec7">To think about, first part </h2>
 
 <p>
 When you are comparing your own code with for example <b>Scikit-Learn</b>'s
@@ -443,16 +443,14 @@ Thus, if we cannot assume that the expected outputs/targets are zero
 when all predictors are zero (the columns in the design matrix), it
 may be a bad idea to implement a model which penalizes the intercept.
 Furthermore, in for example Ridge and Lasso regression, the solutions
-(when not shrinking <p>&nbsp;<br>
-$$\beta_0$$
-<p>&nbsp;<br>) for the unknown parameters
+(when not shrinking \( \beta_0 \)) for the unknown parameters
 \( \boldsymbol{\beta} \) are derived&#160;under the assumption that both \( \boldsymbol{y} \) and
 \( \boldsymbol{X} \) are zero centered, that is we subtract the mean values.
 </section>
 
 
 <section>
-<h2 id="more-thinking">More thinking </h2>
+<h2 id="___sec8">More thinking </h2>
 
 <p>
 If our predictors&#160;represent different&#160;scales, then it is important to
@@ -486,7 +484,7 @@ This can clearly lead to problems in evaluating the cost/loss functions.
 
 
 <section>
-<h2 id="still-thinking">Still thinking </h2>
+<h2 id="___sec9">Still thinking </h2>
 
 <p>
 Keep in mind that when you transform your data set before training a model, the same transformation needs to be done
@@ -495,7 +493,7 @@ on your eventual new data set  before making a prediction. If we translate this
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #228B22">#Model training, we compute the mean value of y and X</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22">#Model training, we compute the mean value of y and X</span>
 y_train_mean = np.mean(y_train)
 X_train_mean = np.mean(X_train,axis=<span style="color: #B452CD">0</span>)
 X_train = X_train - X_train_mean
@@ -514,7 +512,7 @@ y_pred = y_pred + y_train_mean
 
 
 <section>
-<h2 id="linear-regression-code-intercept-handling-first">Linear Regression code, Intercept handling first </h2>
+<h2 id="___sec10">Linear Regression code, Intercept handling first </h2>
 
 <p>
 This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (<em>code example thanks to  &#216;yvind Sigmundson Sch&#248;yen</em>). Here our scaling of the data is done by subtracting the mean values only.
@@ -522,7 +520,7 @@ This code shows a simple first-order fit to a data set using the above transform
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LinearRegression
@@ -597,7 +595,7 @@ plt.show()
 
 
 <section>
-<h2 id="what-does-centering-subtracting-the-mean-values-mean-mathematically">What does centering (subtracting the mean values) mean mathematically? </h2>
+<h2 id="___sec11">What does centering (subtracting the mean values) mean mathematically? </h2>
 
 <p>
 Let us try to understand what this may imply mathematically when we subtract the mean values, also known as <em>zero centering</em>. To catch many birds with just one stone, we will focus on Ridge regression.
@@ -642,7 +640,7 @@ If we assume that every column of \( \boldsymbol{X} \) is centered, which we can
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>X = X - np.mean(X,axis=<span style="color: #B452CD">0</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>X = X - np.mean(X,axis=<span style="color: #B452CD">0</span>)
 </pre></div>
 <p>
 the sum \( \sum_{i=0}^{n-1} X_{ij} \)
@@ -696,7 +694,7 @@ and \( \tilde{X}_{ij} = X_{ij} - \frac{1}{n}\sum_{k=1}^{n-1}X_{kj} \).
 
 
 <section>
-<h2 id="code-examples">Code Examples </h2>
+<h2 id="___sec12">Code Examples </h2>
 
 <p>
 Armed with this wisdom, we attempt first simply set the intercept eqault to <b>False</b> in our implementation of Ridge regression for a vanilla data set.
@@ -704,7 +702,7 @@ Armed with this wisdom, we attempt first simply set the intercept eqault to <b>F
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> train_test_split
@@ -781,11 +779,11 @@ Let us see how we can change this code by zero centering.
 
 
 <section>
-<h2 id="taking-out-the-mean">Taking out the mean </h2>
+<h2 id="___sec13">Taking out the mean </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> train_test_split
@@ -875,7 +873,7 @@ plt.show()
 
 
 <section>
-<h2 id="more-complicated-example-the-ising-model">More complicated Example: The Ising model </h2>
+<h2 id="___sec14">More complicated Example: The Ising model </h2>
 
 <p>
 The one-dimensional Ising model with nearest neighbor interaction, no
@@ -903,7 +901,7 @@ with their respective energies.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">mpl_toolkits.axes_grid1</span> <span style="color: #8B008B; font-weight: bold">import</span> make_axes_locatable
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">seaborn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sns</span>
@@ -934,7 +932,7 @@ the coupling constant to achieve this.
 
 
 <section>
-<h2 id="reformulating-the-problem-to-suit-regression">Reformulating the problem to suit regression </h2>
+<h2 id="___sec15">Reformulating the problem to suit regression </h2>
 
 <p>
 A more general form for the one-dimensional Ising model is
@@ -981,7 +979,7 @@ We split the data in training and test data as discussed in the previous example
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>X = np.zeros((n, L ** <span style="color: #B452CD">2</span>))
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>X = np.zeros((n, L ** <span style="color: #B452CD">2</span>))
 <span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(n):
     X[i] = np.outer(spins[i], spins[i]).ravel()
 y = energies
@@ -991,7 +989,7 @@ X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=<span style=
 
 
 <section>
-<h2 id="linear-regression">Linear regression </h2>
+<h2 id="___sec16">Linear regression </h2>
 
 <p>
 In the ordinary least squares method we choose the cost function
@@ -1024,7 +1022,7 @@ first column of \( \boldsymbol{X} \) consists of \( 1 \). We do this here
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>X_train_own = np.concatenate(
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>X_train_own = np.concatenate(
     (np.ones(<span style="color: #658b00">len</span>(X_train))[:, np.newaxis], X_train),
     axis=<span style="color: #B452CD">1</span>
 )
@@ -1036,7 +1034,7 @@ X_test_own = np.concatenate(
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">ols_inv</span>(x: np.ndarray, y: np.ndarray) -&gt; np.ndarray:
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">ols_inv</span>(x: np.ndarray, y: np.ndarray) -&gt; np.ndarray:
     <span style="color: #8B008B; font-weight: bold">return</span> scl.inv(x.T @ x) @ (x.T @ y)
 beta = ols_inv(X_train_own, y_train)
 </pre></div>
@@ -1044,7 +1042,7 @@ beta = ols_inv(X_train_own, y_train)
 
 
 <section>
-<h2 id="singular-value-decomposition">Singular Value decomposition </h2>
+<h2 id="___sec17">Singular Value decomposition </h2>
 
 <p>
 Doing the inversion directly turns out to be a bad idea since the matrix
@@ -1092,14 +1090,14 @@ linear system as an equation would reduce this down to
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">ols_svd</span>(x: np.ndarray, y: np.ndarray) -&gt; np.ndarray:
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">ols_svd</span>(x: np.ndarray, y: np.ndarray) -&gt; np.ndarray:
     u, s, v = scl.svd(x)
     <span style="color: #8B008B; font-weight: bold">return</span> v.T @ scl.pinv(scl.diagsvd(s, u.shape[<span style="color: #B452CD">0</span>], v.shape[<span style="color: #B452CD">0</span>])) @ u.T @ y
 </pre></div>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>beta = ols_svd(X_train_own,y_train)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>beta = ols_svd(X_train_own,y_train)
 </pre></div>
 <p>
 When extracting the \( J \)-matrix  we need to make sure that we remove the intercept, as is done here
@@ -1107,7 +1105,7 @@ When extracting the \( J \)-matrix  we need to make sure that we remove the inte
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>J = beta[<span style="color: #B452CD">1</span>:].reshape(L, L)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>J = beta[<span style="color: #B452CD">1</span>:].reshape(L, L)
 </pre></div>
 <p>
 A way of looking at the coefficients in \( J \) is to plot the matrices as images.
@@ -1115,7 +1113,7 @@ A way of looking at the coefficients in \( J \) is to plot the matrices as image
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
 im = plt.imshow(J, **cmap_args)
 plt.title(<span style="color: #CD5555">&quot;OLS&quot;</span>, fontsize=<span style="color: #B452CD">18</span>)
 plt.xticks(fontsize=<span style="color: #B452CD">18</span>)
@@ -1137,7 +1135,7 @@ In this case our matrix inversion was actually possible. The obvious question no
 
 
 <section>
-<h2 id="the-one-dimensional-ising-model">The one-dimensional Ising model </h2>
+<h2 id="___sec18">The one-dimensional Ising model </h2>
 
 <p>
 Let us bring back the Ising model again, but now with an additional
@@ -1164,7 +1162,7 @@ We will look at a system of \( L = 40 \) spins with a coupling constant of \( J
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">mpl_toolkits.axes_grid1</span> <span style="color: #8B008B; font-weight: bold">import</span> make_axes_locatable
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">seaborn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sns</span>
@@ -1228,7 +1226,7 @@ We organize the data as we did above
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>X = np.zeros((n, L ** <span style="color: #B452CD">2</span>))
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>X = np.zeros((n, L ** <span style="color: #B452CD">2</span>))
 <span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(n):
     X[i] = np.outer(spins[i], spins[i]).ravel()
 y = energies
@@ -1250,21 +1248,21 @@ We will do all fitting with <b>Scikit-Learn</b>,
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>clf = skl.LinearRegression().fit(X_train, y_train)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>clf = skl.LinearRegression().fit(X_train, y_train)
 </pre></div>
 <p>
 When  extracting the \( J \)-matrix we make sure to remove the intercept
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>J_sk = clf.coef_.reshape(L, L)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>J_sk = clf.coef_.reshape(L, L)
 </pre></div>
 <p>
 And then we plot the results
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
 im = plt.imshow(J_sk, **cmap_args)
 plt.title(<span style="color: #CD5555">&quot;LinearRegression from Scikit-learn&quot;</span>, fontsize=<span style="color: #B452CD">18</span>)
 plt.xticks(fontsize=<span style="color: #B452CD">18</span>)
@@ -1279,7 +1277,7 @@ The results perfectly with our previous discussion where we used our own code.
 
 
 <section>
-<h2 id="ridge-regression">Ridge regression </h2>
+<h2 id="___sec19">Ridge regression </h2>
 
 <p>
 Having explored the ordinary least squares we move on to ridge
@@ -1300,7 +1298,7 @@ $$
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>_lambda = <span style="color: #B452CD">0.1</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>_lambda = <span style="color: #B452CD">0.1</span>
 clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train)
 J_ridge_sk = clf_ridge.coef_.reshape(L, L)
 fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
@@ -1317,7 +1315,7 @@ plt.show()
 
 
 <section>
-<h2 id="lasso-regression">LASSO regression </h2>
+<h2 id="___sec20">LASSO regression </h2>
 
 <p>
 In the <b>Least Absolute Shrinkage and Selection Operator</b> (LASSO)-method we get a third cost function.
@@ -1337,7 +1335,7 @@ Finding the extremal point of this cost function is not so straight-forward as i
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)
 J_lasso_sk = clf_lasso.coef_.reshape(L, L)
 fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
 im = plt.imshow(J_lasso_sk, **cmap_args)
@@ -1357,7 +1355,7 @@ constant as opposed to ridge and OLS. We get a sparse solution with
 
 
 <section>
-<h2 id="performance-as-function-of-the-regularization-parameter">Performance as  function of the regularization parameter </h2>
+<h2 id="___sec21">Performance as  function of the regularization parameter </h2>
 
 <p>
 We see how the different models perform for a different set of values for \( \lambda \).
@@ -1365,7 +1363,7 @@ We see how the different models perform for a different set of values for \( \la
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>lambdas = np.logspace(-<span style="color: #B452CD">4</span>, <span style="color: #B452CD">5</span>, <span style="color: #B452CD">10</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>lambdas = np.logspace(-<span style="color: #B452CD">4</span>, <span style="color: #B452CD">5</span>, <span style="color: #B452CD">10</span>)
 
 train_errors = {
     <span style="color: #CD5555">&quot;ols_sk&quot;</span>: np.zeros(lambdas.size),
@@ -1411,7 +1409,7 @@ much. Ridge is more stable over a larger range of values for
 
 
 <section>
-<h2 id="finding-the-optimal-value-of-lambda">Finding the optimal value of \( \lambda \) </h2>
+<h2 id="___sec22">Finding the optimal value of \( \lambda \) </h2>
 
 <p>
 To determine which value of \( \lambda \) is best we plot the accuracy of
@@ -1424,7 +1422,7 @@ testing set that is close to the accuracy of the training set.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
 
 colors = {
     <span style="color: #CD5555">&quot;ols_sk&quot;</span>: <span style="color: #CD5555">&quot;r&quot;</span>,
@@ -1463,7 +1461,7 @@ other models for all values of \( \lambda \).
 
 
 <section>
-<h2 id="logistic-regression">Logistic Regression </h2>
+<h2 id="___sec23">Logistic Regression </h2>
 
 <p>
 In linear regression our main interest was centered on learning the
@@ -1481,7 +1479,7 @@ simple recipe for fitting our data.
 
 
 <section>
-<h2 id="classification-problems">Classification problems </h2>
+<h2 id="___sec24">Classification problems </h2>
 
 <p>
 Classification problems, however, are concerned with outcomes taking
@@ -1504,7 +1502,7 @@ failure etc.
 
 
 <section>
-<h2 id="optimization-and-deep-learning">Optimization and Deep learning </h2>
+<h2 id="___sec25">Optimization and Deep learning </h2>
 
 <p>
 Logistic regression will also serve as our stepping stone towards
@@ -1525,7 +1523,7 @@ models, as we will see later.
 
 
 <section>
-<h2 id="basics">Basics </h2>
+<h2 id="___sec26">Basics </h2>
 
 <p>
 We consider the case where the dependent variables, also called the
@@ -1554,7 +1552,7 @@ $$
 
 
 <section>
-<h2 id="linear-classifier">Linear classifier </h2>
+<h2 id="___sec27">Linear classifier </h2>
 
 <p>
 Before moving to the logistic model, let us try to use our linear
@@ -1580,7 +1578,7 @@ where \( \boldsymbol{y} \) is a vector representing the possible outcomes, \( \b
 
 
 <section>
-<h2 id="some-selected-properties">Some selected properties </h2>
+<h2 id="___sec28">Some selected properties </h2>
 
 <p>
 The main problem with our function is that it takes values on the
@@ -1602,7 +1600,7 @@ the probability of a given category. This leads us to the logistic function.
 
 
 <section>
-<h2 id="simple-example">Simple example </h2>
+<h2 id="___sec29">Simple example </h2>
 
 <p>
 The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput  is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful.
@@ -1610,7 +1608,7 @@ The following example on data for coronary heart disease (CHD) as function of ag
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #228B22"># Common imports</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># Common imports</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">os</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
@@ -1669,7 +1667,7 @@ plt.show()
 
 
 <section>
-<h2 id="plotting-the-mean-value-for-each-group">Plotting the mean value for each group </h2>
+<h2 id="___sec30">Plotting the mean value for each group </h2>
 
 <p>
 What we could attempt however is to plot the mean value for each group.
@@ -1677,7 +1675,7 @@ What we could attempt however is to plot the mean value for each group.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>agegroupmean = np.array([<span style="color: #B452CD">0.1</span>, <span style="color: #B452CD">0.133</span>, <span style="color: #B452CD">0.250</span>, <span style="color: #B452CD">0.333</span>, <span style="color: #B452CD">0.462</span>, <span style="color: #B452CD">0.625</span>, <span style="color: #B452CD">0.765</span>, <span style="color: #B452CD">0.800</span>])
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>agegroupmean = np.array([<span style="color: #B452CD">0.1</span>, <span style="color: #B452CD">0.133</span>, <span style="color: #B452CD">0.250</span>, <span style="color: #B452CD">0.333</span>, <span style="color: #B452CD">0.462</span>, <span style="color: #B452CD">0.625</span>, <span style="color: #B452CD">0.765</span>, <span style="color: #B452CD">0.800</span>])
 group = np.array([<span style="color: #B452CD">1</span>, <span style="color: #B452CD">2</span>, <span style="color: #B452CD">3</span>, <span style="color: #B452CD">4</span>, <span style="color: #B452CD">5</span>, <span style="color: #B452CD">6</span>, <span style="color: #B452CD">7</span>, <span style="color: #B452CD">8</span>])
 plt.plot(group, agegroupmean, <span style="color: #CD5555">&quot;r-&quot;</span>)
 plt.axis([<span style="color: #B452CD">0</span>,<span style="color: #B452CD">9</span>,<span style="color: #B452CD">0</span>, <span style="color: #B452CD">1.0</span>])
@@ -1710,7 +1708,7 @@ representing the probability for finding a value of \( y_i \) with a given
 
 
 <section>
-<h2 id="the-logistic-function">The logistic function </h2>
+<h2 id="___sec31">The logistic function </h2>
 
 <p>
 Another widely studied model, is the so-called 
@@ -1735,7 +1733,7 @@ Note that \( 1-p(t)= p(-t) \).
 
 
 <section>
-<h2 id="examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks">Examples of likelihood functions used in logistic regression and nueral networks </h2>
+<h2 id="___sec32">Examples of likelihood functions used in logistic regression and nueral networks </h2>
 
 <p>
 The following code plots the logistic function, the step function and other functions we will encounter from here and on.
@@ -1743,7 +1741,7 @@ The following code plots the logistic function, the step function and other func
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #CD5555">&quot;&quot;&quot;The sigmoid function (or the logistic curve) is a</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #CD5555">&quot;&quot;&quot;The sigmoid function (or the logistic curve) is a</span>
 <span style="color: #CD5555">function that takes any real number, z, and outputs a number (0,1).</span>
 <span style="color: #CD5555">It is useful in neural networks for assigning weights on a relative scale.</span>
 <span style="color: #CD5555">The value z is the weighted sum of parameters involved in the learning algorithm.&quot;&quot;&quot;</span>
@@ -1802,7 +1800,7 @@ plt.show()
 
 
 <section>
-<h2 id="two-parameters">Two parameters </h2>
+<h2 id="___sec33">Two parameters </h2>
 
 <p>
 We assume now that we have two classes with \( y_i \) either \( 0 \) or \( 1 \). Furthermore we assume also that we have only two parameters \( \beta \) in our fitting of the Sigmoid function, that is we define probabilities 
@@ -1828,7 +1826,7 @@ $$
 
 
 <section>
-<h2 id="maximum-likelihood">Maximum likelihood </h2>
+<h2 id="___sec34">Maximum likelihood </h2>
 
 <p>
 In order to define the total likelihood for all possible outcomes from a  
@@ -1855,7 +1853,7 @@ $$
 
 
 <section>
-<h2 id="the-cost-function-rewritten">The cost function rewritten </h2>
+<h2 id="___sec35">The cost function rewritten </h2>
 
 <p>
 Reordering the logarithms, we can rewrite the <b>cost/loss</b> function as
@@ -1880,7 +1878,7 @@ in practice we often supplement the cross-entropy with additional regularization
 
 
 <section>
-<h2 id="minimizing-the-cross-entropy">Minimizing the cross entropy </h2>
+<h2 id="___sec36">Minimizing the cross entropy </h2>
 
 <p>
 The cross entropy is a convex function of the weights \( \boldsymbol{\beta} \) and,
@@ -1906,7 +1904,7 @@ $$
 
 
 <section>
-<h2 id="a-more-compact-expression">A more compact expression </h2>
+<h2 id="___sec37">A more compact expression </h2>
 
 <p>
 Let us now define a vector \( \boldsymbol{y} \) with \( n \) elements \( y_i \), an
@@ -1933,7 +1931,7 @@ $$
 
 
 <section>
-<h2 id="extending-to-more-predictors">Extending to more predictors </h2>
+<h2 id="___sec38">Extending to more predictors </h2>
 
 <p>
 Within a binary classification problem, we can easily expand our model to include multiple predictors. Our ratio between likelihoods is then with \( p \) predictors
@@ -1953,7 +1951,7 @@ $$
 
 
 <section>
-<h2 id="including-more-classes">Including more classes </h2>
+<h2 id="___sec39">Including more classes </h2>
 
 <p>
 Till now we have mainly focused on two classes, the so-called binary
@@ -1987,7 +1985,7 @@ and the model is specified in term of \( K-1 \) so-called log-odds or
 
 
 <section>
-<h2 id="more-classes">More classes </h2>
+<h2 id="___sec40">More classes </h2>
 
 <p>
 In our discussion of neural networks we will encounter the above again
@@ -2031,12 +2029,12 @@ methods</a>.
 
 
 <section>
-<h2 id="friday-september-24">Friday September 24 </h2>
+<h2 id="___sec41">Friday September 24 </h2>
 </section>
 
 
 <section>
-<h2 id="wisconsin-cancer-data">Wisconsin Cancer Data  </h2>
+<h2 id="___sec42">Wisconsin Cancer Data  </h2>
 
 <p>
 We show here how we can use a simple regression case on the breast
@@ -2046,7 +2044,7 @@ classification.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span>  train_test_split 
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.datasets</span> <span style="color: #8B008B; font-weight: bold">import</span> load_breast_cancer
@@ -2076,7 +2074,7 @@ logreg.fit(X_train_scaled, y_train)
 
 
 <section>
-<h2 id="using-the-correlation-matrix">Using the correlation matrix </h2>
+<h2 id="___sec43">Using the correlation matrix </h2>
 
 <p>
 In addition to the above scores, we could also study the covariance (and the correlation matrix).
@@ -2084,7 +2082,7 @@ We use <b>Pandas</b> to compute the correlation matrix.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span>  train_test_split 
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.datasets</span> <span style="color: #8B008B; font-weight: bold">import</span> load_breast_cancer
@@ -2123,7 +2121,7 @@ plt.show()
 
 
 <section>
-<h2 id="discussing-the-correlation-data">Discussing the correlation data </h2>
+<h2 id="___sec44">Discussing the correlation data </h2>
 
 <p>
 In the above example we note two things. In the first plot we display
@@ -2144,14 +2142,14 @@ We constructed this matrix using <b>pandas</b> via the statements
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)
 </pre></div>
 <p>
 and then
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>correlation_matrix = cancerpd.corr().round(<span style="color: #B452CD">1</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>correlation_matrix = cancerpd.corr().round(<span style="color: #B452CD">1</span>)
 </pre></div>
 <p>
 Diagonalizing this matrix we can in turn say something about which
@@ -2162,11 +2160,11 @@ applications. This will be discussed later this semester (<a href="https://compp
 
 
 <section>
-<h2 id="other-measures-in-classification-studies-cancer-data-again">Other measures in classification studies: Cancer Data  again </h2>
+<h2 id="___sec45">Other measures in classification studies: Cancer Data  again </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span>  train_test_split 
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.datasets</span> <span style="color: #8B008B; font-weight: bold">import</span> load_breast_cancer
@@ -2215,7 +2213,7 @@ plt.show()
 
 
 <section>
-<h2 id="optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm </h2>
+<h2 id="___sec46">Optimization, the central part of any Machine Learning algortithm </h2>
 
 <p>
 <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/OverarchingAimsWeek39.mp4?vrtx=view-as-webpage" target="_blank">Overview Video, why do we care about gradient methods?</a>
@@ -2233,7 +2231,7 @@ some approximative/numerical method to compute the minimum.
 
 
 <section>
-<h2 id="revisiting-our-logistic-regression-case">Revisiting our Logistic Regression case </h2>
+<h2 id="___sec47">Revisiting our Logistic Regression case </h2>
 
 <p>
 In our discussion on Logistic Regression we studied the 
@@ -2257,7 +2255,7 @@ where \( \boldsymbol{\beta} \) are the weights we wish to extract from data, in
 
 
 <section>
-<h2 id="the-equations-to-solve">The equations to solve </h2>
+<h2 id="___sec48">The equations to solve </h2>
 
 <p>
 Our compact equations used a definition of a vector \( \boldsymbol{y} \) with \( n \)
@@ -2287,7 +2285,7 @@ This defines what is called  the Hessian matrix.
 
 
 <section>
-<h2 id="solving-using-newton-raphson-s-method">Solving using Newton-Raphson's method </h2>
+<h2 id="___sec49">Solving using Newton-Raphson's method </h2>
 
 <p>
 If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the  matrices that define the first and second derivatives.
@@ -2317,7 +2315,7 @@ If we can compute these matrices, in particular the Hessian, the above is often
 
 
 <section>
-<h2 id="brief-reminder-on-newton-raphson-s-method">Brief reminder on Newton-Raphson's method </h2>
+<h2 id="___sec50">Brief reminder on Newton-Raphson's method </h2>
 
 <p>
 Let us quickly remind ourselves how we derive the above method.
@@ -2334,7 +2332,7 @@ normally discourage the use of this method.
 
 
 <section>
-<h2 id="the-equations">The equations </h2>
+<h2 id="___sec51">The equations </h2>
 
 <p>
 The Newton-Raphson formula consists geometrically of extending the
@@ -2378,7 +2376,7 @@ $$
 
 
 <section>
-<h2 id="simple-geometric-interpretation">Simple geometric interpretation </h2>
+<h2 id="___sec52">Simple geometric interpretation </h2>
 
 <p>
 The above is Newton-Raphson's method. It has a simple geometric
@@ -2396,7 +2394,7 @@ vanishes, then Newton-Raphson may fail totally
 
 
 <section>
-<h2 id="extending-to-more-than-one-variable">Extending to more than one variable </h2>
+<h2 id="___sec53">Extending to more than one variable </h2>
 
 <p>
 Newton's method can be generalized to systems of several non-linear equations
@@ -2461,7 +2459,7 @@ more than two non-linear equations. In our case, the Jacobian matrix is given by
 
 
 <section>
-<h2 id="steepest-descent">Steepest descent </h2>
+<h2 id="___sec54">Steepest descent </h2>
 
 <p>
 The basic idea of gradient descent is
@@ -2487,7 +2485,7 @@ we are always moving towards smaller function values, i.e a minimum.
 
 
 <section>
-<h2 id="more-on-steepest-descent">More on Steepest descent </h2>
+<h2 id="___sec55">More on Steepest descent </h2>
 
 <p>
 The previous observation is the basis of the method of steepest
@@ -2508,7 +2506,7 @@ the learning rate within the context of Machine Learning.
 
 
 <section>
-<h2 id="the-ideal">The ideal </h2>
+<h2 id="___sec56">The ideal </h2>
 
 <p>
 Ideally the sequence \( \{\mathbf{x}_k \}_{k=0} \) converges to a global
@@ -2534,7 +2532,7 @@ Note that the gradient is a function of \( \mathbf{x} =
 
 
 <section>
-<h2 id="the-sensitiveness-of-the-gradient-descent">The sensitiveness of the gradient descent </h2>
+<h2 id="___sec57">The sensitiveness of the gradient descent </h2>
 
 <p>
 The gradient descent method 
@@ -2553,7 +2551,7 @@ randomness. One such method is that of Stochastic Gradient Descent
 
 
 <section>
-<h2 id="convex-functions">Convex functions </h2>
+<h2 id="___sec58">Convex functions </h2>
 
 <p>
 Ideally we want our cost/loss function to be convex(concave).
@@ -2573,7 +2571,7 @@ regular polygons (triangles, rectangles, pentagons, etc...).
 
 
 <section>
-<h2 id="convex-function">Convex function </h2>
+<h2 id="___sec59">Convex function </h2>
 
 <p>
 <b>Convex function</b>: Let \( X \subset \mathbb{R}^n \) be a convex set. Assume that the function \( f: X \rightarrow \mathbb{R} \) is continuous, then \( f \) is said to be convex if <p>&nbsp;<br>
@@ -2583,7 +2581,7 @@ $$f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) $$
 
 
 <section>
-<h2 id="conditions-on-convex-functions">Conditions on convex functions </h2>
+<h2 id="___sec60">Conditions on convex functions </h2>
 
 <p>
 In the following we state first and second-order conditions which
@@ -2593,7 +2591,7 @@ details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/, 2004
 
 <p>
 <div class="alert alert-block alert-block alert-text-normal">
-<b>First order condition</b>
+<b>First order condition.</b>
 <p>
 Suppose \( f \) is differentiable (i.e \( \nabla f(x) \) is well defined for
 all \( x \) in the domain of \( f \)). Then \( f \) is convex if and only if \( D_f \)
@@ -2609,7 +2607,7 @@ note that it is always below the graph.
 
 <p>
 <div class="alert alert-block alert-block alert-text-normal">
-<b>Second order condition</b>
+<b>Second order condition.</b>
 <p>
 Assume that \( f \) is twice
 differentiable, i.e the Hessian matrix exists at each point in
@@ -2625,7 +2623,7 @@ This condition is particularly useful since it gives us an procedure for determi
 
 
 <section>
-<h2 id="more-on-convex-functions">More on convex functions </h2>
+<h2 id="___sec61">More on convex functions </h2>
 
 <p>
 The next result is of great importance to us and the reason why we are
@@ -2641,7 +2639,7 @@ is convex the following result provides invaluable information:
 
 <p>
 <div class="alert alert-block alert-block alert-text-normal">
-<b>Any minimum is global for convex functions</b>
+<b>Any minimum is global for convex functions.</b>
 <p>
 Consider the problem of finding \( x \in \mathbb{R}^n \) such that \( f(x) \)
 is minimal, where \( f \) is convex and differentiable. Then, any point
@@ -2654,7 +2652,7 @@ This result means that if we know that the cost/loss function is convex and we a
 
 
 <section>
-<h2 id="some-simple-problems">Some simple problems </h2>
+<h2 id="___sec62">Some simple problems </h2>
 
 <ol>
 <p><li> Show that \( f(x)=x^2 \) is convex for \( x \in \mathbb{R} \) using the definition of convexity. Hint: If you re-write the definition, \( f \) is convex if the following holds for all \( x,y \in D_f \) and any \( \lambda \in [0,1] \) $\lambda f(x)+(1-\lambda)f(y)-f(\lambda x + (1-\lambda) y ) \geq 0$.</li>
@@ -2681,7 +2679,7 @@ Using the definition of convexity, try to show that a function satisfying the pr
 
 
 <section>
-<h2 id="friday-september-25">Friday September 25 </h2>
+<h2 id="___sec63">Friday September 25 </h2>
 
 <p>
 <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureSeptember25.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture</a> and <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesSeptember25.pdf" target="_blank">link to handwritten notes</a>.
@@ -2689,7 +2687,7 @@ Using the definition of convexity, try to show that a function satisfying the pr
 
 
 <section>
-<h2 id="standard-steepest-descent">Standard steepest descent </h2>
+<h2 id="___sec64">Standard steepest descent </h2>
 
 <p>
 Before we proceed, we would like to discuss the approach called the
@@ -2729,7 +2727,7 @@ When we have found the exact solution, \( \boldsymbol{r}=0 \).
 
 
 <section>
-<h2 id="gradient-method">Gradient method </h2>
+<h2 id="___sec65">Gradient method </h2>
 
 <p>
 The residual is zero when we reach the minimum of the quadratic equation
@@ -2748,7 +2746,7 @@ symmetric.  This defines also the Hessian and we want it to be  positive definit
 
 
 <section>
-<h2 id="steepest-descent-method">Steepest descent  method </h2>
+<h2 id="___sec66">Steepest descent  method </h2>
 
 <p>
 We denote the initial guess for \( \boldsymbol{x} \) as \( \boldsymbol{x}_0 \). 
@@ -2775,7 +2773,7 @@ instead.
 
 
 <section>
-<h2 id="steepest-descent-method">Steepest descent  method </h2>
+<h2 id="___sec67">Steepest descent  method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2808,7 +2806,7 @@ and
 
 
 <section>
-<h2 id="final-expressions">Final expressions </h2>
+<h2 id="___sec68">Final expressions </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2860,12 +2858,12 @@ $$
 
 
 <section>
-<h2 id="steepest-descent-example">Steepest descent example </h2>
+<h2 id="___sec69">Steepest descent example </h2>
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy.linalg</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">la</span>
 
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">scipy.optimize</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sopt</span>
@@ -2891,7 +2889,7 @@ And then as countor plot
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>pt.axis(<span style="color: #CD5555">&quot;equal&quot;</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>pt.axis(<span style="color: #CD5555">&quot;equal&quot;</span>)
 pt.contour(xmesh, ymesh, fmesh)
 guesses = [np.array([<span style="color: #B452CD">2</span>, <span style="color: #B452CD">2.</span>/<span style="color: #B452CD">5</span>])]
 </pre></div>
@@ -2900,7 +2898,7 @@ Find guesses
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>x = guesses[-<span style="color: #B452CD">1</span>]
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>x = guesses[-<span style="color: #B452CD">1</span>]
 s = -df(x)
 </pre></div>
 <p>
@@ -2908,7 +2906,7 @@ Run it!
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">f1d</span>(alpha):
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">f1d</span>(alpha):
     <span style="color: #8B008B; font-weight: bold">return</span> f(x + alpha*s)
 
 alpha_opt = sopt.golden(f1d)
@@ -2921,7 +2919,7 @@ What happened?
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>pt.axis(<span style="color: #CD5555">&quot;equal&quot;</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>pt.axis(<span style="color: #CD5555">&quot;equal&quot;</span>)
 pt.contour(xmesh, ymesh, fmesh, <span style="color: #B452CD">50</span>)
 it_array = np.array(guesses)
 pt.plot(it_array.T[<span style="color: #B452CD">0</span>], it_array.T[<span style="color: #B452CD">1</span>], <span style="color: #CD5555">&quot;x-&quot;</span>)
@@ -2930,7 +2928,7 @@ pt.plot(it_array.T[<span style="color: #B452CD">0</span>], it_array.T[<span styl
 
 
 <section>
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec70">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2963,7 +2961,7 @@ this inner product. Being conjugate is a symmetric relation: if \( \boldsymbol{s
 
 
 <section>
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec71">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2982,7 +2980,7 @@ which is zero unless \( i=j \).
 
 
 <section>
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec72">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3012,7 +3010,7 @@ $$
 
 
 <section>
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec73">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3049,7 +3047,7 @@ $$
 
 
 <section>
-<h2 id="conjugate-gradient-method-and-iterations">Conjugate gradient method and iterations </h2>
+<h2 id="___sec74">Conjugate gradient method and iterations </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3086,7 +3084,7 @@ instead.
 
 
 <section>
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec75">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3119,7 +3117,7 @@ hence the name conjugate gradient method.
 
 
 <section>
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec76">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3151,7 +3149,7 @@ $$
 
 
 <section>
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec77">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3196,7 +3194,7 @@ $$
 
 
 <section>
-<h2 id="revisiting-some-of-our-first-linear-regression-encounters">Revisiting some of our first Linear Regression Encounters  </h2>
+<h2 id="___sec78">Revisiting some of our first Linear Regression Encounters  </h2>
 
 <p>
 We will use linear regression as a case study for the gradient descent
@@ -3216,7 +3214,7 @@ We revisit an example similar to what we had in the first homework set. We had a
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>x = <span style="color: #B452CD">2</span>*np.random.rand(m,<span style="color: #B452CD">1</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>x = <span style="color: #B452CD">2</span>*np.random.rand(m,<span style="color: #B452CD">1</span>)
 y = <span style="color: #B452CD">4</span>+<span style="color: #B452CD">3</span>*x+np.random.randn(m,<span style="color: #B452CD">1</span>)
 </pre></div>
 <p>
@@ -3238,7 +3236,7 @@ $$
 
 
 <section>
-<h2 id="gradient-descent-example">Gradient descent example </h2>
+<h2 id="___sec79">Gradient descent example </h2>
 
 <p>
 Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\boldsymbol{y}} = (\boldsymbol{y}_1,\cdots,\boldsymbol{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
@@ -3267,7 +3265,7 @@ and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
 
 
 <section>
-<h2 id="the-derivative-of-the-cost-loss-function">The derivative of the cost/loss function </h2>
+<h2 id="___sec80">The derivative of the cost/loss function </h2>
 
 <p>
 Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show  that the gradient can be written as
@@ -3284,7 +3282,7 @@ where \( X \) is the design matrix defined above.
 
 
 <section>
-<h2 id="the-hessian-matrix">The Hessian matrix </h2>
+<h2 id="___sec81">The Hessian matrix </h2>
 The Hessian matrix of \( C(\beta) \) is given by 
 <p>&nbsp;<br>
 $$
@@ -3300,7 +3298,7 @@ This result implies that \( C(\beta) \) is a convex function since the matrix \(
 
 
 <section>
-<h2 id="simple-program">Simple program </h2>
+<h2 id="___sec82">Simple program </h2>
 
 <p>
 We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to 
@@ -3322,14 +3320,14 @@ And finally we can compare our solution for \( \beta \) with the analytic result
 
 
 <section>
-<h2 id="gradient-descent-example">Gradient Descent Example </h2>
+<h2 id="___sec83">Gradient Descent Example </h2>
 
 <p>
 Here our simple example
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #228B22"># Importing various packages</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># Importing various packages</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">random</span> <span style="color: #8B008B; font-weight: bold">import</span> random, seed
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
@@ -3379,12 +3377,12 @@ plt.show()
 
 
 <section>
-<h2 id="and-a-corresponding-example-using-_scikit-learn_">And a corresponding example using <b>scikit-learn</b> </h2>
+<h2 id="___sec84">And a corresponding example using <b>scikit-learn</b> </h2>
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #228B22"># Importing various packages</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># Importing various packages</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">random</span> <span style="color: #8B008B; font-weight: bold">import</span> random, seed
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
@@ -3405,7 +3403,7 @@ sgdreg.fit(x,y.ravel())
 
 
 <section>
-<h2 id="gradient-descent-and-ridge">Gradient descent and Ridge </h2>
+<h2 id="___sec85">Gradient descent and Ridge </h2>
 
 <p>
 We have also discussed Ridge regression where the loss function contains a regularized term given by the \( L_2 \) norm of \( \beta \), 
@@ -3436,11 +3434,11 @@ $$
 
 
 <section>
-<h2 id="program-example-for-gradient-descent-with-ridge-regression">Program example for gradient descent with Ridge Regression </h2>
+<h2 id="___sec86">Program example for gradient descent with Ridge Regression </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">random</span> <span style="color: #8B008B; font-weight: bold">import</span> random, seed
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">random</span> <span style="color: #8B008B; font-weight: bold">import</span> random, seed
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">mpl_toolkits.mplot3d</span> <span style="color: #8B008B; font-weight: bold">import</span> Axes3D
@@ -3488,7 +3486,7 @@ plt.show()
 
 
 <section>
-<h2 id="using-gradient-descent-methods-limitations">Using gradient descent methods, limitations </h2>
+<h2 id="___sec87">Using gradient descent methods, limitations </h2>
 
 <ul>
 <p><li> <b>Gradient descent (GD) finds local minima of our function</b>. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our cost/loss/risk function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.</li>
diff --git a/doc/pub/week38/html/week38-solarized.html b/doc/pub/week38/html/week38-solarized.html
index 8fa62e020..348714114 100644
--- a/doc/pub/week38/html/week38-solarized.html
+++ b/doc/pub/week38/html/week38-solarized.html
@@ -1,19 +1,19 @@
 <!--
 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
 -->
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
 <title>Data Analysis and Machine Learning: Logistic Regression</title>
 
 
-<link href="https://cdn.rawgit.com/doconce/doconce/master/bundled/html_styles/style_solarized_box/css/solarized_light_code.css" rel="stylesheet" type="text/css" title="light"/>
-<script src="https://cdn.rawgit.com/doconce/doconce/master/bundled/html_styles/style_solarized_box/js/highlight.pack.js"></script>
+<link href="https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_styles/style_solarized_box/css/solarized_light_code.css" rel="stylesheet" type="text/css" title="light"/>
+<script src="https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_styles/style_solarized_box/js/highlight.pack.js"></script>
 <script>hljs.initHighlightingOnLoad();</script>
 
 <link href="https://thomasf.github.io/solarized-css/solarized-light.min.css" rel="stylesheet">
@@ -48,10 +48,10 @@ pre {
 .alert-block > p, .alert-block > ul {margin-bottom:1em}
 .alert li {margin-top: 1em}
 .alert-block p+p {margin-top:5px}
-.alert-notice { background-image: url(https://cdn.rawgit.com/doconce/doconce/master/bundled/html_images/small_yellow_notice.png); }
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-.alert-question {background-image:url(https://cdn.rawgit.com/doconce/doconce/master/bundled/html_images/small_yellow_question.png); }
+.alert-notice { background-image: url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_yellow_notice.png); }
+.alert-summary  { background-image:url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_yellow_summary.png); }
+.alert-warning { background-image: url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_yellow_warning.png); }
+.alert-question {background-image:url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_yellow_question.png); }
 
 div { text-align: justify; text-justify: inter-word; }
 </style>
@@ -61,239 +61,146 @@ div { text-align: justify; text-justify: inter-word; }
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -340,7 +247,7 @@ MathJax.Hub.Config({
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="plans-for-week-38">Plans for week 38 </h2>
+<h2 id="___sec0">Plans for week 38 </h2>
 
 <ul>
 <li> Thursday: Summary of regression methods and discussion of project 1.  Start Logistic Regression</li>
@@ -349,12 +256,12 @@ MathJax.Hub.Config({
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="thursday-september-23">Thursday September 23 </h2>
+<h2 id="___sec1">Thursday September 23 </h2>
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="ridge-and-lasso-regression-reminder">Ridge and LASSO Regression, reminder </h2>
+<h2 id="___sec2">Ridge and LASSO Regression, reminder </h2>
 
 <p>
 The expression for the standard Mean Squared Error (MSE) which we used to define our cost function and the equations for the ordinary least squares (OLS) method, that is 
@@ -412,7 +319,7 @@ $$
 <p>
 <!-- !split  -->
 
-<h2 id="various-steps-in-cross-validation">Various steps in cross-validation </h2>
+<h2 id="___sec3">Various steps in cross-validation </h2>
 
 <p>
 When the repetitive splitting of the data set is done randomly,
@@ -433,7 +340,7 @@ cross-validation (LOOCV).
 <p>
 <!-- !split  -->
 
-<h2 id="how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">How to set up the cross-validation for Ridge and/or Lasso </h2>
+<h2 id="___sec4">How to set up the cross-validation for Ridge and/or Lasso </h2>
 
 <ul>
 <li> Define a range of interest for the penalty parameter.</li>
@@ -465,7 +372,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="cross-validation-in-brief">Cross-validation in brief </h2>
+<h2 id="___sec5">Cross-validation in brief </h2>
 
 <p>
 For the various values of \( k \)
@@ -487,14 +394,14 @@ For the various values of \( k \)
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="code-example-for-cross-validation-and-k-fold-cross-validation">Code Example for Cross-validation and \( k \)-fold Cross-validation </h2>
+<h2 id="___sec6">Code Example for Cross-validation and \( k \)-fold Cross-validation </h2>
 
 <p>
 The code here uses Ridge regression with cross-validation (CV)  resampling and \( k \)-fold CV in order to fit a specific polynomial. 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> KFold
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> Ridge
@@ -587,7 +494,7 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="to-think-about-first-part">To think about, first part </h2>
+<h2 id="___sec7">To think about, first part </h2>
 
 <p>
 When you are comparing your own code with for example <b>Scikit-Learn</b>'s
@@ -606,14 +513,14 @@ Thus, if we cannot assume that the expected outputs/targets are zero
 when all predictors are zero (the columns in the design matrix), it
 may be a bad idea to implement a model which penalizes the intercept.
 Furthermore, in for example Ridge and Lasso regression, the solutions
-(when not shrinking $$\beta_0$$) for the unknown parameters
+(when not shrinking \( \beta_0 \)) for the unknown parameters
 \( \boldsymbol{\beta} \) are derived&#160;under the assumption that both \( \boldsymbol{y} \) and
 \( \boldsymbol{X} \) are zero centered, that is we subtract the mean values.
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="more-thinking">More thinking </h2>
+<h2 id="___sec8">More thinking </h2>
 
 <p>
 If our predictors&#160;represent different&#160;scales, then it is important to
@@ -647,7 +554,7 @@ This can clearly lead to problems in evaluating the cost/loss functions.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="still-thinking">Still thinking </h2>
+<h2 id="___sec9">Still thinking </h2>
 
 <p>
 Keep in mind that when you transform your data set before training a model, the same transformation needs to be done
@@ -656,7 +563,7 @@ on your eventual new data set  before making a prediction. If we translate this
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #228B22">#Model training, we compute the mean value of y and X</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22">#Model training, we compute the mean value of y and X</span>
 y_train_mean = np.mean(y_train)
 X_train_mean = np.mean(X_train,axis=<span style="color: #B452CD">0</span>)
 X_train = X_train - X_train_mean
@@ -674,7 +581,7 @@ y_pred = y_pred + y_train_mean
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="linear-regression-code-intercept-handling-first">Linear Regression code, Intercept handling first </h2>
+<h2 id="___sec10">Linear Regression code, Intercept handling first </h2>
 
 <p>
 This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (<em>code example thanks to  &#216;yvind Sigmundson Sch&#248;yen</em>). Here our scaling of the data is done by subtracting the mean values only.
@@ -682,7 +589,7 @@ This code shows a simple first-order fit to a data set using the above transform
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LinearRegression
@@ -756,7 +663,7 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="what-does-centering-subtracting-the-mean-values-mean-mathematically">What does centering (subtracting the mean values) mean mathematically? </h2>
+<h2 id="___sec11">What does centering (subtracting the mean values) mean mathematically? </h2>
 
 <p>
 Let us try to understand what this may imply mathematically when we subtract the mean values, also known as <em>zero centering</em>. To catch many birds with just one stone, we will focus on Ridge regression.
@@ -793,7 +700,7 @@ If we assume that every column of \( \boldsymbol{X} \) is centered, which we can
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>X = X - np.mean(X,axis=<span style="color: #B452CD">0</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>X = X - np.mean(X,axis=<span style="color: #B452CD">0</span>)
 </pre></div>
 <p>
 the sum \( \sum_{i=0}^{n-1} X_{ij} \)
@@ -837,7 +744,7 @@ and \( \tilde{X}_{ij} = X_{ij} - \frac{1}{n}\sum_{k=1}^{n-1}X_{kj} \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="code-examples">Code Examples </h2>
+<h2 id="___sec12">Code Examples </h2>
 
 <p>
 Armed with this wisdom, we attempt first simply set the intercept eqault to <b>False</b> in our implementation of Ridge regression for a vanilla data set.
@@ -845,7 +752,7 @@ Armed with this wisdom, we attempt first simply set the intercept eqault to <b>F
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> train_test_split
@@ -922,11 +829,11 @@ Let us see how we can change this code by zero centering.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="taking-out-the-mean">Taking out the mean </h2>
+<h2 id="___sec13">Taking out the mean </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> train_test_split
@@ -1015,7 +922,7 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="more-complicated-example-the-ising-model">More complicated Example: The Ising model </h2>
+<h2 id="___sec14">More complicated Example: The Ising model </h2>
 
 <p>
 The one-dimensional Ising model with nearest neighbor interaction, no
@@ -1041,7 +948,7 @@ with their respective energies.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">mpl_toolkits.axes_grid1</span> <span style="color: #8B008B; font-weight: bold">import</span> make_axes_locatable
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">seaborn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sns</span>
@@ -1072,7 +979,7 @@ the coupling constant to achieve this.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="reformulating-the-problem-to-suit-regression">Reformulating the problem to suit regression </h2>
+<h2 id="___sec15">Reformulating the problem to suit regression </h2>
 
 <p>
 A more general form for the one-dimensional Ising model is
@@ -1113,7 +1020,7 @@ We split the data in training and test data as discussed in the previous example
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>X = np.zeros((n, L ** <span style="color: #B452CD">2</span>))
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>X = np.zeros((n, L ** <span style="color: #B452CD">2</span>))
 <span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(n):
     X[i] = np.outer(spins[i], spins[i]).ravel()
 y = energies
@@ -1122,7 +1029,7 @@ X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=<span style=
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="linear-regression">Linear regression </h2>
+<h2 id="___sec16">Linear regression </h2>
 
 <p>
 In the ordinary least squares method we choose the cost function
@@ -1151,7 +1058,7 @@ first column of \( \boldsymbol{X} \) consists of \( 1 \). We do this here
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>X_train_own = np.concatenate(
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>X_train_own = np.concatenate(
     (np.ones(<span style="color: #658b00">len</span>(X_train))[:, np.newaxis], X_train),
     axis=<span style="color: #B452CD">1</span>
 )
@@ -1163,14 +1070,14 @@ X_test_own = np.concatenate(
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">ols_inv</span>(x: np.ndarray, y: np.ndarray) -&gt; np.ndarray:
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">ols_inv</span>(x: np.ndarray, y: np.ndarray) -&gt; np.ndarray:
     <span style="color: #8B008B; font-weight: bold">return</span> scl.inv(x.T @ x) @ (x.T @ y)
 beta = ols_inv(X_train_own, y_train)
 </pre></div>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="singular-value-decomposition">Singular Value decomposition </h2>
+<h2 id="___sec17">Singular Value decomposition </h2>
 
 <p>
 Doing the inversion directly turns out to be a bad idea since the matrix
@@ -1212,14 +1119,14 @@ linear system as an equation would reduce this down to
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">ols_svd</span>(x: np.ndarray, y: np.ndarray) -&gt; np.ndarray:
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">ols_svd</span>(x: np.ndarray, y: np.ndarray) -&gt; np.ndarray:
     u, s, v = scl.svd(x)
     <span style="color: #8B008B; font-weight: bold">return</span> v.T @ scl.pinv(scl.diagsvd(s, u.shape[<span style="color: #B452CD">0</span>], v.shape[<span style="color: #B452CD">0</span>])) @ u.T @ y
 </pre></div>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>beta = ols_svd(X_train_own,y_train)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>beta = ols_svd(X_train_own,y_train)
 </pre></div>
 <p>
 When extracting the \( J \)-matrix  we need to make sure that we remove the intercept, as is done here
@@ -1227,7 +1134,7 @@ When extracting the \( J \)-matrix  we need to make sure that we remove the inte
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>J = beta[<span style="color: #B452CD">1</span>:].reshape(L, L)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>J = beta[<span style="color: #B452CD">1</span>:].reshape(L, L)
 </pre></div>
 <p>
 A way of looking at the coefficients in \( J \) is to plot the matrices as images.
@@ -1235,7 +1142,7 @@ A way of looking at the coefficients in \( J \) is to plot the matrices as image
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
 im = plt.imshow(J, **cmap_args)
 plt.title(<span style="color: #CD5555">&quot;OLS&quot;</span>, fontsize=<span style="color: #B452CD">18</span>)
 plt.xticks(fontsize=<span style="color: #B452CD">18</span>)
@@ -1257,7 +1164,7 @@ In this case our matrix inversion was actually possible. The obvious question no
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-one-dimensional-ising-model">The one-dimensional Ising model </h2>
+<h2 id="___sec18">The one-dimensional Ising model </h2>
 
 <p>
 Let us bring back the Ising model again, but now with an additional
@@ -1282,7 +1189,7 @@ We will look at a system of \( L = 40 \) spins with a coupling constant of \( J
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">mpl_toolkits.axes_grid1</span> <span style="color: #8B008B; font-weight: bold">import</span> make_axes_locatable
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">seaborn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sns</span>
@@ -1340,7 +1247,7 @@ We organize the data as we did above
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>X = np.zeros((n, L ** <span style="color: #B452CD">2</span>))
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>X = np.zeros((n, L ** <span style="color: #B452CD">2</span>))
 <span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(n):
     X[i] = np.outer(spins[i], spins[i]).ravel()
 y = energies
@@ -1362,21 +1269,21 @@ We will do all fitting with <b>Scikit-Learn</b>,
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>clf = skl.LinearRegression().fit(X_train, y_train)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>clf = skl.LinearRegression().fit(X_train, y_train)
 </pre></div>
 <p>
 When  extracting the \( J \)-matrix we make sure to remove the intercept
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>J_sk = clf.coef_.reshape(L, L)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>J_sk = clf.coef_.reshape(L, L)
 </pre></div>
 <p>
 And then we plot the results
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
 im = plt.imshow(J_sk, **cmap_args)
 plt.title(<span style="color: #CD5555">&quot;LinearRegression from Scikit-learn&quot;</span>, fontsize=<span style="color: #B452CD">18</span>)
 plt.xticks(fontsize=<span style="color: #B452CD">18</span>)
@@ -1391,7 +1298,7 @@ The results perfectly with our previous discussion where we used our own code.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="ridge-regression">Ridge regression </h2>
+<h2 id="___sec19">Ridge regression </h2>
 
 <p>
 Having explored the ordinary least squares we move on to ridge
@@ -1410,7 +1317,7 @@ $$
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>_lambda = <span style="color: #B452CD">0.1</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>_lambda = <span style="color: #B452CD">0.1</span>
 clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train)
 J_ridge_sk = clf_ridge.coef_.reshape(L, L)
 fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
@@ -1426,7 +1333,7 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="lasso-regression">LASSO regression </h2>
+<h2 id="___sec20">LASSO regression </h2>
 
 <p>
 In the <b>Least Absolute Shrinkage and Selection Operator</b> (LASSO)-method we get a third cost function.
@@ -1444,7 +1351,7 @@ Finding the extremal point of this cost function is not so straight-forward as i
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)
 J_lasso_sk = clf_lasso.coef_.reshape(L, L)
 fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
 im = plt.imshow(J_lasso_sk, **cmap_args)
@@ -1464,7 +1371,7 @@ constant as opposed to ridge and OLS. We get a sparse solution with
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="performance-as-function-of-the-regularization-parameter">Performance as  function of the regularization parameter </h2>
+<h2 id="___sec21">Performance as  function of the regularization parameter </h2>
 
 <p>
 We see how the different models perform for a different set of values for \( \lambda \).
@@ -1472,7 +1379,7 @@ We see how the different models perform for a different set of values for \( \la
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>lambdas = np.logspace(-<span style="color: #B452CD">4</span>, <span style="color: #B452CD">5</span>, <span style="color: #B452CD">10</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>lambdas = np.logspace(-<span style="color: #B452CD">4</span>, <span style="color: #B452CD">5</span>, <span style="color: #B452CD">10</span>)
 
 train_errors = {
     <span style="color: #CD5555">&quot;ols_sk&quot;</span>: np.zeros(lambdas.size),
@@ -1518,7 +1425,7 @@ much. Ridge is more stable over a larger range of values for
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="finding-the-optimal-value-of-lambda">Finding the optimal value of \( \lambda \) </h2>
+<h2 id="___sec22">Finding the optimal value of \( \lambda \) </h2>
 
 <p>
 To determine which value of \( \lambda \) is best we plot the accuracy of
@@ -1531,7 +1438,7 @@ testing set that is close to the accuracy of the training set.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>fig = plt.figure(figsize=(<span style="color: #B452CD">20</span>, <span style="color: #B452CD">14</span>))
 
 colors = {
     <span style="color: #CD5555">&quot;ols_sk&quot;</span>: <span style="color: #CD5555">&quot;r&quot;</span>,
@@ -1570,7 +1477,7 @@ other models for all values of \( \lambda \).
 <p>
 <!-- !split  -->
 
-<h2 id="logistic-regression">Logistic Regression </h2>
+<h2 id="___sec23">Logistic Regression </h2>
 
 <p>
 In linear regression our main interest was centered on learning the
@@ -1588,7 +1495,7 @@ simple recipe for fitting our data.
 <p>
 <!-- !split  -->
 
-<h2 id="classification-problems">Classification problems </h2>
+<h2 id="___sec24">Classification problems </h2>
 
 <p>
 Classification problems, however, are concerned with outcomes taking
@@ -1611,7 +1518,7 @@ failure etc.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="optimization-and-deep-learning">Optimization and Deep learning </h2>
+<h2 id="___sec25">Optimization and Deep learning </h2>
 
 <p>
 Logistic regression will also serve as our stepping stone towards
@@ -1632,7 +1539,7 @@ models, as we will see later.
 <p>
 <!-- !split  -->
 
-<h2 id="basics">Basics </h2>
+<h2 id="___sec26">Basics </h2>
 
 <p>
 We consider the case where the dependent variables, also called the
@@ -1659,7 +1566,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="linear-classifier">Linear classifier </h2>
+<h2 id="___sec27">Linear classifier </h2>
 
 <p>
 Before moving to the logistic model, let us try to use our linear
@@ -1683,7 +1590,7 @@ where \( \boldsymbol{y} \) is a vector representing the possible outcomes, \( \b
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="some-selected-properties">Some selected properties </h2>
+<h2 id="___sec28">Some selected properties </h2>
 
 <p>
 The main problem with our function is that it takes values on the
@@ -1705,7 +1612,7 @@ the probability of a given category. This leads us to the logistic function.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="simple-example">Simple example </h2>
+<h2 id="___sec29">Simple example </h2>
 
 <p>
 The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput  is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful.
@@ -1713,7 +1620,7 @@ The following example on data for coronary heart disease (CHD) as function of ag
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #228B22"># Common imports</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># Common imports</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">os</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
@@ -1771,7 +1678,7 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="plotting-the-mean-value-for-each-group">Plotting the mean value for each group </h2>
+<h2 id="___sec30">Plotting the mean value for each group </h2>
 
 <p>
 What we could attempt however is to plot the mean value for each group.
@@ -1779,7 +1686,7 @@ What we could attempt however is to plot the mean value for each group.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>agegroupmean = np.array([<span style="color: #B452CD">0.1</span>, <span style="color: #B452CD">0.133</span>, <span style="color: #B452CD">0.250</span>, <span style="color: #B452CD">0.333</span>, <span style="color: #B452CD">0.462</span>, <span style="color: #B452CD">0.625</span>, <span style="color: #B452CD">0.765</span>, <span style="color: #B452CD">0.800</span>])
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>agegroupmean = np.array([<span style="color: #B452CD">0.1</span>, <span style="color: #B452CD">0.133</span>, <span style="color: #B452CD">0.250</span>, <span style="color: #B452CD">0.333</span>, <span style="color: #B452CD">0.462</span>, <span style="color: #B452CD">0.625</span>, <span style="color: #B452CD">0.765</span>, <span style="color: #B452CD">0.800</span>])
 group = np.array([<span style="color: #B452CD">1</span>, <span style="color: #B452CD">2</span>, <span style="color: #B452CD">3</span>, <span style="color: #B452CD">4</span>, <span style="color: #B452CD">5</span>, <span style="color: #B452CD">6</span>, <span style="color: #B452CD">7</span>, <span style="color: #B452CD">8</span>])
 plt.plot(group, agegroupmean, <span style="color: #CD5555">&quot;r-&quot;</span>)
 plt.axis([<span style="color: #B452CD">0</span>,<span style="color: #B452CD">9</span>,<span style="color: #B452CD">0</span>, <span style="color: #B452CD">1.0</span>])
@@ -1810,7 +1717,7 @@ representing the probability for finding a value of \( y_i \) with a given
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-logistic-function">The logistic function </h2>
+<h2 id="___sec31">The logistic function </h2>
 
 <p>
 Another widely studied model, is the so-called 
@@ -1833,7 +1740,7 @@ Note that \( 1-p(t)= p(-t) \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks">Examples of likelihood functions used in logistic regression and nueral networks </h2>
+<h2 id="___sec32">Examples of likelihood functions used in logistic regression and nueral networks </h2>
 
 <p>
 The following code plots the logistic function, the step function and other functions we will encounter from here and on.
@@ -1841,7 +1748,7 @@ The following code plots the logistic function, the step function and other func
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #CD5555">&quot;&quot;&quot;The sigmoid function (or the logistic curve) is a</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #CD5555">&quot;&quot;&quot;The sigmoid function (or the logistic curve) is a</span>
 <span style="color: #CD5555">function that takes any real number, z, and outputs a number (0,1).</span>
 <span style="color: #CD5555">It is useful in neural networks for assigning weights on a relative scale.</span>
 <span style="color: #CD5555">The value z is the weighted sum of parameters involved in the learning algorithm.&quot;&quot;&quot;</span>
@@ -1899,7 +1806,7 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="two-parameters">Two parameters </h2>
+<h2 id="___sec33">Two parameters </h2>
 
 <p>
 We assume now that we have two classes with \( y_i \) either \( 0 \) or \( 1 \). Furthermore we assume also that we have only two parameters \( \beta \) in our fitting of the Sigmoid function, that is we define probabilities 
@@ -1921,7 +1828,7 @@ $$
 <p>
 <!-- !split  -->
 
-<h2 id="maximum-likelihood">Maximum likelihood </h2>
+<h2 id="___sec34">Maximum likelihood </h2>
 
 <p>
 In order to define the total likelihood for all possible outcomes from a  
@@ -1944,7 +1851,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-cost-function-rewritten">The cost function rewritten </h2>
+<h2 id="___sec35">The cost function rewritten </h2>
 
 <p>
 Reordering the logarithms, we can rewrite the <b>cost/loss</b> function as
@@ -1965,7 +1872,7 @@ in practice we often supplement the cross-entropy with additional regularization
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="minimizing-the-cross-entropy">Minimizing the cross entropy </h2>
+<h2 id="___sec36">Minimizing the cross entropy </h2>
 
 <p>
 The cross entropy is a convex function of the weights \( \boldsymbol{\beta} \) and,
@@ -1987,7 +1894,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="a-more-compact-expression">A more compact expression </h2>
+<h2 id="___sec37">A more compact expression </h2>
 
 <p>
 Let us now define a vector \( \boldsymbol{y} \) with \( n \) elements \( y_i \), an
@@ -2010,7 +1917,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="extending-to-more-predictors">Extending to more predictors </h2>
+<h2 id="___sec38">Extending to more predictors </h2>
 
 <p>
 Within a binary classification problem, we can easily expand our model to include multiple predictors. Our ratio between likelihoods is then with \( p \) predictors
@@ -2026,7 +1933,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="including-more-classes">Including more classes </h2>
+<h2 id="___sec39">Including more classes </h2>
 
 <p>
 Till now we have mainly focused on two classes, the so-called binary
@@ -2054,7 +1961,7 @@ and the model is specified in term of \( K-1 \) so-called log-odds or
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="more-classes">More classes </h2>
+<h2 id="___sec40">More classes </h2>
 
 <p>
 In our discussion of neural networks we will encounter the above again
@@ -2094,12 +2001,12 @@ methods</a>.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="friday-september-24">Friday September 24 </h2>
+<h2 id="___sec41">Friday September 24 </h2>
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="wisconsin-cancer-data">Wisconsin Cancer Data  </h2>
+<h2 id="___sec42">Wisconsin Cancer Data  </h2>
 
 <p>
 We show here how we can use a simple regression case on the breast
@@ -2109,7 +2016,7 @@ classification.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span>  train_test_split 
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.datasets</span> <span style="color: #8B008B; font-weight: bold">import</span> load_breast_cancer
@@ -2138,7 +2045,7 @@ logreg.fit(X_train_scaled, y_train)
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="using-the-correlation-matrix">Using the correlation matrix </h2>
+<h2 id="___sec43">Using the correlation matrix </h2>
 
 <p>
 In addition to the above scores, we could also study the covariance (and the correlation matrix).
@@ -2146,7 +2053,7 @@ We use <b>Pandas</b> to compute the correlation matrix.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span>  train_test_split 
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.datasets</span> <span style="color: #8B008B; font-weight: bold">import</span> load_breast_cancer
@@ -2184,7 +2091,7 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="discussing-the-correlation-data">Discussing the correlation data </h2>
+<h2 id="___sec44">Discussing the correlation data </h2>
 
 <p>
 In the above example we note two things. In the first plot we display
@@ -2205,14 +2112,14 @@ We constructed this matrix using <b>pandas</b> via the statements
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)
 </pre></div>
 <p>
 and then
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>correlation_matrix = cancerpd.corr().round(<span style="color: #B452CD">1</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>correlation_matrix = cancerpd.corr().round(<span style="color: #B452CD">1</span>)
 </pre></div>
 <p>
 Diagonalizing this matrix we can in turn say something about which
@@ -2223,11 +2130,11 @@ applications. This will be discussed later this semester (<a href="https://compp
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="other-measures-in-classification-studies-cancer-data-again">Other measures in classification studies: Cancer Data  again </h2>
+<h2 id="___sec45">Other measures in classification studies: Cancer Data  again </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span>  train_test_split 
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.datasets</span> <span style="color: #8B008B; font-weight: bold">import</span> load_breast_cancer
@@ -2275,7 +2182,7 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm </h2>
+<h2 id="___sec46">Optimization, the central part of any Machine Learning algortithm </h2>
 
 <p>
 <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/OverarchingAimsWeek39.mp4?vrtx=view-as-webpage" target="_blank">Overview Video, why do we care about gradient methods?</a>
@@ -2293,7 +2200,7 @@ some approximative/numerical method to compute the minimum.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="revisiting-our-logistic-regression-case">Revisiting our Logistic Regression case </h2>
+<h2 id="___sec47">Revisiting our Logistic Regression case </h2>
 
 <p>
 In our discussion on Logistic Regression we studied the 
@@ -2315,7 +2222,7 @@ where \( \boldsymbol{\beta} \) are the weights we wish to extract from data, in
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-equations-to-solve">The equations to solve </h2>
+<h2 id="___sec48">The equations to solve </h2>
 
 <p>
 Our compact equations used a definition of a vector \( \boldsymbol{y} \) with \( n \)
@@ -2341,7 +2248,7 @@ This defines what is called  the Hessian matrix.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="solving-using-newton-raphson-s-method">Solving using Newton-Raphson's method </h2>
+<h2 id="___sec49">Solving using Newton-Raphson's method </h2>
 
 <p>
 If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the  matrices that define the first and second derivatives.
@@ -2367,7 +2274,7 @@ If we can compute these matrices, in particular the Hessian, the above is often
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="brief-reminder-on-newton-raphson-s-method">Brief reminder on Newton-Raphson's method </h2>
+<h2 id="___sec50">Brief reminder on Newton-Raphson's method </h2>
 
 <p>
 Let us quickly remind ourselves how we derive the above method.
@@ -2384,7 +2291,7 @@ normally discourage the use of this method.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-equations">The equations </h2>
+<h2 id="___sec51">The equations </h2>
 
 <p>
 The Newton-Raphson formula consists geometrically of extending the
@@ -2420,7 +2327,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="simple-geometric-interpretation">Simple geometric interpretation </h2>
+<h2 id="___sec52">Simple geometric interpretation </h2>
 
 <p>
 The above is Newton-Raphson's method. It has a simple geometric
@@ -2438,7 +2345,7 @@ vanishes, then Newton-Raphson may fail totally
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="extending-to-more-than-one-variable">Extending to more than one variable </h2>
+<h2 id="___sec53">Extending to more than one variable </h2>
 
 <p>
 Newton's method can be generalized to systems of several non-linear equations
@@ -2493,7 +2400,7 @@ more than two non-linear equations. In our case, the Jacobian matrix is given by
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="steepest-descent">Steepest descent </h2>
+<h2 id="___sec54">Steepest descent </h2>
 
 <p>
 The basic idea of gradient descent is
@@ -2517,7 +2424,7 @@ we are always moving towards smaller function values, i.e a minimum.
 <p>
 <!-- !split  -->
 
-<h2 id="more-on-steepest-descent">More on Steepest descent </h2>
+<h2 id="___sec55">More on Steepest descent </h2>
 
 <p>
 The previous observation is the basis of the method of steepest
@@ -2536,7 +2443,7 @@ the learning rate within the context of Machine Learning.
 <p>
 <!-- !split  -->
 
-<h2 id="the-ideal">The ideal </h2>
+<h2 id="___sec56">The ideal </h2>
 
 <p>
 Ideally the sequence \( \{\mathbf{x}_k \}_{k=0} \) converges to a global
@@ -2562,7 +2469,7 @@ Note that the gradient is a function of \( \mathbf{x} =
 <p>
 <!-- !split  -->
 
-<h2 id="the-sensitiveness-of-the-gradient-descent">The sensitiveness of the gradient descent </h2>
+<h2 id="___sec57">The sensitiveness of the gradient descent </h2>
 
 <p>
 The gradient descent method 
@@ -2581,7 +2488,7 @@ randomness. One such method is that of Stochastic Gradient Descent
 <p>
 <!-- !split  -->
 
-<h2 id="convex-functions">Convex functions </h2>
+<h2 id="___sec58">Convex functions </h2>
 
 <p>
 Ideally we want our cost/loss function to be convex(concave).
@@ -2601,7 +2508,7 @@ regular polygons (triangles, rectangles, pentagons, etc...).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="convex-function">Convex function </h2>
+<h2 id="___sec59">Convex function </h2>
 
 <p>
 <b>Convex function</b>: Let \( X \subset \mathbb{R}^n \) be a convex set. Assume that the function \( f: X \rightarrow \mathbb{R} \) is continuous, then \( f \) is said to be convex if $$f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) $$ for all \( x_1, x_2 \in X \) and for all \( t \in [0,1] \). If \( \leq \) is replaced with a strict inequaltiy in the definition, we demand \( x_1 \neq x_2 \) and \( t\in(0,1) \) then \( f \) is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting \( f(x_1) \) and \( f(x_2) \), the value of the function on the interval \( [x_1,x_2] \) is always below the line as illustrated below.
@@ -2609,7 +2516,7 @@ regular polygons (triangles, rectangles, pentagons, etc...).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conditions-on-convex-functions">Conditions on convex functions </h2>
+<h2 id="___sec60">Conditions on convex functions </h2>
 
 <p>
 In the following we state first and second-order conditions which
@@ -2619,7 +2526,7 @@ details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/, 2004
 
 <p>
 <div class="alert alert-block alert-block alert-text-normal">
-<b>First order condition</b>
+<b>First order condition.</b>
 <p>
 Suppose \( f \) is differentiable (i.e \( \nabla f(x) \) is well defined for
 all \( x \) in the domain of \( f \)). Then \( f \) is convex if and only if \( D_f \)
@@ -2634,7 +2541,7 @@ note that it is always below the graph.
 
 <p>
 <div class="alert alert-block alert-block alert-text-normal">
-<b>Second order condition</b>
+<b>Second order condition.</b>
 <p>
 Assume that \( f \) is twice
 differentiable, i.e the Hessian matrix exists at each point in
@@ -2651,7 +2558,7 @@ This condition is particularly useful since it gives us an procedure for determi
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="more-on-convex-functions">More on convex functions </h2>
+<h2 id="___sec61">More on convex functions </h2>
 
 <p>
 The next result is of great importance to us and the reason why we are
@@ -2667,7 +2574,7 @@ is convex the following result provides invaluable information:
 
 <p>
 <div class="alert alert-block alert-block alert-text-normal">
-<b>Any minimum is global for convex functions</b>
+<b>Any minimum is global for convex functions.</b>
 <p>
 Consider the problem of finding \( x \in \mathbb{R}^n \) such that \( f(x) \)
 is minimal, where \( f \) is convex and differentiable. Then, any point
@@ -2681,7 +2588,7 @@ This result means that if we know that the cost/loss function is convex and we a
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="some-simple-problems">Some simple problems </h2>
+<h2 id="___sec62">Some simple problems </h2>
 
 <ol>
 <li> Show that \( f(x)=x^2 \) is convex for \( x \in \mathbb{R} \) using the definition of convexity. Hint: If you re-write the definition, \( f \) is convex if the following holds for all \( x,y \in D_f \) and any \( \lambda \in [0,1] \) $\lambda f(x)+(1-\lambda)f(y)-f(\lambda x + (1-\lambda) y ) \geq 0$.</li>
@@ -2708,7 +2615,7 @@ Using the definition of convexity, try to show that a function satisfying the pr
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="friday-september-25">Friday September 25 </h2>
+<h2 id="___sec63">Friday September 25 </h2>
 
 <p>
 <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureSeptember25.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture</a> and <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesSeptember25.pdf" target="_blank">link to handwritten notes</a>.
@@ -2716,7 +2623,7 @@ Using the definition of convexity, try to show that a function satisfying the pr
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="standard-steepest-descent">Standard steepest descent </h2>
+<h2 id="___sec64">Standard steepest descent </h2>
 
 <p>
 Before we proceed, we would like to discuss the approach called the
@@ -2752,7 +2659,7 @@ When we have found the exact solution, \( \boldsymbol{r}=0 \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="gradient-method">Gradient method </h2>
+<h2 id="___sec65">Gradient method </h2>
 
 <p>
 The residual is zero when we reach the minimum of the quadratic equation
@@ -2769,7 +2676,7 @@ symmetric.  This defines also the Hessian and we want it to be  positive definit
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="steepest-descent-method">Steepest descent  method </h2>
+<h2 id="___sec66">Steepest descent  method </h2>
 
 <p>
 We denote the initial guess for \( \boldsymbol{x} \) as \( \boldsymbol{x}_0 \). 
@@ -2792,7 +2699,7 @@ instead.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="steepest-descent-method">Steepest descent  method </h2>
+<h2 id="___sec67">Steepest descent  method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2822,7 +2729,7 @@ and
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="final-expressions">Final expressions </h2>
+<h2 id="___sec68">Final expressions </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2865,12 +2772,12 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="steepest-descent-example">Steepest descent example </h2>
+<h2 id="___sec69">Steepest descent example </h2>
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy.linalg</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">la</span>
 
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">scipy.optimize</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sopt</span>
@@ -2896,7 +2803,7 @@ And then as countor plot
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>pt.axis(<span style="color: #CD5555">&quot;equal&quot;</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>pt.axis(<span style="color: #CD5555">&quot;equal&quot;</span>)
 pt.contour(xmesh, ymesh, fmesh)
 guesses = [np.array([<span style="color: #B452CD">2</span>, <span style="color: #B452CD">2.</span>/<span style="color: #B452CD">5</span>])]
 </pre></div>
@@ -2905,7 +2812,7 @@ Find guesses
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>x = guesses[-<span style="color: #B452CD">1</span>]
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>x = guesses[-<span style="color: #B452CD">1</span>]
 s = -df(x)
 </pre></div>
 <p>
@@ -2913,7 +2820,7 @@ Run it!
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">f1d</span>(alpha):
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">f1d</span>(alpha):
     <span style="color: #8B008B; font-weight: bold">return</span> f(x + alpha*s)
 
 alpha_opt = sopt.golden(f1d)
@@ -2926,7 +2833,7 @@ What happened?
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>pt.axis(<span style="color: #CD5555">&quot;equal&quot;</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>pt.axis(<span style="color: #CD5555">&quot;equal&quot;</span>)
 pt.contour(xmesh, ymesh, fmesh, <span style="color: #B452CD">50</span>)
 it_array = np.array(guesses)
 pt.plot(it_array.T[<span style="color: #B452CD">0</span>], it_array.T[<span style="color: #B452CD">1</span>], <span style="color: #CD5555">&quot;x-&quot;</span>)
@@ -2934,7 +2841,7 @@ pt.plot(it_array.T[<span style="color: #B452CD">0</span>], it_array.T[<span styl
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec70">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2964,7 +2871,7 @@ this inner product. Being conjugate is a symmetric relation: if \( \boldsymbol{s
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec71">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2982,7 +2889,7 @@ which is zero unless \( i=j \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec72">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3009,7 +2916,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec73">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3041,7 +2948,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method-and-iterations">Conjugate gradient method and iterations </h2>
+<h2 id="___sec74">Conjugate gradient method and iterations </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3077,7 +2984,7 @@ instead.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec75">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3107,7 +3014,7 @@ hence the name conjugate gradient method.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec76">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3136,7 +3043,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec77">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3174,7 +3081,7 @@ $$
 <p>
 <!-- !split  -->
 
-<h2 id="revisiting-some-of-our-first-linear-regression-encounters">Revisiting some of our first Linear Regression Encounters  </h2>
+<h2 id="___sec78">Revisiting some of our first Linear Regression Encounters  </h2>
 
 <p>
 We will use linear regression as a case study for the gradient descent
@@ -3193,7 +3100,7 @@ We revisit an example similar to what we had in the first homework set. We had a
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span>x = <span style="color: #B452CD">2</span>*np.random.rand(m,<span style="color: #B452CD">1</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>x = <span style="color: #B452CD">2</span>*np.random.rand(m,<span style="color: #B452CD">1</span>)
 y = <span style="color: #B452CD">4</span>+<span style="color: #B452CD">3</span>*x+np.random.randn(m,<span style="color: #B452CD">1</span>)
 </pre></div>
 <p>
@@ -3211,7 +3118,7 @@ $$
 <p>
 <!-- !split  -->
 
-<h2 id="gradient-descent-example">Gradient descent example </h2>
+<h2 id="___sec79">Gradient descent example </h2>
 
 <p>
 Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\boldsymbol{y}} = (\boldsymbol{y}_1,\cdots,\boldsymbol{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
@@ -3236,7 +3143,7 @@ and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-derivative-of-the-cost-loss-function">The derivative of the cost/loss function </h2>
+<h2 id="___sec80">The derivative of the cost/loss function </h2>
 
 <p>
 Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show  that the gradient can be written as
@@ -3251,7 +3158,7 @@ where \( X \) is the design matrix defined above.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-hessian-matrix">The Hessian matrix </h2>
+<h2 id="___sec81">The Hessian matrix </h2>
 The Hessian matrix of \( C(\beta) \) is given by 
 $$
 \boldsymbol{H} \equiv \begin{bmatrix}
@@ -3265,7 +3172,7 @@ This result implies that \( C(\beta) \) is a convex function since the matrix \(
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="simple-program">Simple program </h2>
+<h2 id="___sec82">Simple program </h2>
 
 <p>
 We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to 
@@ -3285,14 +3192,14 @@ And finally we can compare our solution for \( \beta \) with the analytic result
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="gradient-descent-example">Gradient Descent Example </h2>
+<h2 id="___sec83">Gradient Descent Example </h2>
 
 <p>
 Here our simple example
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #228B22"># Importing various packages</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># Importing various packages</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">random</span> <span style="color: #8B008B; font-weight: bold">import</span> random, seed
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
@@ -3341,12 +3248,12 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="and-a-corresponding-example-using-_scikit-learn_">And a corresponding example using <b>scikit-learn</b> </h2>
+<h2 id="___sec84">And a corresponding example using <b>scikit-learn</b> </h2>
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #228B22"># Importing various packages</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># Importing various packages</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">random</span> <span style="color: #8B008B; font-weight: bold">import</span> random, seed
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
@@ -3366,7 +3273,7 @@ sgdreg.fit(x,y.ravel())
 <p>
 <!-- !split  -->
 
-<h2 id="gradient-descent-and-ridge">Gradient descent and Ridge </h2>
+<h2 id="___sec85">Gradient descent and Ridge </h2>
 
 <p>
 We have also discussed Ridge regression where the loss function contains a regularized term given by the \( L_2 \) norm of \( \beta \), 
@@ -3391,11 +3298,11 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="program-example-for-gradient-descent-with-ridge-regression">Program example for gradient descent with Ridge Regression </h2>
+<h2 id="___sec86">Program example for gradient descent with Ridge Regression </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">random</span> <span style="color: #8B008B; font-weight: bold">import</span> random, seed
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">random</span> <span style="color: #8B008B; font-weight: bold">import</span> random, seed
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">mpl_toolkits.mplot3d</span> <span style="color: #8B008B; font-weight: bold">import</span> Axes3D
@@ -3442,7 +3349,7 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="using-gradient-descent-methods-limitations">Using gradient descent methods, limitations </h2>
+<h2 id="___sec87">Using gradient descent methods, limitations </h2>
 
 <ul>
 <li> <b>Gradient descent (GD) finds local minima of our function</b>. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our cost/loss/risk function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.</li>
diff --git a/doc/pub/week38/html/week38.html b/doc/pub/week38/html/week38.html
index ce3344d1d..77dcd9ae6 100644
--- a/doc/pub/week38/html/week38.html
+++ b/doc/pub/week38/html/week38.html
@@ -1,11 +1,11 @@
 <!--
 Automatically generated HTML file from DocOnce source
-(https://github.com/doconce/doconce/)
+(https://github.com/hplgit/doconce/)
 -->
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 <meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
 
@@ -53,10 +53,10 @@ hr.figure { border: 0; width: 80%; border-bottom: 1px solid #aaa}
 .alert-block > p, .alert-block > ul {margin-bottom:1em}
 .alert li {margin-top: 1em}
 .alert-block p+p {margin-top:5px}
-.alert-notice { background-image: url(https://cdn.rawgit.com/doconce/doconce/master/bundled/html_images/small_gray_notice.png); }
-.alert-summary  { background-image:url(https://cdn.rawgit.com/doconce/doconce/master/bundled/html_images/small_gray_summary.png); }
-.alert-warning { background-image: url(https://cdn.rawgit.com/doconce/doconce/master/bundled/html_images/small_gray_warning.png); }
-.alert-question {background-image:url(https://cdn.rawgit.com/doconce/doconce/master/bundled/html_images/small_gray_question.png); }
+.alert-notice { background-image: url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_notice.png); }
+.alert-summary  { background-image:url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_summary.png); }
+.alert-warning { background-image: url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_warning.png); }
+.alert-question {background-image:url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_question.png); }
 
 div { text-align: justify; text-justify: inter-word; }
 </style>
@@ -66,239 +66,146 @@ div { text-align: justify; text-justify: inter-word; }
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Plans for week 38', 2, None, 'plans-for-week-38'),
-              ('Thursday September 23', 2, None, 'thursday-september-23'),
-              ('Ridge and LASSO Regression, reminder',
-               2,
-               None,
-               'ridge-and-lasso-regression-reminder'),
-              ('Various steps in cross-validation',
-               2,
-               None,
-               'various-steps-in-cross-validation'),
+ 'sections': [('Plans for week 38', 2, None, '___sec0'),
+              ('Thursday September 23', 2, None, '___sec1'),
+              ('Ridge and LASSO Regression, reminder', 2, None, '___sec2'),
+              ('Various steps in cross-validation', 2, None, '___sec3'),
               ('How to set up the cross-validation for Ridge and/or Lasso',
                2,
                None,
-               'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
-              ('Cross-validation in brief',
-               2,
-               None,
-               'cross-validation-in-brief'),
+               '___sec4'),
+              ('Cross-validation in brief', 2, None, '___sec5'),
               ('Code Example for Cross-validation and $k$-fold '
                'Cross-validation',
                2,
                None,
-               'code-example-for-cross-validation-and-k-fold-cross-validation'),
-              ('To think about, first part',
-               2,
-               None,
-               'to-think-about-first-part'),
-              ('More thinking', 2, None, 'more-thinking'),
-              ('Still thinking', 2, None, 'still-thinking'),
+               '___sec6'),
+              ('To think about, first part', 2, None, '___sec7'),
+              ('More thinking', 2, None, '___sec8'),
+              ('Still thinking', 2, None, '___sec9'),
               ('Linear Regression code, Intercept handling first',
                2,
                None,
-               'linear-regression-code-intercept-handling-first'),
+               '___sec10'),
               ('What does centering (subtracting the mean values) mean '
                'mathematically?',
                2,
                None,
-               'what-does-centering-subtracting-the-mean-values-mean-mathematically'),
-              ('Code Examples', 2, None, 'code-examples'),
-              ('Taking out the mean', 2, None, 'taking-out-the-mean'),
+               '___sec11'),
+              ('Code Examples', 2, None, '___sec12'),
+              ('Taking out the mean', 2, None, '___sec13'),
               ('More complicated Example: The Ising model',
                2,
                None,
-               'more-complicated-example-the-ising-model'),
+               '___sec14'),
               ('Reformulating the problem to suit regression',
                2,
                None,
-               'reformulating-the-problem-to-suit-regression'),
-              ('Linear regression', 2, None, 'linear-regression'),
-              ('Singular Value decomposition',
-               2,
-               None,
-               'singular-value-decomposition'),
-              ('The one-dimensional Ising model',
-               2,
-               None,
-               'the-one-dimensional-ising-model'),
-              ('Ridge regression', 2, None, 'ridge-regression'),
-              ('LASSO regression', 2, None, 'lasso-regression'),
+               '___sec15'),
+              ('Linear regression', 2, None, '___sec16'),
+              ('Singular Value decomposition', 2, None, '___sec17'),
+              ('The one-dimensional Ising model', 2, None, '___sec18'),
+              ('Ridge regression', 2, None, '___sec19'),
+              ('LASSO regression', 2, None, '___sec20'),
               ('Performance as  function of the regularization parameter',
                2,
                None,
-               'performance-as-function-of-the-regularization-parameter'),
-              ('Finding the optimal value of $\\lambda$',
-               2,
-               None,
-               'finding-the-optimal-value-of-lambda'),
-              ('Logistic Regression', 2, None, 'logistic-regression'),
-              ('Classification problems', 2, None, 'classification-problems'),
-              ('Optimization and Deep learning',
-               2,
-               None,
-               'optimization-and-deep-learning'),
-              ('Basics', 2, None, 'basics'),
-              ('Linear classifier', 2, None, 'linear-classifier'),
-              ('Some selected properties', 2, None, 'some-selected-properties'),
-              ('Simple example', 2, None, 'simple-example'),
-              ('Plotting the mean value for each group',
-               2,
-               None,
-               'plotting-the-mean-value-for-each-group'),
-              ('The logistic function', 2, None, 'the-logistic-function'),
+               '___sec21'),
+              ('Finding the optimal value of $\\lambda$', 2, None, '___sec22'),
+              ('Logistic Regression', 2, None, '___sec23'),
+              ('Classification problems', 2, None, '___sec24'),
+              ('Optimization and Deep learning', 2, None, '___sec25'),
+              ('Basics', 2, None, '___sec26'),
+              ('Linear classifier', 2, None, '___sec27'),
+              ('Some selected properties', 2, None, '___sec28'),
+              ('Simple example', 2, None, '___sec29'),
+              ('Plotting the mean value for each group', 2, None, '___sec30'),
+              ('The logistic function', 2, None, '___sec31'),
               ('Examples of likelihood functions used in logistic regression '
                'and nueral networks',
                2,
                None,
-               'examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks'),
-              ('Two parameters', 2, None, 'two-parameters'),
-              ('Maximum likelihood', 2, None, 'maximum-likelihood'),
-              ('The cost function rewritten',
-               2,
-               None,
-               'the-cost-function-rewritten'),
-              ('Minimizing the cross entropy',
-               2,
-               None,
-               'minimizing-the-cross-entropy'),
-              ('A more compact expression',
-               2,
-               None,
-               'a-more-compact-expression'),
-              ('Extending to more predictors',
-               2,
-               None,
-               'extending-to-more-predictors'),
-              ('Including more classes', 2, None, 'including-more-classes'),
-              ('More classes', 2, None, 'more-classes'),
-              ('Friday September 24', 2, None, 'friday-september-24'),
-              ('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
-              ('Using the correlation matrix',
-               2,
-               None,
-               'using-the-correlation-matrix'),
-              ('Discussing the correlation data',
-               2,
-               None,
-               'discussing-the-correlation-data'),
+               '___sec32'),
+              ('Two parameters', 2, None, '___sec33'),
+              ('Maximum likelihood', 2, None, '___sec34'),
+              ('The cost function rewritten', 2, None, '___sec35'),
+              ('Minimizing the cross entropy', 2, None, '___sec36'),
+              ('A more compact expression', 2, None, '___sec37'),
+              ('Extending to more predictors', 2, None, '___sec38'),
+              ('Including more classes', 2, None, '___sec39'),
+              ('More classes', 2, None, '___sec40'),
+              ('Friday September 24', 2, None, '___sec41'),
+              ('Wisconsin Cancer Data', 2, None, '___sec42'),
+              ('Using the correlation matrix', 2, None, '___sec43'),
+              ('Discussing the correlation data', 2, None, '___sec44'),
               ('Other measures in classification studies: Cancer Data  again',
                2,
                None,
-               'other-measures-in-classification-studies-cancer-data-again'),
+               '___sec45'),
               ('Optimization, the central part of any Machine Learning '
                'algortithm',
                2,
                None,
-               'optimization-the-central-part-of-any-machine-learning-algortithm'),
-              ('Revisiting our Logistic Regression case',
-               2,
-               None,
-               'revisiting-our-logistic-regression-case'),
-              ('The equations to solve', 2, None, 'the-equations-to-solve'),
-              ("Solving using Newton-Raphson's method",
-               2,
-               None,
-               'solving-using-newton-raphson-s-method'),
+               '___sec46'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec47'),
+              ('The equations to solve', 2, None, '___sec48'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec49'),
               ("Brief reminder on Newton-Raphson's method",
                2,
                None,
-               'brief-reminder-on-newton-raphson-s-method'),
-              ('The equations', 2, None, 'the-equations'),
-              ('Simple geometric interpretation',
-               2,
-               None,
-               'simple-geometric-interpretation'),
-              ('Extending to more than one variable',
-               2,
-               None,
-               'extending-to-more-than-one-variable'),
-              ('Steepest descent', 2, None, 'steepest-descent'),
-              ('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
-              ('The ideal', 2, None, 'the-ideal'),
+               '___sec50'),
+              ('The equations', 2, None, '___sec51'),
+              ('Simple geometric interpretation', 2, None, '___sec52'),
+              ('Extending to more than one variable', 2, None, '___sec53'),
+              ('Steepest descent', 2, None, '___sec54'),
+              ('More on Steepest descent', 2, None, '___sec55'),
+              ('The ideal', 2, None, '___sec56'),
               ('The sensitiveness of the gradient descent',
                2,
                None,
-               'the-sensitiveness-of-the-gradient-descent'),
-              ('Convex functions', 2, None, 'convex-functions'),
-              ('Convex function', 2, None, 'convex-function'),
-              ('Conditions on convex functions',
-               2,
-               None,
-               'conditions-on-convex-functions'),
-              ('More on convex functions', 2, None, 'more-on-convex-functions'),
-              ('Some simple problems', 2, None, 'some-simple-problems'),
-              ('Friday September 25', 2, None, 'friday-september-25'),
-              ('Standard steepest descent',
-               2,
-               None,
-               'standard-steepest-descent'),
-              ('Gradient method', 2, None, 'gradient-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Steepest descent  method', 2, None, 'steepest-descent-method'),
-              ('Final expressions', 2, None, 'final-expressions'),
-              ('Steepest descent example', 2, None, 'steepest-descent-example'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method and iterations',
-               2,
-               None,
-               'conjugate-gradient-method-and-iterations'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
-              ('Conjugate gradient method',
-               2,
-               None,
-               'conjugate-gradient-method'),
+               '___sec57'),
+              ('Convex functions', 2, None, '___sec58'),
+              ('Convex function', 2, None, '___sec59'),
+              ('Conditions on convex functions', 2, None, '___sec60'),
+              ('More on convex functions', 2, None, '___sec61'),
+              ('Some simple problems', 2, None, '___sec62'),
+              ('Friday September 25', 2, None, '___sec63'),
+              ('Standard steepest descent', 2, None, '___sec64'),
+              ('Gradient method', 2, None, '___sec65'),
+              ('Steepest descent  method', 2, None, '___sec66'),
+              ('Steepest descent  method', 2, None, '___sec67'),
+              ('Final expressions', 2, None, '___sec68'),
+              ('Steepest descent example', 2, None, '___sec69'),
+              ('Conjugate gradient method', 2, None, '___sec70'),
+              ('Conjugate gradient method', 2, None, '___sec71'),
+              ('Conjugate gradient method', 2, None, '___sec72'),
+              ('Conjugate gradient method', 2, None, '___sec73'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec74'),
+              ('Conjugate gradient method', 2, None, '___sec75'),
+              ('Conjugate gradient method', 2, None, '___sec76'),
+              ('Conjugate gradient method', 2, None, '___sec77'),
               ('Revisiting some of our first Linear Regression Encounters',
                2,
                None,
-               'revisiting-some-of-our-first-linear-regression-encounters'),
-              ('Gradient descent example', 2, None, 'gradient-descent-example'),
-              ('The derivative of the cost/loss function',
-               2,
-               None,
-               'the-derivative-of-the-cost-loss-function'),
-              ('The Hessian matrix', 2, None, 'the-hessian-matrix'),
-              ('Simple program', 2, None, 'simple-program'),
-              ('Gradient Descent Example', 2, None, 'gradient-descent-example'),
+               '___sec78'),
+              ('Gradient descent example', 2, None, '___sec79'),
+              ('The derivative of the cost/loss function', 2, None, '___sec80'),
+              ('The Hessian matrix', 2, None, '___sec81'),
+              ('Simple program', 2, None, '___sec82'),
+              ('Gradient Descent Example', 2, None, '___sec83'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               'and-a-corresponding-example-using-_scikit-learn_'),
-              ('Gradient descent and Ridge',
-               2,
-               None,
-               'gradient-descent-and-ridge'),
+               '___sec84'),
+              ('Gradient descent and Ridge', 2, None, '___sec85'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
-               'program-example-for-gradient-descent-with-ridge-regression'),
+               '___sec86'),
               ('Using gradient descent methods, limitations',
                2,
                None,
-               'using-gradient-descent-methods-limitations')]}
+               '___sec87')]}
 end of tocinfo -->
 
 <body>
@@ -345,7 +252,7 @@ MathJax.Hub.Config({
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="plans-for-week-38">Plans for week 38 </h2>
+<h2 id="___sec0">Plans for week 38 </h2>
 
 <ul>
 <li> Thursday: Summary of regression methods and discussion of project 1.  Start Logistic Regression</li>
@@ -354,12 +261,12 @@ MathJax.Hub.Config({
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="thursday-september-23">Thursday September 23 </h2>
+<h2 id="___sec1">Thursday September 23 </h2>
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="ridge-and-lasso-regression-reminder">Ridge and LASSO Regression, reminder </h2>
+<h2 id="___sec2">Ridge and LASSO Regression, reminder </h2>
 
 <p>
 The expression for the standard Mean Squared Error (MSE) which we used to define our cost function and the equations for the ordinary least squares (OLS) method, that is 
@@ -417,7 +324,7 @@ $$
 <p>
 <!-- !split  -->
 
-<h2 id="various-steps-in-cross-validation">Various steps in cross-validation </h2>
+<h2 id="___sec3">Various steps in cross-validation </h2>
 
 <p>
 When the repetitive splitting of the data set is done randomly,
@@ -438,7 +345,7 @@ cross-validation (LOOCV).
 <p>
 <!-- !split  -->
 
-<h2 id="how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">How to set up the cross-validation for Ridge and/or Lasso </h2>
+<h2 id="___sec4">How to set up the cross-validation for Ridge and/or Lasso </h2>
 
 <ul>
 <li> Define a range of interest for the penalty parameter.</li>
@@ -470,7 +377,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="cross-validation-in-brief">Cross-validation in brief </h2>
+<h2 id="___sec5">Cross-validation in brief </h2>
 
 <p>
 For the various values of \( k \)
@@ -492,14 +399,14 @@ For the various values of \( k \)
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="code-example-for-cross-validation-and-k-fold-cross-validation">Code Example for Cross-validation and \( k \)-fold Cross-validation </h2>
+<h2 id="___sec6">Code Example for Cross-validation and \( k \)-fold Cross-validation </h2>
 
 <p>
 The code here uses Ridge regression with cross-validation (CV)  resampling and \( k \)-fold CV in order to fit a specific polynomial. 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> KFold
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> Ridge
@@ -592,7 +499,7 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="to-think-about-first-part">To think about, first part </h2>
+<h2 id="___sec7">To think about, first part </h2>
 
 <p>
 When you are comparing your own code with for example <b>Scikit-Learn</b>'s
@@ -611,14 +518,14 @@ Thus, if we cannot assume that the expected outputs/targets are zero
 when all predictors are zero (the columns in the design matrix), it
 may be a bad idea to implement a model which penalizes the intercept.
 Furthermore, in for example Ridge and Lasso regression, the solutions
-(when not shrinking $$\beta_0$$) for the unknown parameters
+(when not shrinking \( \beta_0 \)) for the unknown parameters
 \( \boldsymbol{\beta} \) are derived&#160;under the assumption that both \( \boldsymbol{y} \) and
 \( \boldsymbol{X} \) are zero centered, that is we subtract the mean values.
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="more-thinking">More thinking </h2>
+<h2 id="___sec8">More thinking </h2>
 
 <p>
 If our predictors&#160;represent different&#160;scales, then it is important to
@@ -652,7 +559,7 @@ This can clearly lead to problems in evaluating the cost/loss functions.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="still-thinking">Still thinking </h2>
+<h2 id="___sec9">Still thinking </h2>
 
 <p>
 Keep in mind that when you transform your data set before training a model, the same transformation needs to be done
@@ -661,7 +568,7 @@ on your eventual new data set  before making a prediction. If we translate this
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #408080; font-style: italic">#Model training, we compute the mean value of y and X</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic">#Model training, we compute the mean value of y and X</span>
 y_train_mean <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean(y_train)
 X_train_mean <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean(X_train,axis<span style="color: #666666">=0</span>)
 X_train <span style="color: #666666">=</span> X_train <span style="color: #666666">-</span> X_train_mean
@@ -679,7 +586,7 @@ y_pred <span style="color: #666666">=</span> y_pred <span style="color: #666666"
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="linear-regression-code-intercept-handling-first">Linear Regression code, Intercept handling first </h2>
+<h2 id="___sec10">Linear Regression code, Intercept handling first </h2>
 
 <p>
 This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (<em>code example thanks to  &#216;yvind Sigmundson Sch&#248;yen</em>). Here our scaling of the data is done by subtracting the mean values only.
@@ -687,7 +594,7 @@ This code shows a simple first-order fit to a data set using the above transform
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LinearRegression
@@ -761,7 +668,7 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="what-does-centering-subtracting-the-mean-values-mean-mathematically">What does centering (subtracting the mean values) mean mathematically? </h2>
+<h2 id="___sec11">What does centering (subtracting the mean values) mean mathematically? </h2>
 
 <p>
 Let us try to understand what this may imply mathematically when we subtract the mean values, also known as <em>zero centering</em>. To catch many birds with just one stone, we will focus on Ridge regression.
@@ -798,7 +705,7 @@ If we assume that every column of \( \boldsymbol{X} \) is centered, which we can
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>X <span style="color: #666666">=</span> X <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(X,axis<span style="color: #666666">=0</span>)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>X <span style="color: #666666">=</span> X <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(X,axis<span style="color: #666666">=0</span>)
 </pre></div>
 <p>
 the sum \( \sum_{i=0}^{n-1} X_{ij} \)
@@ -842,7 +749,7 @@ and \( \tilde{X}_{ij} = X_{ij} - \frac{1}{n}\sum_{k=1}^{n-1}X_{kj} \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="code-examples">Code Examples </h2>
+<h2 id="___sec12">Code Examples </h2>
 
 <p>
 Armed with this wisdom, we attempt first simply set the intercept eqault to <b>False</b> in our implementation of Ridge regression for a vanilla data set.
@@ -850,7 +757,7 @@ Armed with this wisdom, we attempt first simply set the intercept eqault to <b>F
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
@@ -927,11 +834,11 @@ Let us see how we can change this code by zero centering.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="taking-out-the-mean">Taking out the mean </h2>
+<h2 id="___sec13">Taking out the mean </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
@@ -1020,7 +927,7 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="more-complicated-example-the-ising-model">More complicated Example: The Ising model </h2>
+<h2 id="___sec14">More complicated Example: The Ising model </h2>
 
 <p>
 The one-dimensional Ising model with nearest neighbor interaction, no
@@ -1046,7 +953,7 @@ with their respective energies.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">mpl_toolkits.axes_grid1</span> <span style="color: #008000; font-weight: bold">import</span> make_axes_locatable
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">seaborn</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sns</span>
@@ -1077,7 +984,7 @@ the coupling constant to achieve this.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="reformulating-the-problem-to-suit-regression">Reformulating the problem to suit regression </h2>
+<h2 id="___sec15">Reformulating the problem to suit regression </h2>
 
 <p>
 A more general form for the one-dimensional Ising model is
@@ -1118,7 +1025,7 @@ We split the data in training and test data as discussed in the previous example
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((n, L <span style="color: #666666">**</span> <span style="color: #666666">2</span>))
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((n, L <span style="color: #666666">**</span> <span style="color: #666666">2</span>))
 <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(n):
     X[i] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>outer(spins[i], spins[i])<span style="color: #666666">.</span>ravel()
 y <span style="color: #666666">=</span> energies
@@ -1127,7 +1034,7 @@ X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_tes
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="linear-regression">Linear regression </h2>
+<h2 id="___sec16">Linear regression </h2>
 
 <p>
 In the ordinary least squares method we choose the cost function
@@ -1156,7 +1063,7 @@ first column of \( \boldsymbol{X} \) consists of \( 1 \). We do this here
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>X_train_own <span style="color: #666666">=</span> np<span style="color: #666666">.</span>concatenate(
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>X_train_own <span style="color: #666666">=</span> np<span style="color: #666666">.</span>concatenate(
     (np<span style="color: #666666">.</span>ones(<span style="color: #008000">len</span>(X_train))[:, np<span style="color: #666666">.</span>newaxis], X_train),
     axis<span style="color: #666666">=1</span>
 )
@@ -1168,14 +1075,14 @@ X_test_own <span style="color: #666666">=</span> np<span style="color: #666666">
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">ols_inv</span>(x: np<span style="color: #666666">.</span>ndarray, y: np<span style="color: #666666">.</span>ndarray) <span style="color: #666666">-&gt;</span> np<span style="color: #666666">.</span>ndarray:
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">ols_inv</span>(x: np<span style="color: #666666">.</span>ndarray, y: np<span style="color: #666666">.</span>ndarray) <span style="color: #666666">-&gt;</span> np<span style="color: #666666">.</span>ndarray:
     <span style="color: #008000; font-weight: bold">return</span> scl<span style="color: #666666">.</span>inv(x<span style="color: #666666">.</span>T <span style="color: #666666">@</span> x) <span style="color: #666666">@</span> (x<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y)
 beta <span style="color: #666666">=</span> ols_inv(X_train_own, y_train)
 </pre></div>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="singular-value-decomposition">Singular Value decomposition </h2>
+<h2 id="___sec17">Singular Value decomposition </h2>
 
 <p>
 Doing the inversion directly turns out to be a bad idea since the matrix
@@ -1217,14 +1124,14 @@ linear system as an equation would reduce this down to
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">ols_svd</span>(x: np<span style="color: #666666">.</span>ndarray, y: np<span style="color: #666666">.</span>ndarray) <span style="color: #666666">-&gt;</span> np<span style="color: #666666">.</span>ndarray:
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">ols_svd</span>(x: np<span style="color: #666666">.</span>ndarray, y: np<span style="color: #666666">.</span>ndarray) <span style="color: #666666">-&gt;</span> np<span style="color: #666666">.</span>ndarray:
     u, s, v <span style="color: #666666">=</span> scl<span style="color: #666666">.</span>svd(x)
     <span style="color: #008000; font-weight: bold">return</span> v<span style="color: #666666">.</span>T <span style="color: #666666">@</span> scl<span style="color: #666666">.</span>pinv(scl<span style="color: #666666">.</span>diagsvd(s, u<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>], v<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>])) <span style="color: #666666">@</span> u<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y
 </pre></div>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>beta <span style="color: #666666">=</span> ols_svd(X_train_own,y_train)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>beta <span style="color: #666666">=</span> ols_svd(X_train_own,y_train)
 </pre></div>
 <p>
 When extracting the \( J \)-matrix  we need to make sure that we remove the intercept, as is done here
@@ -1232,7 +1139,7 @@ When extracting the \( J \)-matrix  we need to make sure that we remove the inte
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>J <span style="color: #666666">=</span> beta[<span style="color: #666666">1</span>:]<span style="color: #666666">.</span>reshape(L, L)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>J <span style="color: #666666">=</span> beta[<span style="color: #666666">1</span>:]<span style="color: #666666">.</span>reshape(L, L)
 </pre></div>
 <p>
 A way of looking at the coefficients in \( J \) is to plot the matrices as images.
@@ -1240,7 +1147,7 @@ A way of looking at the coefficients in \( J \) is to plot the matrices as image
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
 im <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>imshow(J, <span style="color: #666666">**</span>cmap_args)
 plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;OLS&quot;</span>, fontsize<span style="color: #666666">=18</span>)
 plt<span style="color: #666666">.</span>xticks(fontsize<span style="color: #666666">=18</span>)
@@ -1262,7 +1169,7 @@ In this case our matrix inversion was actually possible. The obvious question no
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-one-dimensional-ising-model">The one-dimensional Ising model </h2>
+<h2 id="___sec18">The one-dimensional Ising model </h2>
 
 <p>
 Let us bring back the Ising model again, but now with an additional
@@ -1287,7 +1194,7 @@ We will look at a system of \( L = 40 \) spins with a coupling constant of \( J
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">mpl_toolkits.axes_grid1</span> <span style="color: #008000; font-weight: bold">import</span> make_axes_locatable
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">seaborn</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sns</span>
@@ -1345,7 +1252,7 @@ We organize the data as we did above
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((n, L <span style="color: #666666">**</span> <span style="color: #666666">2</span>))
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((n, L <span style="color: #666666">**</span> <span style="color: #666666">2</span>))
 <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(n):
     X[i] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>outer(spins[i], spins[i])<span style="color: #666666">.</span>ravel()
 y <span style="color: #666666">=</span> energies
@@ -1367,21 +1274,21 @@ We will do all fitting with <b>Scikit-Learn</b>,
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>clf <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>LinearRegression()<span style="color: #666666">.</span>fit(X_train, y_train)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>clf <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>LinearRegression()<span style="color: #666666">.</span>fit(X_train, y_train)
 </pre></div>
 <p>
 When  extracting the \( J \)-matrix we make sure to remove the intercept
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>J_sk <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>coef_<span style="color: #666666">.</span>reshape(L, L)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>J_sk <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>coef_<span style="color: #666666">.</span>reshape(L, L)
 </pre></div>
 <p>
 And then we plot the results
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
 im <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>imshow(J_sk, <span style="color: #666666">**</span>cmap_args)
 plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;LinearRegression from Scikit-learn&quot;</span>, fontsize<span style="color: #666666">=18</span>)
 plt<span style="color: #666666">.</span>xticks(fontsize<span style="color: #666666">=18</span>)
@@ -1396,7 +1303,7 @@ The results perfectly with our previous discussion where we used our own code.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="ridge-regression">Ridge regression </h2>
+<h2 id="___sec19">Ridge regression </h2>
 
 <p>
 Having explored the ordinary least squares we move on to ridge
@@ -1415,7 +1322,7 @@ $$
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>_lambda <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>_lambda <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
 clf_ridge <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>Ridge(alpha<span style="color: #666666">=</span>_lambda)<span style="color: #666666">.</span>fit(X_train, y_train)
 J_ridge_sk <span style="color: #666666">=</span> clf_ridge<span style="color: #666666">.</span>coef_<span style="color: #666666">.</span>reshape(L, L)
 fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
@@ -1431,7 +1338,7 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="lasso-regression">LASSO regression </h2>
+<h2 id="___sec20">LASSO regression </h2>
 
 <p>
 In the <b>Least Absolute Shrinkage and Selection Operator</b> (LASSO)-method we get a third cost function.
@@ -1449,7 +1356,7 @@ Finding the extremal point of this cost function is not so straight-forward as i
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>clf_lasso <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>Lasso(alpha<span style="color: #666666">=</span>_lambda)<span style="color: #666666">.</span>fit(X_train, y_train)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>clf_lasso <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>Lasso(alpha<span style="color: #666666">=</span>_lambda)<span style="color: #666666">.</span>fit(X_train, y_train)
 J_lasso_sk <span style="color: #666666">=</span> clf_lasso<span style="color: #666666">.</span>coef_<span style="color: #666666">.</span>reshape(L, L)
 fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
 im <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>imshow(J_lasso_sk, <span style="color: #666666">**</span>cmap_args)
@@ -1469,7 +1376,7 @@ constant as opposed to ridge and OLS. We get a sparse solution with
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="performance-as-function-of-the-regularization-parameter">Performance as  function of the regularization parameter </h2>
+<h2 id="___sec21">Performance as  function of the regularization parameter </h2>
 
 <p>
 We see how the different models perform for a different set of values for \( \lambda \).
@@ -1477,7 +1384,7 @@ We see how the different models perform for a different set of values for \( \la
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">5</span>, <span style="color: #666666">10</span>)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">5</span>, <span style="color: #666666">10</span>)
 
 train_errors <span style="color: #666666">=</span> {
     <span style="color: #BA2121">&quot;ols_sk&quot;</span>: np<span style="color: #666666">.</span>zeros(lambdas<span style="color: #666666">.</span>size),
@@ -1523,7 +1430,7 @@ much. Ridge is more stable over a larger range of values for
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="finding-the-optimal-value-of-lambda">Finding the optimal value of \( \lambda \) </h2>
+<h2 id="___sec22">Finding the optimal value of \( \lambda \) </h2>
 
 <p>
 To determine which value of \( \lambda \) is best we plot the accuracy of
@@ -1536,7 +1443,7 @@ testing set that is close to the accuracy of the training set.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">20</span>, <span style="color: #666666">14</span>))
 
 colors <span style="color: #666666">=</span> {
     <span style="color: #BA2121">&quot;ols_sk&quot;</span>: <span style="color: #BA2121">&quot;r&quot;</span>,
@@ -1575,7 +1482,7 @@ other models for all values of \( \lambda \).
 <p>
 <!-- !split  -->
 
-<h2 id="logistic-regression">Logistic Regression </h2>
+<h2 id="___sec23">Logistic Regression </h2>
 
 <p>
 In linear regression our main interest was centered on learning the
@@ -1593,7 +1500,7 @@ simple recipe for fitting our data.
 <p>
 <!-- !split  -->
 
-<h2 id="classification-problems">Classification problems </h2>
+<h2 id="___sec24">Classification problems </h2>
 
 <p>
 Classification problems, however, are concerned with outcomes taking
@@ -1616,7 +1523,7 @@ failure etc.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="optimization-and-deep-learning">Optimization and Deep learning </h2>
+<h2 id="___sec25">Optimization and Deep learning </h2>
 
 <p>
 Logistic regression will also serve as our stepping stone towards
@@ -1637,7 +1544,7 @@ models, as we will see later.
 <p>
 <!-- !split  -->
 
-<h2 id="basics">Basics </h2>
+<h2 id="___sec26">Basics </h2>
 
 <p>
 We consider the case where the dependent variables, also called the
@@ -1664,7 +1571,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="linear-classifier">Linear classifier </h2>
+<h2 id="___sec27">Linear classifier </h2>
 
 <p>
 Before moving to the logistic model, let us try to use our linear
@@ -1688,7 +1595,7 @@ where \( \boldsymbol{y} \) is a vector representing the possible outcomes, \( \b
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="some-selected-properties">Some selected properties </h2>
+<h2 id="___sec28">Some selected properties </h2>
 
 <p>
 The main problem with our function is that it takes values on the
@@ -1710,7 +1617,7 @@ the probability of a given category. This leads us to the logistic function.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="simple-example">Simple example </h2>
+<h2 id="___sec29">Simple example </h2>
 
 <p>
 The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput  is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful.
@@ -1718,7 +1625,7 @@ The following example on data for coronary heart disease (CHD) as function of ag
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #408080; font-style: italic"># Common imports</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># Common imports</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">os</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
@@ -1776,7 +1683,7 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="plotting-the-mean-value-for-each-group">Plotting the mean value for each group </h2>
+<h2 id="___sec30">Plotting the mean value for each group </h2>
 
 <p>
 What we could attempt however is to plot the mean value for each group.
@@ -1784,7 +1691,7 @@ What we could attempt however is to plot the mean value for each group.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>agegroupmean <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">0.1</span>, <span style="color: #666666">0.133</span>, <span style="color: #666666">0.250</span>, <span style="color: #666666">0.333</span>, <span style="color: #666666">0.462</span>, <span style="color: #666666">0.625</span>, <span style="color: #666666">0.765</span>, <span style="color: #666666">0.800</span>])
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>agegroupmean <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">0.1</span>, <span style="color: #666666">0.133</span>, <span style="color: #666666">0.250</span>, <span style="color: #666666">0.333</span>, <span style="color: #666666">0.462</span>, <span style="color: #666666">0.625</span>, <span style="color: #666666">0.765</span>, <span style="color: #666666">0.800</span>])
 group <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">1</span>, <span style="color: #666666">2</span>, <span style="color: #666666">3</span>, <span style="color: #666666">4</span>, <span style="color: #666666">5</span>, <span style="color: #666666">6</span>, <span style="color: #666666">7</span>, <span style="color: #666666">8</span>])
 plt<span style="color: #666666">.</span>plot(group, agegroupmean, <span style="color: #BA2121">&quot;r-&quot;</span>)
 plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0</span>,<span style="color: #666666">9</span>,<span style="color: #666666">0</span>, <span style="color: #666666">1.0</span>])
@@ -1815,7 +1722,7 @@ representing the probability for finding a value of \( y_i \) with a given
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-logistic-function">The logistic function </h2>
+<h2 id="___sec31">The logistic function </h2>
 
 <p>
 Another widely studied model, is the so-called 
@@ -1838,7 +1745,7 @@ Note that \( 1-p(t)= p(-t) \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks">Examples of likelihood functions used in logistic regression and nueral networks </h2>
+<h2 id="___sec32">Examples of likelihood functions used in logistic regression and nueral networks </h2>
 
 <p>
 The following code plots the logistic function, the step function and other functions we will encounter from here and on.
@@ -1846,7 +1753,7 @@ The following code plots the logistic function, the step function and other func
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;The sigmoid function (or the logistic curve) is a</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;The sigmoid function (or the logistic curve) is a</span>
 <span style="color: #BA2121; font-style: italic">function that takes any real number, z, and outputs a number (0,1).</span>
 <span style="color: #BA2121; font-style: italic">It is useful in neural networks for assigning weights on a relative scale.</span>
 <span style="color: #BA2121; font-style: italic">The value z is the weighted sum of parameters involved in the learning algorithm.&quot;&quot;&quot;</span>
@@ -1904,7 +1811,7 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="two-parameters">Two parameters </h2>
+<h2 id="___sec33">Two parameters </h2>
 
 <p>
 We assume now that we have two classes with \( y_i \) either \( 0 \) or \( 1 \). Furthermore we assume also that we have only two parameters \( \beta \) in our fitting of the Sigmoid function, that is we define probabilities 
@@ -1926,7 +1833,7 @@ $$
 <p>
 <!-- !split  -->
 
-<h2 id="maximum-likelihood">Maximum likelihood </h2>
+<h2 id="___sec34">Maximum likelihood </h2>
 
 <p>
 In order to define the total likelihood for all possible outcomes from a  
@@ -1949,7 +1856,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-cost-function-rewritten">The cost function rewritten </h2>
+<h2 id="___sec35">The cost function rewritten </h2>
 
 <p>
 Reordering the logarithms, we can rewrite the <b>cost/loss</b> function as
@@ -1970,7 +1877,7 @@ in practice we often supplement the cross-entropy with additional regularization
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="minimizing-the-cross-entropy">Minimizing the cross entropy </h2>
+<h2 id="___sec36">Minimizing the cross entropy </h2>
 
 <p>
 The cross entropy is a convex function of the weights \( \boldsymbol{\beta} \) and,
@@ -1992,7 +1899,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="a-more-compact-expression">A more compact expression </h2>
+<h2 id="___sec37">A more compact expression </h2>
 
 <p>
 Let us now define a vector \( \boldsymbol{y} \) with \( n \) elements \( y_i \), an
@@ -2015,7 +1922,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="extending-to-more-predictors">Extending to more predictors </h2>
+<h2 id="___sec38">Extending to more predictors </h2>
 
 <p>
 Within a binary classification problem, we can easily expand our model to include multiple predictors. Our ratio between likelihoods is then with \( p \) predictors
@@ -2031,7 +1938,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="including-more-classes">Including more classes </h2>
+<h2 id="___sec39">Including more classes </h2>
 
 <p>
 Till now we have mainly focused on two classes, the so-called binary
@@ -2059,7 +1966,7 @@ and the model is specified in term of \( K-1 \) so-called log-odds or
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="more-classes">More classes </h2>
+<h2 id="___sec40">More classes </h2>
 
 <p>
 In our discussion of neural networks we will encounter the above again
@@ -2099,12 +2006,12 @@ methods</a>.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="friday-september-24">Friday September 24 </h2>
+<h2 id="___sec41">Friday September 24 </h2>
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="wisconsin-cancer-data">Wisconsin Cancer Data  </h2>
+<h2 id="___sec42">Wisconsin Cancer Data  </h2>
 
 <p>
 We show here how we can use a simple regression case on the breast
@@ -2114,7 +2021,7 @@ classification.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span>  train_test_split 
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_breast_cancer
@@ -2143,7 +2050,7 @@ logreg<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="using-the-correlation-matrix">Using the correlation matrix </h2>
+<h2 id="___sec43">Using the correlation matrix </h2>
 
 <p>
 In addition to the above scores, we could also study the covariance (and the correlation matrix).
@@ -2151,7 +2058,7 @@ We use <b>Pandas</b> to compute the correlation matrix.
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span>  train_test_split 
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_breast_cancer
@@ -2189,7 +2096,7 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="discussing-the-correlation-data">Discussing the correlation data </h2>
+<h2 id="___sec44">Discussing the correlation data </h2>
 
 <p>
 In the above example we note two things. In the first plot we display
@@ -2210,14 +2117,14 @@ We constructed this matrix using <b>pandas</b> via the statements
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>cancerpd <span style="color: #666666">=</span> pd<span style="color: #666666">.</span>DataFrame(cancer<span style="color: #666666">.</span>data, columns<span style="color: #666666">=</span>cancer<span style="color: #666666">.</span>feature_names)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>cancerpd <span style="color: #666666">=</span> pd<span style="color: #666666">.</span>DataFrame(cancer<span style="color: #666666">.</span>data, columns<span style="color: #666666">=</span>cancer<span style="color: #666666">.</span>feature_names)
 </pre></div>
 <p>
 and then
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>correlation_matrix <span style="color: #666666">=</span> cancerpd<span style="color: #666666">.</span>corr()<span style="color: #666666">.</span>round(<span style="color: #666666">1</span>)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>correlation_matrix <span style="color: #666666">=</span> cancerpd<span style="color: #666666">.</span>corr()<span style="color: #666666">.</span>round(<span style="color: #666666">1</span>)
 </pre></div>
 <p>
 Diagonalizing this matrix we can in turn say something about which
@@ -2228,11 +2135,11 @@ applications. This will be discussed later this semester (<a href="https://compp
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="other-measures-in-classification-studies-cancer-data-again">Other measures in classification studies: Cancer Data  again </h2>
+<h2 id="___sec45">Other measures in classification studies: Cancer Data  again </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span>  train_test_split 
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_breast_cancer
@@ -2280,7 +2187,7 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm </h2>
+<h2 id="___sec46">Optimization, the central part of any Machine Learning algortithm </h2>
 
 <p>
 <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/OverarchingAimsWeek39.mp4?vrtx=view-as-webpage" target="_blank">Overview Video, why do we care about gradient methods?</a>
@@ -2298,7 +2205,7 @@ some approximative/numerical method to compute the minimum.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="revisiting-our-logistic-regression-case">Revisiting our Logistic Regression case </h2>
+<h2 id="___sec47">Revisiting our Logistic Regression case </h2>
 
 <p>
 In our discussion on Logistic Regression we studied the 
@@ -2320,7 +2227,7 @@ where \( \boldsymbol{\beta} \) are the weights we wish to extract from data, in
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-equations-to-solve">The equations to solve </h2>
+<h2 id="___sec48">The equations to solve </h2>
 
 <p>
 Our compact equations used a definition of a vector \( \boldsymbol{y} \) with \( n \)
@@ -2346,7 +2253,7 @@ This defines what is called  the Hessian matrix.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="solving-using-newton-raphson-s-method">Solving using Newton-Raphson's method </h2>
+<h2 id="___sec49">Solving using Newton-Raphson's method </h2>
 
 <p>
 If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the  matrices that define the first and second derivatives.
@@ -2372,7 +2279,7 @@ If we can compute these matrices, in particular the Hessian, the above is often
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="brief-reminder-on-newton-raphson-s-method">Brief reminder on Newton-Raphson's method </h2>
+<h2 id="___sec50">Brief reminder on Newton-Raphson's method </h2>
 
 <p>
 Let us quickly remind ourselves how we derive the above method.
@@ -2389,7 +2296,7 @@ normally discourage the use of this method.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-equations">The equations </h2>
+<h2 id="___sec51">The equations </h2>
 
 <p>
 The Newton-Raphson formula consists geometrically of extending the
@@ -2425,7 +2332,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="simple-geometric-interpretation">Simple geometric interpretation </h2>
+<h2 id="___sec52">Simple geometric interpretation </h2>
 
 <p>
 The above is Newton-Raphson's method. It has a simple geometric
@@ -2443,7 +2350,7 @@ vanishes, then Newton-Raphson may fail totally
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="extending-to-more-than-one-variable">Extending to more than one variable </h2>
+<h2 id="___sec53">Extending to more than one variable </h2>
 
 <p>
 Newton's method can be generalized to systems of several non-linear equations
@@ -2498,7 +2405,7 @@ more than two non-linear equations. In our case, the Jacobian matrix is given by
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="steepest-descent">Steepest descent </h2>
+<h2 id="___sec54">Steepest descent </h2>
 
 <p>
 The basic idea of gradient descent is
@@ -2522,7 +2429,7 @@ we are always moving towards smaller function values, i.e a minimum.
 <p>
 <!-- !split  -->
 
-<h2 id="more-on-steepest-descent">More on Steepest descent </h2>
+<h2 id="___sec55">More on Steepest descent </h2>
 
 <p>
 The previous observation is the basis of the method of steepest
@@ -2541,7 +2448,7 @@ the learning rate within the context of Machine Learning.
 <p>
 <!-- !split  -->
 
-<h2 id="the-ideal">The ideal </h2>
+<h2 id="___sec56">The ideal </h2>
 
 <p>
 Ideally the sequence \( \{\mathbf{x}_k \}_{k=0} \) converges to a global
@@ -2567,7 +2474,7 @@ Note that the gradient is a function of \( \mathbf{x} =
 <p>
 <!-- !split  -->
 
-<h2 id="the-sensitiveness-of-the-gradient-descent">The sensitiveness of the gradient descent </h2>
+<h2 id="___sec57">The sensitiveness of the gradient descent </h2>
 
 <p>
 The gradient descent method 
@@ -2586,7 +2493,7 @@ randomness. One such method is that of Stochastic Gradient Descent
 <p>
 <!-- !split  -->
 
-<h2 id="convex-functions">Convex functions </h2>
+<h2 id="___sec58">Convex functions </h2>
 
 <p>
 Ideally we want our cost/loss function to be convex(concave).
@@ -2606,7 +2513,7 @@ regular polygons (triangles, rectangles, pentagons, etc...).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="convex-function">Convex function </h2>
+<h2 id="___sec59">Convex function </h2>
 
 <p>
 <b>Convex function</b>: Let \( X \subset \mathbb{R}^n \) be a convex set. Assume that the function \( f: X \rightarrow \mathbb{R} \) is continuous, then \( f \) is said to be convex if $$f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) $$ for all \( x_1, x_2 \in X \) and for all \( t \in [0,1] \). If \( \leq \) is replaced with a strict inequaltiy in the definition, we demand \( x_1 \neq x_2 \) and \( t\in(0,1) \) then \( f \) is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting \( f(x_1) \) and \( f(x_2) \), the value of the function on the interval \( [x_1,x_2] \) is always below the line as illustrated below.
@@ -2614,7 +2521,7 @@ regular polygons (triangles, rectangles, pentagons, etc...).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conditions-on-convex-functions">Conditions on convex functions </h2>
+<h2 id="___sec60">Conditions on convex functions </h2>
 
 <p>
 In the following we state first and second-order conditions which
@@ -2624,7 +2531,7 @@ details and proofs we refer to: <a href="http://stanford.edu/boyd/cvxbook/, 2004
 
 <p>
 <div class="alert alert-block alert-block alert-text-normal">
-<b>First order condition</b>
+<b>First order condition.</b>
 <p>
 Suppose \( f \) is differentiable (i.e \( \nabla f(x) \) is well defined for
 all \( x \) in the domain of \( f \)). Then \( f \) is convex if and only if \( D_f \)
@@ -2639,7 +2546,7 @@ note that it is always below the graph.
 
 <p>
 <div class="alert alert-block alert-block alert-text-normal">
-<b>Second order condition</b>
+<b>Second order condition.</b>
 <p>
 Assume that \( f \) is twice
 differentiable, i.e the Hessian matrix exists at each point in
@@ -2656,7 +2563,7 @@ This condition is particularly useful since it gives us an procedure for determi
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="more-on-convex-functions">More on convex functions </h2>
+<h2 id="___sec61">More on convex functions </h2>
 
 <p>
 The next result is of great importance to us and the reason why we are
@@ -2672,7 +2579,7 @@ is convex the following result provides invaluable information:
 
 <p>
 <div class="alert alert-block alert-block alert-text-normal">
-<b>Any minimum is global for convex functions</b>
+<b>Any minimum is global for convex functions.</b>
 <p>
 Consider the problem of finding \( x \in \mathbb{R}^n \) such that \( f(x) \)
 is minimal, where \( f \) is convex and differentiable. Then, any point
@@ -2686,7 +2593,7 @@ This result means that if we know that the cost/loss function is convex and we a
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="some-simple-problems">Some simple problems </h2>
+<h2 id="___sec62">Some simple problems </h2>
 
 <ol>
 <li> Show that \( f(x)=x^2 \) is convex for \( x \in \mathbb{R} \) using the definition of convexity. Hint: If you re-write the definition, \( f \) is convex if the following holds for all \( x,y \in D_f \) and any \( \lambda \in [0,1] \) $\lambda f(x)+(1-\lambda)f(y)-f(\lambda x + (1-\lambda) y ) \geq 0$.</li>
@@ -2713,7 +2620,7 @@ Using the definition of convexity, try to show that a function satisfying the pr
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="friday-september-25">Friday September 25 </h2>
+<h2 id="___sec63">Friday September 25 </h2>
 
 <p>
 <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureSeptember25.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture</a> and <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesSeptember25.pdf" target="_blank">link to handwritten notes</a>.
@@ -2721,7 +2628,7 @@ Using the definition of convexity, try to show that a function satisfying the pr
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="standard-steepest-descent">Standard steepest descent </h2>
+<h2 id="___sec64">Standard steepest descent </h2>
 
 <p>
 Before we proceed, we would like to discuss the approach called the
@@ -2757,7 +2664,7 @@ When we have found the exact solution, \( \boldsymbol{r}=0 \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="gradient-method">Gradient method </h2>
+<h2 id="___sec65">Gradient method </h2>
 
 <p>
 The residual is zero when we reach the minimum of the quadratic equation
@@ -2774,7 +2681,7 @@ symmetric.  This defines also the Hessian and we want it to be  positive definit
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="steepest-descent-method">Steepest descent  method </h2>
+<h2 id="___sec66">Steepest descent  method </h2>
 
 <p>
 We denote the initial guess for \( \boldsymbol{x} \) as \( \boldsymbol{x}_0 \). 
@@ -2797,7 +2704,7 @@ instead.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="steepest-descent-method">Steepest descent  method </h2>
+<h2 id="___sec67">Steepest descent  method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2827,7 +2734,7 @@ and
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="final-expressions">Final expressions </h2>
+<h2 id="___sec68">Final expressions </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2870,12 +2777,12 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="steepest-descent-example">Steepest descent example </h2>
+<h2 id="___sec69">Steepest descent example </h2>
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy.linalg</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">la</span>
 
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scipy.optimize</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sopt</span>
@@ -2901,7 +2808,7 @@ And then as countor plot
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>pt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">&quot;equal&quot;</span>)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">&quot;equal&quot;</span>)
 pt<span style="color: #666666">.</span>contour(xmesh, ymesh, fmesh)
 guesses <span style="color: #666666">=</span> [np<span style="color: #666666">.</span>array([<span style="color: #666666">2</span>, <span style="color: #666666">2./5</span>])]
 </pre></div>
@@ -2910,7 +2817,7 @@ Find guesses
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>x <span style="color: #666666">=</span> guesses[<span style="color: #666666">-1</span>]
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>x <span style="color: #666666">=</span> guesses[<span style="color: #666666">-1</span>]
 s <span style="color: #666666">=</span> <span style="color: #666666">-</span>df(x)
 </pre></div>
 <p>
@@ -2918,7 +2825,7 @@ Run it!
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f1d</span>(alpha):
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f1d</span>(alpha):
     <span style="color: #008000; font-weight: bold">return</span> f(x <span style="color: #666666">+</span> alpha<span style="color: #666666">*</span>s)
 
 alpha_opt <span style="color: #666666">=</span> sopt<span style="color: #666666">.</span>golden(f1d)
@@ -2931,7 +2838,7 @@ What happened?
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>pt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">&quot;equal&quot;</span>)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">&quot;equal&quot;</span>)
 pt<span style="color: #666666">.</span>contour(xmesh, ymesh, fmesh, <span style="color: #666666">50</span>)
 it_array <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array(guesses)
 pt<span style="color: #666666">.</span>plot(it_array<span style="color: #666666">.</span>T[<span style="color: #666666">0</span>], it_array<span style="color: #666666">.</span>T[<span style="color: #666666">1</span>], <span style="color: #BA2121">&quot;x-&quot;</span>)
@@ -2939,7 +2846,7 @@ pt<span style="color: #666666">.</span>plot(it_array<span style="color: #666666"
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec70">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2969,7 +2876,7 @@ this inner product. Being conjugate is a symmetric relation: if \( \boldsymbol{s
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec71">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2987,7 +2894,7 @@ which is zero unless \( i=j \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec72">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3014,7 +2921,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec73">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3046,7 +2953,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method-and-iterations">Conjugate gradient method and iterations </h2>
+<h2 id="___sec74">Conjugate gradient method and iterations </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3082,7 +2989,7 @@ instead.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec75">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3112,7 +3019,7 @@ hence the name conjugate gradient method.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec76">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3141,7 +3048,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
+<h2 id="___sec77">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3179,7 +3086,7 @@ $$
 <p>
 <!-- !split  -->
 
-<h2 id="revisiting-some-of-our-first-linear-regression-encounters">Revisiting some of our first Linear Regression Encounters  </h2>
+<h2 id="___sec78">Revisiting some of our first Linear Regression Encounters  </h2>
 
 <p>
 We will use linear regression as a case study for the gradient descent
@@ -3198,7 +3105,7 @@ We revisit an example similar to what we had in the first homework set. We had a
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(m,<span style="color: #666666">1</span>)
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(m,<span style="color: #666666">1</span>)
 y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(m,<span style="color: #666666">1</span>)
 </pre></div>
 <p>
@@ -3216,7 +3123,7 @@ $$
 <p>
 <!-- !split  -->
 
-<h2 id="gradient-descent-example">Gradient descent example </h2>
+<h2 id="___sec79">Gradient descent example </h2>
 
 <p>
 Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\boldsymbol{y}} = (\boldsymbol{y}_1,\cdots,\boldsymbol{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
@@ -3241,7 +3148,7 @@ and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-derivative-of-the-cost-loss-function">The derivative of the cost/loss function </h2>
+<h2 id="___sec80">The derivative of the cost/loss function </h2>
 
 <p>
 Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show  that the gradient can be written as
@@ -3256,7 +3163,7 @@ where \( X \) is the design matrix defined above.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="the-hessian-matrix">The Hessian matrix </h2>
+<h2 id="___sec81">The Hessian matrix </h2>
 The Hessian matrix of \( C(\beta) \) is given by 
 $$
 \boldsymbol{H} \equiv \begin{bmatrix}
@@ -3270,7 +3177,7 @@ This result implies that \( C(\beta) \) is a convex function since the matrix \(
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="simple-program">Simple program </h2>
+<h2 id="___sec82">Simple program </h2>
 
 <p>
 We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to 
@@ -3290,14 +3197,14 @@ And finally we can compare our solution for \( \beta \) with the analytic result
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="gradient-descent-example">Gradient Descent Example </h2>
+<h2 id="___sec83">Gradient Descent Example </h2>
 
 <p>
 Here our simple example
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #408080; font-style: italic"># Importing various packages</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># Importing various packages</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">random</span> <span style="color: #008000; font-weight: bold">import</span> random, seed
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
@@ -3346,12 +3253,12 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="and-a-corresponding-example-using-_scikit-learn_">And a corresponding example using <b>scikit-learn</b> </h2>
+<h2 id="___sec84">And a corresponding example using <b>scikit-learn</b> </h2>
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #408080; font-style: italic"># Importing various packages</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># Importing various packages</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">random</span> <span style="color: #008000; font-weight: bold">import</span> random, seed
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
@@ -3371,7 +3278,7 @@ sgdreg<span style="color: #666666">.</span>fit(x,y<span style="color: #666666">.
 <p>
 <!-- !split  -->
 
-<h2 id="gradient-descent-and-ridge">Gradient descent and Ridge </h2>
+<h2 id="___sec85">Gradient descent and Ridge </h2>
 
 <p>
 We have also discussed Ridge regression where the loss function contains a regularized term given by the \( L_2 \) norm of \( \beta \), 
@@ -3396,11 +3303,11 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="program-example-for-gradient-descent-with-ridge-regression">Program example for gradient descent with Ridge Regression </h2>
+<h2 id="___sec86">Program example for gradient descent with Ridge Regression </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">random</span> <span style="color: #008000; font-weight: bold">import</span> random, seed
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">random</span> <span style="color: #008000; font-weight: bold">import</span> random, seed
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">mpl_toolkits.mplot3d</span> <span style="color: #008000; font-weight: bold">import</span> Axes3D
@@ -3447,7 +3354,7 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="using-gradient-descent-methods-limitations">Using gradient descent methods, limitations </h2>
+<h2 id="___sec87">Using gradient descent methods, limitations </h2>
 
 <ul>
 <li> <b>Gradient descent (GD) finds local minima of our function</b>. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our cost/loss/risk function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.</li>
diff --git a/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz b/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz
index d8c28c5c9..7501e019b 100644
Binary files a/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz and b/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz differ
diff --git a/doc/pub/week38/ipynb/week38.ipynb b/doc/pub/week38/ipynb/week38.ipynb
index 99ebbf473..e07012486 100644
--- a/doc/pub/week38/ipynb/week38.ipynb
+++ b/doc/pub/week38/ipynb/week38.ipynb
@@ -249,10 +249,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -371,7 +370,7 @@
     "when all predictors are zero (the columns in the design matrix), it\n",
     "may be a bad idea to implement a model which penalizes the intercept.\n",
     "Furthermore, in for example Ridge and Lasso regression, the solutions\n",
-    "(when not shrinking $$\\beta_0$$) for the unknown parameters\n",
+    "(when not shrinking $\\beta_0$) for the unknown parameters\n",
     "$\\boldsymbol{\\beta}$ are derived under the assumption that both $\\boldsymbol{y}$ and\n",
     "$\\boldsymbol{X}$ are zero centered, that is we subtract the mean values.\n",
     "\n",
@@ -413,10 +412,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -447,10 +445,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -605,10 +602,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -715,10 +711,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 5,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -804,10 +799,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -938,10 +932,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1054,10 +1047,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 8,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1121,10 +1113,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 9,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1140,10 +1131,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 10,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1228,10 +1218,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 11,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1242,10 +1231,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 12,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1261,10 +1249,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 13,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1280,10 +1267,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 14,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1349,10 +1335,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 15,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1458,10 +1443,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 16,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1491,10 +1475,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 17,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1510,10 +1493,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 18,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1529,10 +1511,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 19,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1587,10 +1568,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 20,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1641,10 +1621,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1678,10 +1657,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 22,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1744,10 +1722,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 23,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -1938,10 +1915,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 24,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -2012,10 +1988,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 25,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -2099,10 +2074,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 26,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -2521,10 +2495,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 27,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -2567,10 +2540,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 28,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -2633,10 +2605,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 29,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -2652,10 +2623,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 30,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -2678,10 +2648,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 31,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -3498,10 +3467,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 32,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -3536,10 +3504,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 33,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -3557,10 +3524,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 34,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -3577,10 +3543,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 35,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -3602,10 +3567,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 36,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -3981,10 +3945,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 37,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -4151,10 +4114,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 38,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -4215,10 +4177,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 39,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -4302,10 +4263,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 40,
    "metadata": {
-    "collapsed": false,
-    "editable": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
diff --git a/doc/src/week38/week38.do.txt b/doc/src/week38/week38.do.txt
index 4fd68da1f..7b27400ca 100644
--- a/doc/src/week38/week38.do.txt
+++ b/doc/src/week38/week38.do.txt
@@ -259,7 +259,7 @@ Thus, if we cannot assume that the expected outputs/targets are zero
 when all predictors are zero (the columns in the design matrix), it
 may be a bad idea to implement a model which penalizes the intercept.
 Furthermore, in for example Ridge and Lasso regression, the solutions
-(when not shrinking $$\beta_0$$) for the unknown parameters
+(when not shrinking $\beta_0$) for the unknown parameters
 $\bm{\beta}$ are derived under the assumption that both $\bm{y}$ and
 $\bm{X}$ are zero centered, that is we subtract the mean values.