wrong dates in week 38
This commit is contained in:
Morten Hjorth-Jensen
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
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2,
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None,
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'plans-for-the-lab-sessions'),
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('Material for lecture Thursday September 21',
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('Material for lecture Monday September 16',
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2,
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None,
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'material-for-lecture-thursday-september-21'),
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'material-for-lecture-monday-september-16'),
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('Logistic Regression', 2, None, 'logistic-regression'),
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('Classification problems', 2, None, 'classification-problems'),
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('Optimization and Deep learning',
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@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
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'extending-to-more-predictors'),
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('Including more classes', 2, None, 'including-more-classes'),
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('More classes', 2, None, 'more-classes'),
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('Friday September 23', 2, None, 'friday-september-23'),
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('Searching for Optimal Regularization Parameters $\\lambda$',
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2,
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None,
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@@ -249,7 +248,7 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
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@@ -268,48 +267,47 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs031.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>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#and-a-corresponding-example-using-scikit-learn" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
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</ul>
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</li>
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@@ -364,7 +362,7 @@ MathJax.Hub.Config({
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<li><a href="._week38-bs008.html">9</a></li>
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<li><a href="._week38-bs009.html">10</a></li>
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<li><a href="">...</a></li>
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<li><a href="._week38-bs064.html">65</a></li>
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<li><a href="._week38-bs063.html">64</a></li>
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<li><a href="._week38-bs001.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -352,7 +350,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week38-bs009.html">10</a></li>
|
||||
<li><a href="._week38-bs010.html">11</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs002.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -357,7 +355,7 @@ MathJax.Hub.Config({
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||||
<li><a href="._week38-bs010.html">11</a></li>
|
||||
<li><a href="._week38-bs011.html">12</a></li>
|
||||
<li><a href="">...</a></li>
|
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<li><a href="._week38-bs064.html">65</a></li>
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<li><a href="._week38-bs063.html">64</a></li>
|
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<li><a href="._week38-bs003.html">»</a></li>
|
||||
</ul>
|
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<!-- ------------------- end of main content --------------- -->
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@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -354,7 +352,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week38-bs011.html">12</a></li>
|
||||
<li><a href="._week38-bs012.html">13</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs004.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
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|
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@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,7 +319,7 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0004"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="material-for-lecture-thursday-september-21" class="anchor">Material for lecture Thursday September 21 </h2>
|
||||
<h2 id="material-for-lecture-monday-september-16" class="anchor">Material for lecture Monday September 16 </h2>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -342,7 +340,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week38-bs012.html">13</a></li>
|
||||
<li><a href="._week38-bs013.html">14</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs005.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -356,7 +354,7 @@ simple recipe for fitting our data.
|
||||
<li><a href="._week38-bs013.html">14</a></li>
|
||||
<li><a href="._week38-bs014.html">15</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs006.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.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-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -362,7 +360,7 @@ failure etc.
|
||||
<li><a href="._week38-bs014.html">15</a></li>
|
||||
<li><a href="._week38-bs015.html">16</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs007.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.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>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -361,7 +359,7 @@ models, as we will see later.
|
||||
<li><a href="._week38-bs015.html">16</a></li>
|
||||
<li><a href="._week38-bs016.html">17</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
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||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs008.html">»</a></li>
|
||||
</ul>
|
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<!-- ------------------- end of main content --------------- -->
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||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -369,7 +367,7 @@ $$
|
||||
<li><a href="._week38-bs016.html">17</a></li>
|
||||
<li><a href="._week38-bs017.html">18</a></li>
|
||||
<li><a href="">...</a></li>
|
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<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs009.html">»</a></li>
|
||||
</ul>
|
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<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -367,7 +365,7 @@ $$
|
||||
<li><a href="._week38-bs017.html">18</a></li>
|
||||
<li><a href="._week38-bs018.html">19</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs010.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -368,7 +366,7 @@ the probability of a given category. This leads us to the logistic function.
|
||||
<li><a href="._week38-bs018.html">19</a></li>
|
||||
<li><a href="._week38-bs019.html">20</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs011.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -427,7 +425,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week38-bs019.html">20</a></li>
|
||||
<li><a href="._week38-bs020.html">21</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs012.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -399,7 +397,7 @@ representing the probability for finding a value of \( y_i \) with a given
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<li><a href="._week38-bs020.html">21</a></li>
|
||||
<li><a href="._week38-bs021.html">22</a></li>
|
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<li><a href="">...</a></li>
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<li><a href="._week38-bs064.html">65</a></li>
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<li><a href="._week38-bs063.html">64</a></li>
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<li><a href="._week38-bs013.html">»</a></li>
|
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
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2,
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||||
None,
|
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'plans-for-the-lab-sessions'),
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||||
('Material for lecture Thursday September 21',
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('Material for lecture Monday September 16',
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2,
|
||||
None,
|
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'material-for-lecture-thursday-september-21'),
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'material-for-lecture-monday-september-16'),
|
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('Logistic Regression', 2, None, 'logistic-regression'),
|
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('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
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||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
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('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
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None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -366,7 +364,7 @@ $$
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<li><a href="._week38-bs021.html">22</a></li>
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||||
<li><a href="._week38-bs022.html">23</a></li>
|
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<li><a href="">...</a></li>
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<li><a href="._week38-bs064.html">65</a></li>
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<li><a href="._week38-bs063.html">64</a></li>
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<li><a href="._week38-bs014.html">»</a></li>
|
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
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2,
|
||||
None,
|
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'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
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('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
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'material-for-lecture-monday-september-16'),
|
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('Logistic Regression', 2, None, 'logistic-regression'),
|
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('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
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@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
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'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
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('Searching for Optimal Regularization Parameters $\\lambda$',
|
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2,
|
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None,
|
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@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -427,7 +425,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week38-bs022.html">23</a></li>
|
||||
<li><a href="._week38-bs023.html">24</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs015.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -364,7 +362,7 @@ $$
|
||||
<li><a href="._week38-bs023.html">24</a></li>
|
||||
<li><a href="._week38-bs024.html">25</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs016.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -367,7 +365,7 @@ $$
|
||||
<li><a href="._week38-bs024.html">25</a></li>
|
||||
<li><a href="._week38-bs025.html">26</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
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<li><a href="._week38-bs063.html">64</a></li>
|
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<li><a href="._week38-bs017.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -364,7 +362,7 @@ in practice we often supplement the cross-entropy with additional regularization
|
||||
<li><a href="._week38-bs025.html">26</a></li>
|
||||
<li><a href="._week38-bs026.html">27</a></li>
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<li><a href="">...</a></li>
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<li><a href="._week38-bs064.html">65</a></li>
|
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<li><a href="._week38-bs063.html">64</a></li>
|
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<li><a href="._week38-bs018.html">»</a></li>
|
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</ul>
|
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<!-- ------------------- end of main content --------------- -->
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@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
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||||
@@ -366,7 +364,7 @@ $$
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<li><a href="._week38-bs026.html">27</a></li>
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||||
<li><a href="._week38-bs027.html">28</a></li>
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<li><a href="">...</a></li>
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<li><a href="._week38-bs064.html">65</a></li>
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<li><a href="._week38-bs063.html">64</a></li>
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<li><a href="._week38-bs019.html">»</a></li>
|
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
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2,
|
||||
None,
|
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'plans-for-the-lab-sessions'),
|
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('Material for lecture Thursday September 21',
|
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('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
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'material-for-lecture-monday-september-16'),
|
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('Logistic Regression', 2, None, 'logistic-regression'),
|
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('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
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@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
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'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
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('Searching for Optimal Regularization Parameters $\\lambda$',
|
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2,
|
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None,
|
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@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -367,7 +365,7 @@ $$
|
||||
<li><a href="._week38-bs027.html">28</a></li>
|
||||
<li><a href="._week38-bs028.html">29</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs020.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- 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-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -359,7 +357,7 @@ $$
|
||||
<li><a href="._week38-bs028.html">29</a></li>
|
||||
<li><a href="._week38-bs029.html">30</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs021.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.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-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -371,7 +369,7 @@ $$
|
||||
<li><a href="._week38-bs029.html">30</a></li>
|
||||
<li><a href="._week38-bs030.html">31</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs022.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.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-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -383,7 +381,7 @@ methods</a>.
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<li><a href="._week38-bs030.html">31</a></li>
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<li><a href="._week38-bs031.html">32</a></li>
|
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<li><a href="">...</a></li>
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<li><a href="._week38-bs064.html">65</a></li>
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<li><a href="._week38-bs063.html">64</a></li>
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<li><a href="._week38-bs023.html">»</a></li>
|
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</ul>
|
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<!-- ------------------- end of main content --------------- -->
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@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
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None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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="#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,7 +319,86 @@ MathJax.Hub.Config({
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||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
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||||
<a name="part0023"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="friday-september-23" class="anchor">Friday September 23 </h2>
|
||||
<h2 id="searching-for-optimal-regularization-parameters-lambda" class="anchor">Searching for Optimal Regularization Parameters \( \lambda \) </h2>
|
||||
|
||||
<p>In project 1, when using Ridge and Lasso regression, we end up
|
||||
searching for the optimal parameter \( \lambda \) which minimizes our
|
||||
selected scores (MSE or \( R2 \) values for example). The brute force
|
||||
approach, as discussed in the code here for Ridge regression, consists
|
||||
in evaluating the MSE as function of different \( \lambda \) values.
|
||||
Based on these calculations, one tries then to determine the value of the hyperparameter \( \lambda \)
|
||||
which results in optimal scores (for example the smallest MSE or an \( R2=1 \)).
|
||||
</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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||||
<div class="cell border-box-sizing code_cell rendered">
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||||
<div class="input">
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<div class="inner_cell">
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||||
<div class="input_area">
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<div class="highlight" style="background: #f8f8f8">
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<pre style="line-height: 125%;"><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
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> linear_model
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">MSE</span>(y_data,y_model):
|
||||
n <span style="color: #666666">=</span> np<span style="color: #666666">.</span>size(y_model)
|
||||
<span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>sum((y_data<span style="color: #666666">-</span>y_model)<span style="color: #666666">**2</span>)<span style="color: #666666">/</span>n
|
||||
<span style="color: #408080; font-style: italic"># A seed just to ensure that the random numbers are the same for every run.</span>
|
||||
<span style="color: #408080; font-style: italic"># Useful for eventual debugging.</span>
|
||||
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">2021</span>)
|
||||
|
||||
n <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(n)
|
||||
y <span style="color: #666666">=</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>x<span style="color: #666666">**2</span>) <span style="color: #666666">+</span> <span style="color: #666666">1.5</span> <span style="color: #666666">*</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>(x<span style="color: #666666">-2</span>)<span style="color: #666666">**2</span>)<span style="color: #666666">+</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(n)
|
||||
|
||||
Maxpolydegree <span style="color: #666666">=</span> <span style="color: #666666">5</span>
|
||||
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((n,Maxpolydegree<span style="color: #666666">-1</span>))
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>,Maxpolydegree): <span style="color: #408080; font-style: italic">#No intercept column</span>
|
||||
X[:,degree<span style="color: #666666">-1</span>] <span style="color: #666666">=</span> x<span style="color: #666666">**</span>(degree)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># We split the data in test and training data</span>
|
||||
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(X, y, test_size<span style="color: #666666">=0.2</span>)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Decide which values of lambda to use</span>
|
||||
nlambdas <span style="color: #666666">=</span> <span style="color: #666666">500</span>
|
||||
MSERidgePredict <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(nlambdas)
|
||||
lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">2</span>, nlambdas)
|
||||
<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>(nlambdas):
|
||||
lmb <span style="color: #666666">=</span> lambdas[i]
|
||||
RegRidge <span style="color: #666666">=</span> linear_model<span style="color: #666666">.</span>Ridge(lmb)
|
||||
RegRidge<span style="color: #666666">.</span>fit(X_train,y_train)
|
||||
ypredictRidge <span style="color: #666666">=</span> RegRidge<span style="color: #666666">.</span>predict(X_test)
|
||||
MSERidgePredict[i] <span style="color: #666666">=</span> MSE(y_test,ypredictRidge)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Now plot the results</span>
|
||||
plt<span style="color: #666666">.</span>figure()
|
||||
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), MSERidgePredict, <span style="color: #BA2121">'g--'</span>, label <span style="color: #666666">=</span> <span style="color: #BA2121">'MSE SL Ridge Test'</span>)
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">'log10(lambda)'</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">'MSE'</span>)
|
||||
plt<span style="color: #666666">.</span>legend()
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<p>Here we have performed a rather data greedy calculation as function of the regularization parameter \( \lambda \). There is no resampling here. The latter can easily be added by employing the function <b>RidgeCV</b> instead of just calling the <b>Ridge</b> function. For <b>RidgeCV</b> we need to pass the array of \( \lambda \) values.
|
||||
By inspecting the figure we can in turn determine which is the optimal regularization parameter.
|
||||
This becomes however less functional in the long run.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -348,7 +425,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week38-bs031.html">32</a></li>
|
||||
<li><a href="._week38-bs032.html">33</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs024.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,17 +319,14 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0024"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="searching-for-optimal-regularization-parameters-lambda" class="anchor">Searching for Optimal Regularization Parameters \( \lambda \) </h2>
|
||||
<h2 id="grid-search" class="anchor">Grid Search </h2>
|
||||
|
||||
<p>In project 1, when using Ridge and Lasso regression, we end up
|
||||
searching for the optimal parameter \( \lambda \) which minimizes our
|
||||
selected scores (MSE or \( R2 \) values for example). The brute force
|
||||
approach, as discussed in the code here for Ridge regression, consists
|
||||
in evaluating the MSE as function of different \( \lambda \) values.
|
||||
Based on these calculations, one tries then to determine the value of the hyperparameter \( \lambda \)
|
||||
which results in optimal scores (for example the smallest MSE or an \( R2=1 \)).
|
||||
<p>An alternative is to use the so-called grid search functionality
|
||||
included with the library <b>Scikit-Learn</b>, as demonstrated for the same
|
||||
example here.
|
||||
</p>
|
||||
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
@@ -339,14 +334,17 @@ which results in optimal scores (for example the smallest MSE or an \( R2=1 \)).
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;"><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
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> linear_model
|
||||
<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
|
||||
<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> GridSearchCV
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">R2</span>(y_data, y_model):
|
||||
<span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">1</span> <span style="color: #666666">-</span> np<span style="color: #666666">.</span>sum((y_data <span style="color: #666666">-</span> y_model) <span style="color: #666666">**</span> <span style="color: #666666">2</span>) <span style="color: #666666">/</span> np<span style="color: #666666">.</span>sum((y_data <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(y_data)) <span style="color: #666666">**</span> <span style="color: #666666">2</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">MSE</span>(y_data,y_model):
|
||||
n <span style="color: #666666">=</span> np<span style="color: #666666">.</span>size(y_model)
|
||||
<span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>sum((y_data<span style="color: #666666">-</span>y_model)<span style="color: #666666">**2</span>)<span style="color: #666666">/</span>n
|
||||
|
||||
<span style="color: #408080; font-style: italic"># A seed just to ensure that the random numbers are the same for every run.</span>
|
||||
<span style="color: #408080; font-style: italic"># Useful for eventual debugging.</span>
|
||||
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">2021</span>)
|
||||
@@ -365,23 +363,18 @@ X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>z
|
||||
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(X, y, test_size<span style="color: #666666">=0.2</span>)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Decide which values of lambda to use</span>
|
||||
nlambdas <span style="color: #666666">=</span> <span style="color: #666666">500</span>
|
||||
MSERidgePredict <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(nlambdas)
|
||||
nlambdas <span style="color: #666666">=</span> <span style="color: #666666">10</span>
|
||||
lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">2</span>, nlambdas)
|
||||
<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>(nlambdas):
|
||||
lmb <span style="color: #666666">=</span> lambdas[i]
|
||||
RegRidge <span style="color: #666666">=</span> linear_model<span style="color: #666666">.</span>Ridge(lmb)
|
||||
RegRidge<span style="color: #666666">.</span>fit(X_train,y_train)
|
||||
ypredictRidge <span style="color: #666666">=</span> RegRidge<span style="color: #666666">.</span>predict(X_test)
|
||||
MSERidgePredict[i] <span style="color: #666666">=</span> MSE(y_test,ypredictRidge)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Now plot the results</span>
|
||||
plt<span style="color: #666666">.</span>figure()
|
||||
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), MSERidgePredict, <span style="color: #BA2121">'g--'</span>, label <span style="color: #666666">=</span> <span style="color: #BA2121">'MSE SL Ridge Test'</span>)
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">'log10(lambda)'</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">'MSE'</span>)
|
||||
plt<span style="color: #666666">.</span>legend()
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
<span style="color: #408080; font-style: italic"># create and fit a ridge regression model, testing each alpha</span>
|
||||
model <span style="color: #666666">=</span> Ridge()
|
||||
gridsearch <span style="color: #666666">=</span> GridSearchCV(estimator<span style="color: #666666">=</span>model, param_grid<span style="color: #666666">=</span><span style="color: #008000">dict</span>(alpha<span style="color: #666666">=</span>lambdas))
|
||||
gridsearch<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<span style="color: #008000">print</span>(gridsearch)
|
||||
ypredictRidge <span style="color: #666666">=</span> gridsearch<span style="color: #666666">.</span>predict(X_test)
|
||||
<span style="color: #408080; font-style: italic"># summarize the results of the grid search</span>
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">f"Best estimated lambda-value: </span><span style="color: #BB6688; font-weight: bold">{</span>gridsearch<span style="color: #666666">.</span>best_estimator_<span style="color: #666666">.</span>alpha<span style="color: #BB6688; font-weight: bold">}</span><span style="color: #BA2121">"</span>)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">f"MSE score: </span><span style="color: #BB6688; font-weight: bold">{</span>MSE(y_test,ypredictRidge)<span style="color: #BB6688; font-weight: bold">}</span><span style="color: #BA2121">"</span>)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">f"R2 score: </span><span style="color: #BB6688; font-weight: bold">{</span>R2(y_test,ypredictRidge)<span style="color: #BB6688; font-weight: bold">}</span><span style="color: #BA2121">"</span>)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -397,11 +390,14 @@ plt<span style="color: #666666">.</span>show()
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<p>Here we have performed a rather data greedy calculation as function of the regularization parameter \( \lambda \). There is no resampling here. The latter can easily be added by employing the function <b>RidgeCV</b> instead of just calling the <b>Ridge</b> function. For <b>RidgeCV</b> we need to pass the array of \( \lambda \) values.
|
||||
By inspecting the figure we can in turn determine which is the optimal regularization parameter.
|
||||
This becomes however less functional in the long run.
|
||||
<p>By default the grid search function includes cross validation with
|
||||
five folds. The <a href="https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" target="_self">Scikit-Learn
|
||||
documentation</a>
|
||||
contains more information on how to set the different parameters.
|
||||
</p>
|
||||
|
||||
<p>If we take out the random noise, running the above codes results in \( \lambda=0 \) yielding the best fit. </p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -427,7 +423,7 @@ This becomes however less functional in the long run.
|
||||
<li><a href="._week38-bs032.html">33</a></li>
|
||||
<li><a href="._week38-bs033.html">34</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs025.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,11 +319,16 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0025"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="grid-search" class="anchor">Grid Search </h2>
|
||||
<h2 id="randomized-grid-search" class="anchor">Randomized Grid Search </h2>
|
||||
|
||||
<p>An alternative is to use the so-called grid search functionality
|
||||
included with the library <b>Scikit-Learn</b>, as demonstrated for the same
|
||||
example here.
|
||||
<p>An alternative to the above manual grid set up, is to use a random
|
||||
search where the parameters are tuned from a random distribution
|
||||
(uniform below) for a fixed number of iterations. A model is
|
||||
constructed and evaluated for each combination of chosen parameters.
|
||||
We repeat the previous example but now with a random search. Note
|
||||
that values of \( \lambda \) are now limited to be within \( x\in
|
||||
[0,1] \). This domain may not be the most relevant one for the specific
|
||||
case under study.
|
||||
</p>
|
||||
|
||||
|
||||
@@ -339,6 +342,9 @@ example here.
|
||||
<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.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> Ridge
|
||||
<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> GridSearchCV
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">scipy.stats</span> <span style="color: #008000; font-weight: bold">import</span> uniform <span style="color: #008000; font-weight: bold">as</span> randuniform
|
||||
<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> RandomizedSearchCV
|
||||
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">R2</span>(y_data, y_model):
|
||||
<span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">1</span> <span style="color: #666666">-</span> np<span style="color: #666666">.</span>sum((y_data <span style="color: #666666">-</span> y_model) <span style="color: #666666">**</span> <span style="color: #666666">2</span>) <span style="color: #666666">/</span> np<span style="color: #666666">.</span>sum((y_data <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(y_data)) <span style="color: #666666">**</span> <span style="color: #666666">2</span>)
|
||||
@@ -364,12 +370,10 @@ X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>z
|
||||
<span style="color: #408080; font-style: italic"># We split the data in test and training data</span>
|
||||
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(X, y, test_size<span style="color: #666666">=0.2</span>)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Decide which values of lambda to use</span>
|
||||
nlambdas <span style="color: #666666">=</span> <span style="color: #666666">10</span>
|
||||
lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">2</span>, nlambdas)
|
||||
param_grid <span style="color: #666666">=</span> {<span style="color: #BA2121">'alpha'</span>: randuniform()}
|
||||
<span style="color: #408080; font-style: italic"># create and fit a ridge regression model, testing each alpha</span>
|
||||
model <span style="color: #666666">=</span> Ridge()
|
||||
gridsearch <span style="color: #666666">=</span> GridSearchCV(estimator<span style="color: #666666">=</span>model, param_grid<span style="color: #666666">=</span><span style="color: #008000">dict</span>(alpha<span style="color: #666666">=</span>lambdas))
|
||||
gridsearch <span style="color: #666666">=</span> RandomizedSearchCV(estimator<span style="color: #666666">=</span>model, param_distributions<span style="color: #666666">=</span>param_grid, n_iter<span style="color: #666666">=100</span>)
|
||||
gridsearch<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<span style="color: #008000">print</span>(gridsearch)
|
||||
ypredictRidge <span style="color: #666666">=</span> gridsearch<span style="color: #666666">.</span>predict(X_test)
|
||||
@@ -392,13 +396,6 @@ ypredictRidge <span style="color: #666666">=</span> gridsearch<span style="color
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<p>By default the grid search function includes cross validation with
|
||||
five folds. The <a href="https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" target="_self">Scikit-Learn
|
||||
documentation</a>
|
||||
contains more information on how to set the different parameters.
|
||||
</p>
|
||||
|
||||
<p>If we take out the random noise, running the above codes results in \( \lambda=0 \) yielding the best fit. </p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -425,7 +422,7 @@ contains more information on how to set the different parameters.
|
||||
<li><a href="._week38-bs033.html">34</a></li>
|
||||
<li><a href="._week38-bs034.html">35</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs026.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,16 +319,11 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0026"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="randomized-grid-search" class="anchor">Randomized Grid Search </h2>
|
||||
<h2 id="wisconsin-cancer-data" class="anchor">Wisconsin Cancer Data </h2>
|
||||
|
||||
<p>An alternative to the above manual grid set up, is to use a random
|
||||
search where the parameters are tuned from a random distribution
|
||||
(uniform below) for a fixed number of iterations. A model is
|
||||
constructed and evaluated for each combination of chosen parameters.
|
||||
We repeat the previous example but now with a random search. Note
|
||||
that values of \( \lambda \) are now limited to be within \( x\in
|
||||
[0,1] \). This domain may not be the most relevant one for the specific
|
||||
case under study.
|
||||
<p>We show here how we can use a simple regression case on the breast
|
||||
cancer data using Logistic regression as our algorithm for
|
||||
classification.
|
||||
</p>
|
||||
|
||||
|
||||
@@ -340,49 +333,22 @@ case under study.
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;"><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.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> Ridge
|
||||
<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> GridSearchCV
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">scipy.stats</span> <span style="color: #008000; font-weight: bold">import</span> uniform <span style="color: #008000; font-weight: bold">as</span> randuniform
|
||||
<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> RandomizedSearchCV
|
||||
<pre style="line-height: 125%;"><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
|
||||
<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> LogisticRegression
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Load the data</span>
|
||||
cancer <span style="color: #666666">=</span> load_breast_cancer()
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">R2</span>(y_data, y_model):
|
||||
<span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">1</span> <span style="color: #666666">-</span> np<span style="color: #666666">.</span>sum((y_data <span style="color: #666666">-</span> y_model) <span style="color: #666666">**</span> <span style="color: #666666">2</span>) <span style="color: #666666">/</span> np<span style="color: #666666">.</span>sum((y_data <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(y_data)) <span style="color: #666666">**</span> <span style="color: #666666">2</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">MSE</span>(y_data,y_model):
|
||||
n <span style="color: #666666">=</span> np<span style="color: #666666">.</span>size(y_model)
|
||||
<span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>sum((y_data<span style="color: #666666">-</span>y_model)<span style="color: #666666">**2</span>)<span style="color: #666666">/</span>n
|
||||
|
||||
<span style="color: #408080; font-style: italic"># A seed just to ensure that the random numbers are the same for every run.</span>
|
||||
<span style="color: #408080; font-style: italic"># Useful for eventual debugging.</span>
|
||||
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">2021</span>)
|
||||
|
||||
n <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(n)
|
||||
y <span style="color: #666666">=</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>x<span style="color: #666666">**2</span>) <span style="color: #666666">+</span> <span style="color: #666666">1.5</span> <span style="color: #666666">*</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>(x<span style="color: #666666">-2</span>)<span style="color: #666666">**2</span>)<span style="color: #666666">+</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(n)
|
||||
|
||||
Maxpolydegree <span style="color: #666666">=</span> <span style="color: #666666">5</span>
|
||||
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((n,Maxpolydegree<span style="color: #666666">-1</span>))
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>,Maxpolydegree): <span style="color: #408080; font-style: italic">#No intercept column</span>
|
||||
X[:,degree<span style="color: #666666">-1</span>] <span style="color: #666666">=</span> x<span style="color: #666666">**</span>(degree)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># We split the data in test and training data</span>
|
||||
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(X, y, test_size<span style="color: #666666">=0.2</span>)
|
||||
|
||||
param_grid <span style="color: #666666">=</span> {<span style="color: #BA2121">'alpha'</span>: randuniform()}
|
||||
<span style="color: #408080; font-style: italic"># create and fit a ridge regression model, testing each alpha</span>
|
||||
model <span style="color: #666666">=</span> Ridge()
|
||||
gridsearch <span style="color: #666666">=</span> RandomizedSearchCV(estimator<span style="color: #666666">=</span>model, param_distributions<span style="color: #666666">=</span>param_grid, n_iter<span style="color: #666666">=100</span>)
|
||||
gridsearch<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<span style="color: #008000">print</span>(gridsearch)
|
||||
ypredictRidge <span style="color: #666666">=</span> gridsearch<span style="color: #666666">.</span>predict(X_test)
|
||||
<span style="color: #408080; font-style: italic"># summarize the results of the grid search</span>
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">f"Best estimated lambda-value: </span><span style="color: #BB6688; font-weight: bold">{</span>gridsearch<span style="color: #666666">.</span>best_estimator_<span style="color: #666666">.</span>alpha<span style="color: #BB6688; font-weight: bold">}</span><span style="color: #BA2121">"</span>)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">f"MSE score: </span><span style="color: #BB6688; font-weight: bold">{</span>MSE(y_test,ypredictRidge)<span style="color: #BB6688; font-weight: bold">}</span><span style="color: #BA2121">"</span>)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">f"R2 score: </span><span style="color: #BB6688; font-weight: bold">{</span>R2(y_test,ypredictRidge)<span style="color: #BB6688; font-weight: bold">}</span><span style="color: #BA2121">"</span>)
|
||||
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(cancer<span style="color: #666666">.</span>data,cancer<span style="color: #666666">.</span>target,random_state<span style="color: #666666">=0</span>)
|
||||
<span style="color: #008000">print</span>(X_train<span style="color: #666666">.</span>shape)
|
||||
<span style="color: #008000">print</span>(X_test<span style="color: #666666">.</span>shape)
|
||||
<span style="color: #408080; font-style: italic"># Logistic Regression</span>
|
||||
logreg <span style="color: #666666">=</span> LogisticRegression(solver<span style="color: #666666">=</span><span style="color: #BA2121">'lbfgs'</span>)
|
||||
logreg<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"Test set accuracy with Logistic Regression: </span><span style="color: #BB6688; font-weight: bold">{:.2f}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test,y_test)))
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -424,7 +390,7 @@ ypredictRidge <span style="color: #666666">=</span> gridsearch<span style="color
|
||||
<li><a href="._week38-bs034.html">35</a></li>
|
||||
<li><a href="._week38-bs035.html">36</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs027.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,14 +319,12 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0027"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="wisconsin-cancer-data" class="anchor">Wisconsin Cancer Data </h2>
|
||||
<h2 id="using-the-correlation-matrix" class="anchor">Using the correlation matrix </h2>
|
||||
|
||||
<p>We show here how we can use a simple regression case on the breast
|
||||
cancer data using Logistic regression as our algorithm for
|
||||
classification.
|
||||
<p>In addition to the above scores, we could also study the covariance (and the correlation matrix).
|
||||
We use <b>Pandas</b> to compute the correlation matrix.
|
||||
</p>
|
||||
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
@@ -340,17 +336,35 @@ classification.
|
||||
<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
|
||||
<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> LogisticRegression
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Load the data</span>
|
||||
cancer <span style="color: #666666">=</span> load_breast_cancer()
|
||||
<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: #408080; font-style: italic"># Making a data frame</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)
|
||||
|
||||
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(cancer<span style="color: #666666">.</span>data,cancer<span style="color: #666666">.</span>target,random_state<span style="color: #666666">=0</span>)
|
||||
<span style="color: #008000">print</span>(X_train<span style="color: #666666">.</span>shape)
|
||||
<span style="color: #008000">print</span>(X_test<span style="color: #666666">.</span>shape)
|
||||
<span style="color: #408080; font-style: italic"># Logistic Regression</span>
|
||||
logreg <span style="color: #666666">=</span> LogisticRegression(solver<span style="color: #666666">=</span><span style="color: #BA2121">'lbfgs'</span>)
|
||||
logreg<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"Test set accuracy with Logistic Regression: </span><span style="color: #BB6688; font-weight: bold">{:.2f}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test,y_test)))
|
||||
fig, axes <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(<span style="color: #666666">15</span>,<span style="color: #666666">2</span>,figsize<span style="color: #666666">=</span>(<span style="color: #666666">10</span>,<span style="color: #666666">20</span>))
|
||||
malignant <span style="color: #666666">=</span> cancer<span style="color: #666666">.</span>data[cancer<span style="color: #666666">.</span>target <span style="color: #666666">==</span> <span style="color: #666666">0</span>]
|
||||
benign <span style="color: #666666">=</span> cancer<span style="color: #666666">.</span>data[cancer<span style="color: #666666">.</span>target <span style="color: #666666">==</span> <span style="color: #666666">1</span>]
|
||||
ax <span style="color: #666666">=</span> axes<span style="color: #666666">.</span>ravel()
|
||||
|
||||
<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>(<span style="color: #666666">30</span>):
|
||||
_, bins <span style="color: #666666">=</span> np<span style="color: #666666">.</span>histogram(cancer<span style="color: #666666">.</span>data[:,i], bins <span style="color: #666666">=50</span>)
|
||||
ax[i]<span style="color: #666666">.</span>hist(malignant[:,i], bins <span style="color: #666666">=</span> bins, alpha <span style="color: #666666">=</span> <span style="color: #666666">0.5</span>)
|
||||
ax[i]<span style="color: #666666">.</span>hist(benign[:,i], bins <span style="color: #666666">=</span> bins, alpha <span style="color: #666666">=</span> <span style="color: #666666">0.5</span>)
|
||||
ax[i]<span style="color: #666666">.</span>set_title(cancer<span style="color: #666666">.</span>feature_names[i])
|
||||
ax[i]<span style="color: #666666">.</span>set_yticks(())
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"Feature magnitude"</span>)
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"Frequency"</span>)
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>legend([<span style="color: #BA2121">"Malignant"</span>, <span style="color: #BA2121">"Benign"</span>], loc <span style="color: #666666">=</span><span style="color: #BA2121">"best"</span>)
|
||||
fig<span style="color: #666666">.</span>tight_layout()
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
<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>
|
||||
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>)
|
||||
<span style="color: #408080; font-style: italic"># use the heatmap function from seaborn to plot the correlation matrix</span>
|
||||
<span style="color: #408080; font-style: italic"># annot = True to print the values inside the square</span>
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">15</span>,<span style="color: #666666">8</span>))
|
||||
sns<span style="color: #666666">.</span>heatmap(data<span style="color: #666666">=</span>correlation_matrix, annot<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -392,7 +406,7 @@ logreg<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<li><a href="._week38-bs035.html">36</a></li>
|
||||
<li><a href="._week38-bs036.html">37</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs028.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,52 +319,31 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0028"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="using-the-correlation-matrix" class="anchor">Using the correlation matrix </h2>
|
||||
<h2 id="discussing-the-correlation-data" class="anchor">Discussing the correlation data </h2>
|
||||
|
||||
<p>In addition to the above scores, we could also study the covariance (and the correlation matrix).
|
||||
We use <b>Pandas</b> to compute the correlation matrix.
|
||||
<p>In the above example we note two things. In the first plot we display
|
||||
the overlap of benign and malignant tumors as functions of the various
|
||||
features in the Wisconsing breast cancer data set. We see that for
|
||||
some of the features we can distinguish clearly the benign and
|
||||
malignant cases while for other features we cannot. This can point to
|
||||
us which features may be of greater interest when we wish to classify
|
||||
a benign or not benign tumour.
|
||||
</p>
|
||||
|
||||
<p>In the second figure we have computed the so-called correlation
|
||||
matrix, which in our case with thirty features becomes a \( 30\times 30 \)
|
||||
matrix.
|
||||
</p>
|
||||
|
||||
<p>We constructed this matrix using <b>pandas</b> via the statements</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;"><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
|
||||
<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> LogisticRegression
|
||||
cancer <span style="color: #666666">=</span> load_breast_cancer()
|
||||
<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: #408080; font-style: italic"># Making a data frame</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)
|
||||
|
||||
fig, axes <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(<span style="color: #666666">15</span>,<span style="color: #666666">2</span>,figsize<span style="color: #666666">=</span>(<span style="color: #666666">10</span>,<span style="color: #666666">20</span>))
|
||||
malignant <span style="color: #666666">=</span> cancer<span style="color: #666666">.</span>data[cancer<span style="color: #666666">.</span>target <span style="color: #666666">==</span> <span style="color: #666666">0</span>]
|
||||
benign <span style="color: #666666">=</span> cancer<span style="color: #666666">.</span>data[cancer<span style="color: #666666">.</span>target <span style="color: #666666">==</span> <span style="color: #666666">1</span>]
|
||||
ax <span style="color: #666666">=</span> axes<span style="color: #666666">.</span>ravel()
|
||||
|
||||
<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>(<span style="color: #666666">30</span>):
|
||||
_, bins <span style="color: #666666">=</span> np<span style="color: #666666">.</span>histogram(cancer<span style="color: #666666">.</span>data[:,i], bins <span style="color: #666666">=50</span>)
|
||||
ax[i]<span style="color: #666666">.</span>hist(malignant[:,i], bins <span style="color: #666666">=</span> bins, alpha <span style="color: #666666">=</span> <span style="color: #666666">0.5</span>)
|
||||
ax[i]<span style="color: #666666">.</span>hist(benign[:,i], bins <span style="color: #666666">=</span> bins, alpha <span style="color: #666666">=</span> <span style="color: #666666">0.5</span>)
|
||||
ax[i]<span style="color: #666666">.</span>set_title(cancer<span style="color: #666666">.</span>feature_names[i])
|
||||
ax[i]<span style="color: #666666">.</span>set_yticks(())
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"Feature magnitude"</span>)
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"Frequency"</span>)
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>legend([<span style="color: #BA2121">"Malignant"</span>, <span style="color: #BA2121">"Benign"</span>], loc <span style="color: #666666">=</span><span style="color: #BA2121">"best"</span>)
|
||||
fig<span style="color: #666666">.</span>tight_layout()
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
<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>
|
||||
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>)
|
||||
<span style="color: #408080; font-style: italic"># use the heatmap function from seaborn to plot the correlation matrix</span>
|
||||
<span style="color: #408080; font-style: italic"># annot = True to print the values inside the square</span>
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">15</span>,<span style="color: #666666">8</span>))
|
||||
sns<span style="color: #666666">.</span>heatmap(data<span style="color: #666666">=</span>correlation_matrix, annot<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
<pre style="line-height: 125%;">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>
|
||||
</div>
|
||||
@@ -382,6 +359,35 @@ plt<span style="color: #666666">.</span>show()
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<p>and then</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;">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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<p>Diagonalizing this matrix we can in turn say something about which
|
||||
features are of relevance and which are not. This leads us to
|
||||
the classical Principal Component Analysis (PCA) theorem with
|
||||
applications. This will be discussed later this semester (<a href="https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43-bs.html" target="_self">week 43</a>).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -408,7 +414,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week38-bs036.html">37</a></li>
|
||||
<li><a href="._week38-bs037.html">38</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs029.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,23 +319,7 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0029"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="discussing-the-correlation-data" class="anchor">Discussing the correlation data </h2>
|
||||
|
||||
<p>In the above example we note two things. In the first plot we display
|
||||
the overlap of benign and malignant tumors as functions of the various
|
||||
features in the Wisconsing breast cancer data set. We see that for
|
||||
some of the features we can distinguish clearly the benign and
|
||||
malignant cases while for other features we cannot. This can point to
|
||||
us which features may be of greater interest when we wish to classify
|
||||
a benign or not benign tumour.
|
||||
</p>
|
||||
|
||||
<p>In the second figure we have computed the so-called correlation
|
||||
matrix, which in our case with thirty features becomes a \( 30\times 30 \)
|
||||
matrix.
|
||||
</p>
|
||||
|
||||
<p>We constructed this matrix using <b>pandas</b> via the statements</p>
|
||||
<h2 id="other-measures-in-classification-studies-cancer-data-again" class="anchor">Other measures in classification studies: Cancer Data again </h2>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
@@ -345,7 +327,38 @@ matrix.
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;">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 style="line-height: 125%;"><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
|
||||
<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> LogisticRegression
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Load the data</span>
|
||||
cancer <span style="color: #666666">=</span> load_breast_cancer()
|
||||
|
||||
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(cancer<span style="color: #666666">.</span>data,cancer<span style="color: #666666">.</span>target,random_state<span style="color: #666666">=0</span>)
|
||||
<span style="color: #008000">print</span>(X_train<span style="color: #666666">.</span>shape)
|
||||
<span style="color: #008000">print</span>(X_test<span style="color: #666666">.</span>shape)
|
||||
<span style="color: #408080; font-style: italic"># Logistic Regression</span>
|
||||
logreg <span style="color: #666666">=</span> LogisticRegression(solver<span style="color: #666666">=</span><span style="color: #BA2121">'lbfgs'</span>)
|
||||
logreg<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> LabelEncoder
|
||||
<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> cross_validate
|
||||
<span style="color: #408080; font-style: italic">#Cross validation</span>
|
||||
accuracy <span style="color: #666666">=</span> cross_validate(logreg,X_test,y_test,cv<span style="color: #666666">=10</span>)[<span style="color: #BA2121">'test_score'</span>]
|
||||
<span style="color: #008000">print</span>(accuracy)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"Test set accuracy with Logistic Regression: </span><span style="color: #BB6688; font-weight: bold">{:.2f}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test,y_test)))
|
||||
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
|
||||
y_pred <span style="color: #666666">=</span> logreg<span style="color: #666666">.</span>predict(X_test)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_confusion_matrix(y_test, y_pred, normalize<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
y_probas <span style="color: #666666">=</span> logreg<span style="color: #666666">.</span>predict_proba(X_test)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_roc(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_cumulative_gain(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -361,35 +374,6 @@ matrix.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<p>and then</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;">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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<p>Diagonalizing this matrix we can in turn say something about which
|
||||
features are of relevance and which are not. This leads us to
|
||||
the classical Principal Component Analysis (PCA) theorem with
|
||||
applications. This will be discussed later this semester (<a href="https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43-bs.html" target="_self">week 43</a>).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -416,7 +400,7 @@ applications. This will be discussed later this semester (<a href="https://compp
|
||||
<li><a href="._week38-bs037.html">38</a></li>
|
||||
<li><a href="._week38-bs038.html">39</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs030.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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="#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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,61 +319,19 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0030"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="other-measures-in-classification-studies-cancer-data-again" class="anchor">Other measures in classification studies: Cancer Data again </h2>
|
||||
<h2 id="optimization-the-central-part-of-any-machine-learning-algortithm" class="anchor">Optimization, the central part of any Machine Learning algortithm </h2>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;"><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
|
||||
<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> LogisticRegression
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Load the data</span>
|
||||
cancer <span style="color: #666666">=</span> load_breast_cancer()
|
||||
|
||||
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(cancer<span style="color: #666666">.</span>data,cancer<span style="color: #666666">.</span>target,random_state<span style="color: #666666">=0</span>)
|
||||
<span style="color: #008000">print</span>(X_train<span style="color: #666666">.</span>shape)
|
||||
<span style="color: #008000">print</span>(X_test<span style="color: #666666">.</span>shape)
|
||||
<span style="color: #408080; font-style: italic"># Logistic Regression</span>
|
||||
logreg <span style="color: #666666">=</span> LogisticRegression(solver<span style="color: #666666">=</span><span style="color: #BA2121">'lbfgs'</span>)
|
||||
logreg<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> LabelEncoder
|
||||
<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> cross_validate
|
||||
<span style="color: #408080; font-style: italic">#Cross validation</span>
|
||||
accuracy <span style="color: #666666">=</span> cross_validate(logreg,X_test,y_test,cv<span style="color: #666666">=10</span>)[<span style="color: #BA2121">'test_score'</span>]
|
||||
<span style="color: #008000">print</span>(accuracy)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"Test set accuracy with Logistic Regression: </span><span style="color: #BB6688; font-weight: bold">{:.2f}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test,y_test)))
|
||||
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
|
||||
y_pred <span style="color: #666666">=</span> logreg<span style="color: #666666">.</span>predict(X_test)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_confusion_matrix(y_test, y_pred, normalize<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
y_probas <span style="color: #666666">=</span> logreg<span style="color: #666666">.</span>predict_proba(X_test)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_roc(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_cumulative_gain(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/OverarchingAimsWeek39.mp4?vrtx=view-as-webpage" target="_self">Overview Video, why do we care about gradient methods?</a>
|
||||
|
||||
<p>Almost every problem in machine learning and data science starts with
|
||||
a dataset \( X \), a model \( g(\beta) \), which is a function of the
|
||||
parameters \( \beta \) and a cost function \( C(X, g(\beta)) \) that allows
|
||||
us to judge how well the model \( g(\beta) \) explains the observations
|
||||
\( X \). The model is fit by finding the values of \( \beta \) that minimize
|
||||
the cost function. Ideally we would be able to solve for \( \beta \)
|
||||
analytically, however this is not possible in general and we must use
|
||||
some approximative/numerical method to compute the minimum.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -402,7 +358,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week38-bs038.html">39</a></li>
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs031.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
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<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
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<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
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@@ -268,48 +267,47 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
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<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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="#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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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="#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
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</ul>
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</li>
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@@ -321,20 +319,25 @@ MathJax.Hub.Config({
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0031"></a>
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<!-- !split -->
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<h2 id="optimization-the-central-part-of-any-machine-learning-algortithm" class="anchor">Optimization, the central part of any Machine Learning algortithm </h2>
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<h2 id="revisiting-our-logistic-regression-case" class="anchor">Revisiting our Logistic Regression case </h2>
|
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<a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/OverarchingAimsWeek39.mp4?vrtx=view-as-webpage" target="_self">Overview Video, why do we care about gradient methods?</a>
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<p>Almost every problem in machine learning and data science starts with
|
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a dataset \( X \), a model \( g(\beta) \), which is a function of the
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parameters \( \beta \) and a cost function \( C(X, g(\beta)) \) that allows
|
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us to judge how well the model \( g(\beta) \) explains the observations
|
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\( X \). The model is fit by finding the values of \( \beta \) that minimize
|
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the cost function. Ideally we would be able to solve for \( \beta \)
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analytically, however this is not possible in general and we must use
|
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some approximative/numerical method to compute the minimum.
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<p>In our discussion on Logistic Regression we studied the
|
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case of
|
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two classes, with \( y_i \) either
|
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\( 0 \) or \( 1 \). Furthermore we assumed also that we have only two
|
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parameters \( \beta \) in our fitting, that is we
|
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defined probabilities
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</p>
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|
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$$
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||||
\begin{align*}
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p(y_i=1|x_i,\boldsymbol{\beta}) &= \frac{\exp{(\beta_0+\beta_1x_i)}}{1+\exp{(\beta_0+\beta_1x_i)}},\nonumber\\
|
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p(y_i=0|x_i,\boldsymbol{\beta}) &= 1 - p(y_i=1|x_i,\boldsymbol{\beta}),
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||||
\end{align*}
|
||||
$$
|
||||
|
||||
<p>where \( \boldsymbol{\beta} \) are the weights we wish to extract from data, in our case \( \beta_0 \) and \( \beta_1 \). </p>
|
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|
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<p>
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<!-- navigation buttons at the bottom of the page -->
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<ul class="pagination">
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@@ -360,7 +363,7 @@ some approximative/numerical method to compute the minimum.
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<li><a href="._week38-bs039.html">40</a></li>
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<li><a href="._week38-bs040.html">41</a></li>
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<li><a href="">...</a></li>
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<li><a href="._week38-bs064.html">65</a></li>
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<li><a href="._week38-bs063.html">64</a></li>
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<li><a href="._week38-bs032.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
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2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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="#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,24 +319,28 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0032"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="revisiting-our-logistic-regression-case" class="anchor">Revisiting our Logistic Regression case </h2>
|
||||
<h2 id="the-equations-to-solve" class="anchor">The equations to solve </h2>
|
||||
|
||||
<p>In our discussion on Logistic Regression we studied the
|
||||
case of
|
||||
two classes, with \( y_i \) either
|
||||
\( 0 \) or \( 1 \). Furthermore we assumed also that we have only two
|
||||
parameters \( \beta \) in our fitting, that is we
|
||||
defined probabilities
|
||||
<p>Our compact equations used a definition of a vector \( \boldsymbol{y} \) with \( n \)
|
||||
elements \( y_i \), an \( n\times p \) matrix \( \boldsymbol{X} \) which contains the
|
||||
\( x_i \) values and a vector \( \boldsymbol{p} \) of fitted probabilities
|
||||
\( p(y_i\vert x_i,\boldsymbol{\beta}) \). We rewrote in a more compact form
|
||||
the first derivative of the cost function as
|
||||
</p>
|
||||
|
||||
$$
|
||||
\begin{align*}
|
||||
p(y_i=1|x_i,\boldsymbol{\beta}) &= \frac{\exp{(\beta_0+\beta_1x_i)}}{1+\exp{(\beta_0+\beta_1x_i)}},\nonumber\\
|
||||
p(y_i=0|x_i,\boldsymbol{\beta}) &= 1 - p(y_i=1|x_i,\boldsymbol{\beta}),
|
||||
\end{align*}
|
||||
\frac{\partial \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}} = -\boldsymbol{X}^T\left(\boldsymbol{y}-\boldsymbol{p}\right).
|
||||
$$
|
||||
|
||||
<p>where \( \boldsymbol{\beta} \) are the weights we wish to extract from data, in our case \( \beta_0 \) and \( \beta_1 \). </p>
|
||||
<p>If we in addition define a diagonal matrix \( \boldsymbol{W} \) with elements
|
||||
\( p(y_i\vert x_i,\boldsymbol{\beta})(1-p(y_i\vert x_i,\boldsymbol{\beta}) \), we can obtain a compact expression of the second derivative as
|
||||
</p>
|
||||
|
||||
$$
|
||||
\frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T} = \boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X}.
|
||||
$$
|
||||
|
||||
<p>This defines what is called the Hessian matrix.</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -365,7 +367,7 @@ $$
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs033.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,28 +319,25 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0033"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="the-equations-to-solve" class="anchor">The equations to solve </h2>
|
||||
<h2 id="solving-using-newton-raphson-s-method" class="anchor">Solving using Newton-Raphson's method </h2>
|
||||
|
||||
<p>Our compact equations used a definition of a vector \( \boldsymbol{y} \) with \( n \)
|
||||
elements \( y_i \), an \( n\times p \) matrix \( \boldsymbol{X} \) which contains the
|
||||
\( x_i \) values and a vector \( \boldsymbol{p} \) of fitted probabilities
|
||||
\( p(y_i\vert x_i,\boldsymbol{\beta}) \). We rewrote in a more compact form
|
||||
the first derivative of the cost function as
|
||||
</p>
|
||||
<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. </p>
|
||||
|
||||
<p>Our iterative scheme is then given by</p>
|
||||
|
||||
$$
|
||||
\frac{\partial \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}} = -\boldsymbol{X}^T\left(\boldsymbol{y}-\boldsymbol{p}\right).
|
||||
\boldsymbol{\beta}^{\mathrm{new}} = \boldsymbol{\beta}^{\mathrm{old}}-\left(\frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T}\right)^{-1}_{\boldsymbol{\beta}^{\mathrm{old}}}\times \left(\frac{\partial \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}}\right)_{\boldsymbol{\beta}^{\mathrm{old}}},
|
||||
$$
|
||||
|
||||
<p>If we in addition define a diagonal matrix \( \boldsymbol{W} \) with elements
|
||||
\( p(y_i\vert x_i,\boldsymbol{\beta})(1-p(y_i\vert x_i,\boldsymbol{\beta}) \), we can obtain a compact expression of the second derivative as
|
||||
</p>
|
||||
<p>or in matrix form as</p>
|
||||
|
||||
$$
|
||||
\frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T} = \boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X}.
|
||||
\boldsymbol{\beta}^{\mathrm{new}} = \boldsymbol{\beta}^{\mathrm{old}}-\left(\boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X} \right)^{-1}\times \left(-\boldsymbol{X}^T(\boldsymbol{y}-\boldsymbol{p}) \right)_{\boldsymbol{\beta}^{\mathrm{old}}}.
|
||||
$$
|
||||
|
||||
<p>This defines what is called the Hessian matrix.</p>
|
||||
<p>The right-hand side is computed with the old values of \( \beta \). </p>
|
||||
|
||||
<p>If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement. </p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -369,7 +364,7 @@ $$
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs034.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,25 +319,18 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0034"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="solving-using-newton-raphson-s-method" class="anchor">Solving using Newton-Raphson's method </h2>
|
||||
<h2 id="brief-reminder-on-newton-raphson-s-method" class="anchor">Brief reminder on 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. </p>
|
||||
<p>Let us quickly remind ourselves how we derive the above method.</p>
|
||||
|
||||
<p>Our iterative scheme is then given by</p>
|
||||
|
||||
$$
|
||||
\boldsymbol{\beta}^{\mathrm{new}} = \boldsymbol{\beta}^{\mathrm{old}}-\left(\frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T}\right)^{-1}_{\boldsymbol{\beta}^{\mathrm{old}}}\times \left(\frac{\partial \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}}\right)_{\boldsymbol{\beta}^{\mathrm{old}}},
|
||||
$$
|
||||
|
||||
<p>or in matrix form as</p>
|
||||
|
||||
$$
|
||||
\boldsymbol{\beta}^{\mathrm{new}} = \boldsymbol{\beta}^{\mathrm{old}}-\left(\boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X} \right)^{-1}\times \left(-\boldsymbol{X}^T(\boldsymbol{y}-\boldsymbol{p}) \right)_{\boldsymbol{\beta}^{\mathrm{old}}}.
|
||||
$$
|
||||
|
||||
<p>The right-hand side is computed with the old values of \( \beta \). </p>
|
||||
|
||||
<p>If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement. </p>
|
||||
<p>Perhaps the most celebrated of all one-dimensional root-finding
|
||||
routines is Newton's method, also called the Newton-Raphson
|
||||
method. This method requires the evaluation of both the
|
||||
function \( f \) and its derivative \( f' \) at arbitrary points.
|
||||
If you can only calculate the derivative
|
||||
numerically and/or your function is not of the smooth type, we
|
||||
normally discourage the use of this method.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -366,7 +357,7 @@ $$
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs043.html">44</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs035.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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="#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,19 +319,39 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0035"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="brief-reminder-on-newton-raphson-s-method" class="anchor">Brief reminder on Newton-Raphson's method </h2>
|
||||
<h2 id="the-equations" class="anchor">The equations </h2>
|
||||
|
||||
<p>Let us quickly remind ourselves how we derive the above method.</p>
|
||||
|
||||
<p>Perhaps the most celebrated of all one-dimensional root-finding
|
||||
routines is Newton's method, also called the Newton-Raphson
|
||||
method. This method requires the evaluation of both the
|
||||
function \( f \) and its derivative \( f' \) at arbitrary points.
|
||||
If you can only calculate the derivative
|
||||
numerically and/or your function is not of the smooth type, we
|
||||
normally discourage the use of this method.
|
||||
<p>The Newton-Raphson formula consists geometrically of extending the
|
||||
tangent line at a current point until it crosses zero, then setting
|
||||
the next guess to the abscissa of that zero-crossing. The mathematics
|
||||
behind this method is rather simple. Employing a Taylor expansion for
|
||||
\( x \) sufficiently close to the solution \( s \), we have
|
||||
</p>
|
||||
|
||||
$$
|
||||
f(s)=0=f(x)+(s-x)f'(x)+\frac{(s-x)^2}{2}f''(x) +\dots.
|
||||
\tag{2}
|
||||
$$
|
||||
|
||||
<p>For small enough values of the function and for well-behaved
|
||||
functions, the terms beyond linear are unimportant, hence we obtain
|
||||
</p>
|
||||
|
||||
$$
|
||||
f(x)+(s-x)f'(x)\approx 0,
|
||||
$$
|
||||
|
||||
<p>yielding</p>
|
||||
$$
|
||||
s\approx x-\frac{f(x)}{f'(x)}.
|
||||
$$
|
||||
|
||||
<p>Having in mind an iterative procedure, it is natural to start iterating with</p>
|
||||
$$
|
||||
x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}.
|
||||
$$
|
||||
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -359,7 +377,7 @@ normally discourage the use of this method.
|
||||
<li><a href="._week38-bs043.html">44</a></li>
|
||||
<li><a href="._week38-bs044.html">45</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs036.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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="#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,39 +319,21 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0036"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="the-equations" class="anchor">The equations </h2>
|
||||
<h2 id="simple-geometric-interpretation" class="anchor">Simple geometric interpretation </h2>
|
||||
|
||||
<p>The Newton-Raphson formula consists geometrically of extending the
|
||||
tangent line at a current point until it crosses zero, then setting
|
||||
the next guess to the abscissa of that zero-crossing. The mathematics
|
||||
behind this method is rather simple. Employing a Taylor expansion for
|
||||
\( x \) sufficiently close to the solution \( s \), we have
|
||||
<p>The above is Newton-Raphson's method. It has a simple geometric
|
||||
interpretation, namely \( x_{n+1} \) is the point where the tangent from
|
||||
\( (x_n,f(x_n)) \) crosses the \( x \)-axis. Close to the solution,
|
||||
Newton-Raphson converges fast to the desired result. However, if we
|
||||
are far from a root, where the higher-order terms in the series are
|
||||
important, the Newton-Raphson formula can give grossly inaccurate
|
||||
results. For instance, the initial guess for the root might be so far
|
||||
from the true root as to let the search interval include a local
|
||||
maximum or minimum of the function. If an iteration places a trial
|
||||
guess near such a local extremum, so that the first derivative nearly
|
||||
vanishes, then Newton-Raphson may fail totally
|
||||
</p>
|
||||
|
||||
$$
|
||||
f(s)=0=f(x)+(s-x)f'(x)+\frac{(s-x)^2}{2}f''(x) +\dots.
|
||||
\tag{2}
|
||||
$$
|
||||
|
||||
<p>For small enough values of the function and for well-behaved
|
||||
functions, the terms beyond linear are unimportant, hence we obtain
|
||||
</p>
|
||||
|
||||
$$
|
||||
f(x)+(s-x)f'(x)\approx 0,
|
||||
$$
|
||||
|
||||
<p>yielding</p>
|
||||
$$
|
||||
s\approx x-\frac{f(x)}{f'(x)}.
|
||||
$$
|
||||
|
||||
<p>Having in mind an iterative procedure, it is natural to start iterating with</p>
|
||||
$$
|
||||
x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}.
|
||||
$$
|
||||
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -379,7 +359,7 @@ $$
|
||||
<li><a href="._week38-bs044.html">45</a></li>
|
||||
<li><a href="._week38-bs045.html">46</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs037.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,19 +319,57 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0037"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="simple-geometric-interpretation" class="anchor">Simple geometric interpretation </h2>
|
||||
<h2 id="extending-to-more-than-one-variable" class="anchor">Extending to more than one variable </h2>
|
||||
|
||||
<p>The above is Newton-Raphson's method. It has a simple geometric
|
||||
interpretation, namely \( x_{n+1} \) is the point where the tangent from
|
||||
\( (x_n,f(x_n)) \) crosses the \( x \)-axis. Close to the solution,
|
||||
Newton-Raphson converges fast to the desired result. However, if we
|
||||
are far from a root, where the higher-order terms in the series are
|
||||
important, the Newton-Raphson formula can give grossly inaccurate
|
||||
results. For instance, the initial guess for the root might be so far
|
||||
from the true root as to let the search interval include a local
|
||||
maximum or minimum of the function. If an iteration places a trial
|
||||
guess near such a local extremum, so that the first derivative nearly
|
||||
vanishes, then Newton-Raphson may fail totally
|
||||
<p>Newton's method can be generalized to systems of several non-linear equations
|
||||
and variables. Consider the case with two equations
|
||||
</p>
|
||||
$$
|
||||
\begin{array}{cc} f_1(x_1,x_2) &=0\\
|
||||
f_2(x_1,x_2) &=0,\end{array}
|
||||
$$
|
||||
|
||||
<p>which we Taylor expand to obtain</p>
|
||||
|
||||
$$
|
||||
\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1
|
||||
\partial f_1/\partial x_1+h_2
|
||||
\partial f_1/\partial x_2+\dots\\
|
||||
0=f_2(x_1+h_1,x_2+h_2)=&f_2(x_1,x_2)+h_1
|
||||
\partial f_2/\partial x_1+h_2
|
||||
\partial f_2/\partial x_2+\dots
|
||||
\end{array}.
|
||||
$$
|
||||
|
||||
<p>Defining the Jacobian matrix \( {\bf \boldsymbol{J}} \) we have</p>
|
||||
$$
|
||||
{\bf \boldsymbol{J}}=\left( \begin{array}{cc}
|
||||
\partial f_1/\partial x_1 & \partial f_1/\partial x_2 \\
|
||||
\partial f_2/\partial x_1 &\partial f_2/\partial x_2
|
||||
\end{array} \right),
|
||||
$$
|
||||
|
||||
<p>we can rephrase Newton's method as</p>
|
||||
$$
|
||||
\left(\begin{array}{c} x_1^{n+1} \\ x_2^{n+1} \end{array} \right)=
|
||||
\left(\begin{array}{c} x_1^{n} \\ x_2^{n} \end{array} \right)+
|
||||
\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right),
|
||||
$$
|
||||
|
||||
<p>where we have defined</p>
|
||||
$$
|
||||
\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right)=
|
||||
-{\bf \boldsymbol{J}}^{-1}
|
||||
\left(\begin{array}{c} f_1(x_1^{n},x_2^{n}) \\ f_2(x_1^{n},x_2^{n}) \end{array} \right).
|
||||
$$
|
||||
|
||||
<p>We need thus to compute the inverse of the Jacobian matrix and it
|
||||
is to understand that difficulties may
|
||||
arise in case \( {\bf \boldsymbol{J}} \) is nearly singular.
|
||||
</p>
|
||||
|
||||
<p>It is rather straightforward to extend the above scheme to systems of
|
||||
more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -361,7 +397,7 @@ vanishes, then Newton-Raphson may fail totally
|
||||
<li><a href="._week38-bs045.html">46</a></li>
|
||||
<li><a href="._week38-bs046.html">47</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs038.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,57 +319,24 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0038"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="extending-to-more-than-one-variable" class="anchor">Extending to more than one variable </h2>
|
||||
<h2 id="steepest-descent" class="anchor">Steepest descent </h2>
|
||||
|
||||
<p>Newton's method can be generalized to systems of several non-linear equations
|
||||
and variables. Consider the case with two equations
|
||||
</p>
|
||||
$$
|
||||
\begin{array}{cc} f_1(x_1,x_2) &=0\\
|
||||
f_2(x_1,x_2) &=0,\end{array}
|
||||
$$
|
||||
|
||||
<p>which we Taylor expand to obtain</p>
|
||||
|
||||
$$
|
||||
\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1
|
||||
\partial f_1/\partial x_1+h_2
|
||||
\partial f_1/\partial x_2+\dots\\
|
||||
0=f_2(x_1+h_1,x_2+h_2)=&f_2(x_1,x_2)+h_1
|
||||
\partial f_2/\partial x_1+h_2
|
||||
\partial f_2/\partial x_2+\dots
|
||||
\end{array}.
|
||||
$$
|
||||
|
||||
<p>Defining the Jacobian matrix \( {\bf \boldsymbol{J}} \) we have</p>
|
||||
$$
|
||||
{\bf \boldsymbol{J}}=\left( \begin{array}{cc}
|
||||
\partial f_1/\partial x_1 & \partial f_1/\partial x_2 \\
|
||||
\partial f_2/\partial x_1 &\partial f_2/\partial x_2
|
||||
\end{array} \right),
|
||||
$$
|
||||
|
||||
<p>we can rephrase Newton's method as</p>
|
||||
$$
|
||||
\left(\begin{array}{c} x_1^{n+1} \\ x_2^{n+1} \end{array} \right)=
|
||||
\left(\begin{array}{c} x_1^{n} \\ x_2^{n} \end{array} \right)+
|
||||
\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right),
|
||||
$$
|
||||
|
||||
<p>where we have defined</p>
|
||||
$$
|
||||
\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right)=
|
||||
-{\bf \boldsymbol{J}}^{-1}
|
||||
\left(\begin{array}{c} f_1(x_1^{n},x_2^{n}) \\ f_2(x_1^{n},x_2^{n}) \end{array} \right).
|
||||
$$
|
||||
|
||||
<p>We need thus to compute the inverse of the Jacobian matrix and it
|
||||
is to understand that difficulties may
|
||||
arise in case \( {\bf \boldsymbol{J}} \) is nearly singular.
|
||||
<p>The basic idea of gradient descent is
|
||||
that a function \( F(\mathbf{x}) \),
|
||||
\( \mathbf{x} \equiv (x_1,\cdots,x_n) \), decreases fastest if one goes from \( \bf {x} \) in the
|
||||
direction of the negative gradient \( -\nabla F(\mathbf{x}) \).
|
||||
</p>
|
||||
|
||||
<p>It is rather straightforward to extend the above scheme to systems of
|
||||
more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function.
|
||||
<p>It can be shown that if </p>
|
||||
$$
|
||||
\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k),
|
||||
$$
|
||||
|
||||
<p>with \( \gamma_k > 0 \).</p>
|
||||
|
||||
<p>For \( \gamma_k \) small enough, then \( F(\mathbf{x}_{k+1}) \leq
|
||||
F(\mathbf{x}_k) \). This means that for a sufficiently small \( \gamma_k \)
|
||||
we are always moving towards smaller function values, i.e a minimum.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -399,7 +364,7 @@ more than two non-linear equations. In our case, the Jacobian matrix is given by
|
||||
<li><a href="._week38-bs046.html">47</a></li>
|
||||
<li><a href="._week38-bs047.html">48</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs039.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -320,25 +318,21 @@ MathJax.Hub.Config({
|
||||
<div class="container">
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0039"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="steepest-descent" class="anchor">Steepest descent </h2>
|
||||
<!-- !split -->
|
||||
<h2 id="more-on-steepest-descent" class="anchor">More on Steepest descent </h2>
|
||||
|
||||
<p>The basic idea of gradient descent is
|
||||
that a function \( F(\mathbf{x}) \),
|
||||
\( \mathbf{x} \equiv (x_1,\cdots,x_n) \), decreases fastest if one goes from \( \bf {x} \) in the
|
||||
direction of the negative gradient \( -\nabla F(\mathbf{x}) \).
|
||||
<p>The previous observation is the basis of the method of steepest
|
||||
descent, which is also referred to as just gradient descent (GD). One
|
||||
starts with an initial guess \( \mathbf{x}_0 \) for a minimum of \( F \) and
|
||||
computes new approximations according to
|
||||
</p>
|
||||
|
||||
<p>It can be shown that if </p>
|
||||
$$
|
||||
\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k),
|
||||
\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k), \ \ k \geq 0.
|
||||
$$
|
||||
|
||||
<p>with \( \gamma_k > 0 \).</p>
|
||||
|
||||
<p>For \( \gamma_k \) small enough, then \( F(\mathbf{x}_{k+1}) \leq
|
||||
F(\mathbf{x}_k) \). This means that for a sufficiently small \( \gamma_k \)
|
||||
we are always moving towards smaller function values, i.e a minimum.
|
||||
<p>The parameter \( \gamma_k \) is often referred to as the step length or
|
||||
the learning rate within the context of Machine Learning.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -366,7 +360,7 @@ we are always moving towards smaller function values, i.e a minimum.
|
||||
<li><a href="._week38-bs047.html">48</a></li>
|
||||
<li><a href="._week38-bs048.html">49</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs040.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,20 +319,27 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0040"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="more-on-steepest-descent" class="anchor">More on Steepest descent </h2>
|
||||
<h2 id="the-ideal" class="anchor">The ideal </h2>
|
||||
|
||||
<p>The previous observation is the basis of the method of steepest
|
||||
descent, which is also referred to as just gradient descent (GD). One
|
||||
starts with an initial guess \( \mathbf{x}_0 \) for a minimum of \( F \) and
|
||||
computes new approximations according to
|
||||
<p>Ideally the sequence \( \{\mathbf{x}_k \}_{k=0} \) converges to a global
|
||||
minimum of the function \( F \). In general we do not know if we are in a
|
||||
global or local minimum. In the special case when \( F \) is a convex
|
||||
function, all local minima are also global minima, so in this case
|
||||
gradient descent can converge to the global solution. The advantage of
|
||||
this scheme is that it is conceptually simple and straightforward to
|
||||
implement. However the method in this form has some severe
|
||||
limitations:
|
||||
</p>
|
||||
|
||||
$$
|
||||
\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k), \ \ k \geq 0.
|
||||
$$
|
||||
<p>In machine learing we are often faced with non-convex high dimensional
|
||||
cost functions with many local minima. Since GD is deterministic we
|
||||
will get stuck in a local minimum, if the method converges, unless we
|
||||
have a very good intial guess. This also implies that the scheme is
|
||||
sensitive to the chosen initial condition.
|
||||
</p>
|
||||
|
||||
<p>The parameter \( \gamma_k \) is often referred to as the step length or
|
||||
the learning rate within the context of Machine Learning.
|
||||
<p>Note that the gradient is a function of \( \mathbf{x} =
|
||||
(x_1,\cdots,x_n) \) which makes it expensive to compute numerically.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -362,7 +367,7 @@ the learning rate within the context of Machine Learning.
|
||||
<li><a href="._week38-bs048.html">49</a></li>
|
||||
<li><a href="._week38-bs049.html">50</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs041.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,27 +319,20 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0041"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="the-ideal" class="anchor">The ideal </h2>
|
||||
<h2 id="the-sensitiveness-of-the-gradient-descent" class="anchor">The sensitiveness of the gradient descent </h2>
|
||||
|
||||
<p>Ideally the sequence \( \{\mathbf{x}_k \}_{k=0} \) converges to a global
|
||||
minimum of the function \( F \). In general we do not know if we are in a
|
||||
global or local minimum. In the special case when \( F \) is a convex
|
||||
function, all local minima are also global minima, so in this case
|
||||
gradient descent can converge to the global solution. The advantage of
|
||||
this scheme is that it is conceptually simple and straightforward to
|
||||
implement. However the method in this form has some severe
|
||||
limitations:
|
||||
<p>The gradient descent method
|
||||
is sensitive to the choice of learning rate \( \gamma_k \). This is due
|
||||
to the fact that we are only guaranteed that \( F(\mathbf{x}_{k+1}) \leq
|
||||
F(\mathbf{x}_k) \) for sufficiently small \( \gamma_k \). The problem is to
|
||||
determine an optimal learning rate. If the learning rate is chosen too
|
||||
small the method will take a long time to converge and if it is too
|
||||
large we can experience erratic behavior.
|
||||
</p>
|
||||
|
||||
<p>In machine learing we are often faced with non-convex high dimensional
|
||||
cost functions with many local minima. Since GD is deterministic we
|
||||
will get stuck in a local minimum, if the method converges, unless we
|
||||
have a very good intial guess. This also implies that the scheme is
|
||||
sensitive to the chosen initial condition.
|
||||
</p>
|
||||
|
||||
<p>Note that the gradient is a function of \( \mathbf{x} =
|
||||
(x_1,\cdots,x_n) \) which makes it expensive to compute numerically.
|
||||
<p>Many of these shortcomings can be alleviated by introducing
|
||||
randomness. One such method is that of Stochastic Gradient Descent
|
||||
(SGD), to be discussed next week.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -369,7 +360,7 @@ sensitive to the chosen initial condition.
|
||||
<li><a href="._week38-bs049.html">50</a></li>
|
||||
<li><a href="._week38-bs050.html">51</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs042.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,20 +319,20 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0042"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="the-sensitiveness-of-the-gradient-descent" class="anchor">The sensitiveness of the gradient descent </h2>
|
||||
<h2 id="convex-functions" class="anchor">Convex functions </h2>
|
||||
|
||||
<p>The gradient descent method
|
||||
is sensitive to the choice of learning rate \( \gamma_k \). This is due
|
||||
to the fact that we are only guaranteed that \( F(\mathbf{x}_{k+1}) \leq
|
||||
F(\mathbf{x}_k) \) for sufficiently small \( \gamma_k \). The problem is to
|
||||
determine an optimal learning rate. If the learning rate is chosen too
|
||||
small the method will take a long time to converge and if it is too
|
||||
large we can experience erratic behavior.
|
||||
<p>Ideally we want our cost/loss function to be convex(concave).</p>
|
||||
|
||||
<p>First we give the definition of a convex set: A set \( C \) in
|
||||
\( \mathbb{R}^n \) is said to be convex if, for all \( x \) and \( y \) in \( C \) and
|
||||
all \( t \in (0,1) \) , the point \( (1 − t)x + ty \) also belongs to
|
||||
C. Geometrically this means that every point on the line segment
|
||||
connecting \( x \) and \( y \) is in \( C \) as discussed below.
|
||||
</p>
|
||||
|
||||
<p>Many of these shortcomings can be alleviated by introducing
|
||||
randomness. One such method is that of Stochastic Gradient Descent
|
||||
(SGD), to be discussed next week.
|
||||
<p>The convex subsets of \( \mathbb{R} \) are the intervals of
|
||||
\( \mathbb{R} \). Examples of convex sets of \( \mathbb{R}^2 \) are the
|
||||
regular polygons (triangles, rectangles, pentagons, etc...).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -362,7 +360,7 @@ randomness. One such method is that of Stochastic Gradient Descent
|
||||
<li><a href="._week38-bs050.html">51</a></li>
|
||||
<li><a href="._week38-bs051.html">52</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs043.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -48,10 +48,10 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -92,7 +92,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -249,7 +248,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs001.html#plans-for-week-38-lecture-monday-september-16" style="font-size: 80%;">Plans for week 38, lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs002.html#suggested-reading-and-videos" style="font-size: 80%;">Suggested reading and videos</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs003.html#plans-for-the-lab-sessions" style="font-size: 80%;">Plans for the lab sessions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-thursday-september-21" style="font-size: 80%;">Material for lecture Thursday September 21</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs004.html#material-for-lecture-monday-september-16" style="font-size: 80%;">Material for lecture Monday September 16</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs005.html#logistic-regression" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs006.html#classification-problems" style="font-size: 80%;">Classification problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs007.html#optimization-and-deep-learning" style="font-size: 80%;">Optimization and Deep learning</a></li>
|
||||
@@ -268,48 +267,47 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs020.html#extending-to-more-predictors" style="font-size: 80%;">Extending to more predictors</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs021.html#including-more-classes" style="font-size: 80%;">Including more classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs022.html#more-classes" style="font-size: 80%;">More classes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs023.html#friday-september-23" style="font-size: 80%;">Friday September 23</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.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-bs031.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-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.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-bs035.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-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.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-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.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-bs043.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs048.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.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-bs051.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.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-bs055.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.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-bs058.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs062.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-bs063.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.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-bs023.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs024.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs025.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs026.html#wisconsin-cancer-data" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.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-bs030.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-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.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-bs034.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-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.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-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.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-bs042.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs043.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs044.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs045.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs046.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs047.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs049.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-bs050.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.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-bs054.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.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-bs057.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#challenge-yourself-the-coming-weekend" style="font-size: 80%;">Challenge yourself the coming weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.html#lab-session-material-from-last-week-and-relevant-for-the-first-project" style="font-size: 80%;">Lab session: Material from last week and relevant for the first project</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs060.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.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>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -364,7 +362,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week38-bs008.html">9</a></li>
|
||||
<li><a href="._week38-bs009.html">10</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs063.html">64</a></li>
|
||||
<li><a href="._week38-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -260,7 +260,7 @@ MathJax.Hub.Config({
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="material-for-lecture-thursday-september-21">Material for lecture Thursday September 21 </h2>
|
||||
<h2 id="material-for-lecture-monday-september-16">Material for lecture Monday September 16 </h2>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
@@ -863,10 +863,6 @@ methods</a>.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="friday-september-23">Friday September 23 </h2>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="searching-for-optimal-regularization-parameters-lambda">Searching for Optimal Regularization Parameters \( \lambda \) </h2>
|
||||
|
||||
|
||||
@@ -75,10 +75,10 @@ div.toc p,a {
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -119,7 +119,6 @@ div.toc p,a {
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -330,7 +329,7 @@ MathJax.Hub.Config({
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="material-for-lecture-thursday-september-21">Material for lecture Thursday September 21 </h2>
|
||||
<h2 id="material-for-lecture-monday-september-16">Material for lecture Monday September 16 </h2>
|
||||
|
||||
<!-- !split -->
|
||||
<h2 id="logistic-regression">Logistic Regression </h2>
|
||||
@@ -880,9 +879,6 @@ discussed in the material on <a href="https://compphysics.github.io/MachineLearn
|
||||
methods</a>.
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="friday-september-23">Friday September 23 </h2>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="searching-for-optimal-regularization-parameters-lambda">Searching for Optimal Regularization Parameters \( \lambda \) </h2>
|
||||
|
||||
|
||||
@@ -152,10 +152,10 @@ div.toc p,a {
|
||||
2,
|
||||
None,
|
||||
'plans-for-the-lab-sessions'),
|
||||
('Material for lecture Thursday September 21',
|
||||
('Material for lecture Monday September 16',
|
||||
2,
|
||||
None,
|
||||
'material-for-lecture-thursday-september-21'),
|
||||
'material-for-lecture-monday-september-16'),
|
||||
('Logistic Regression', 2, None, 'logistic-regression'),
|
||||
('Classification problems', 2, None, 'classification-problems'),
|
||||
('Optimization and Deep learning',
|
||||
@@ -196,7 +196,6 @@ div.toc p,a {
|
||||
'extending-to-more-predictors'),
|
||||
('Including more classes', 2, None, 'including-more-classes'),
|
||||
('More classes', 2, None, 'more-classes'),
|
||||
('Friday September 23', 2, None, 'friday-september-23'),
|
||||
('Searching for Optimal Regularization Parameters $\\lambda$',
|
||||
2,
|
||||
None,
|
||||
@@ -407,7 +406,7 @@ MathJax.Hub.Config({
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="material-for-lecture-thursday-september-21">Material for lecture Thursday September 21 </h2>
|
||||
<h2 id="material-for-lecture-monday-september-16">Material for lecture Monday September 16 </h2>
|
||||
|
||||
<!-- !split -->
|
||||
<h2 id="logistic-regression">Logistic Regression </h2>
|
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@@ -957,9 +956,6 @@ discussed in the material on <a href="https://compphysics.github.io/MachineLearn
|
||||
methods</a>.
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="friday-september-23">Friday September 23 </h2>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="searching-for-optimal-regularization-parameters-lambda">Searching for Optimal Regularization Parameters \( \lambda \) </h2>
|
||||
|
||||
|
||||
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@@ -42,7 +42,7 @@ DATE: September 16-20, 2024
|
||||
|
||||
|
||||
!split
|
||||
===== Material for lecture Thursday September 21 =====
|
||||
===== Material for lecture Monday September 16 =====
|
||||
|
||||
|
||||
!split
|
||||
@@ -539,9 +539,6 @@ discussed in the material on "optimization
|
||||
methods":"https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html".
|
||||
|
||||
|
||||
!split
|
||||
===== Friday September 23 =====
|
||||
|
||||
!split
|
||||
===== Searching for Optimal Regularization Parameters $\lambda$ =====
|
||||
|
||||
|
||||
Reference in New Issue
Block a user