redundant code lines
This commit is contained in:
Morten Hjorth-Jensen
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -412,7 +357,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week38-bs008.html">9</a></li>
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||||
<li><a href="._week38-bs009.html">10</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
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||||
<li><a href="._week38-bs001.html">»</a></li>
|
||||
</ul>
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||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -399,7 +344,7 @@ 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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs002.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -440,7 +385,7 @@ $$
|
||||
<li><a href="._week38-bs010.html">11</a></li>
|
||||
<li><a href="._week38-bs011.html">12</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs003.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -405,7 +350,7 @@ cross-validation (LOOCV).
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs004.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -409,7 +354,7 @@ $$
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs005.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -405,7 +350,7 @@ MathJax.Hub.Config({
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs006.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -505,7 +450,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs007.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -406,7 +351,7 @@ simple recipe for fitting our data.
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs008.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -412,7 +357,7 @@ failure etc.
|
||||
<li><a href="._week38-bs016.html">17</a></li>
|
||||
<li><a href="._week38-bs017.html">18</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs009.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -411,7 +356,7 @@ models, as we will see later.
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs010.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -419,7 +364,7 @@ $$
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs011.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -416,7 +361,7 @@ $$
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs012.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -416,7 +361,7 @@ the probability of a given category. This leads us to the logistic function.
|
||||
<li><a href="._week38-bs020.html">21</a></li>
|
||||
<li><a href="._week38-bs021.html">22</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs013.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -475,7 +420,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week38-bs021.html">22</a></li>
|
||||
<li><a href="._week38-bs022.html">23</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs014.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -447,7 +392,7 @@ representing the probability for finding a value of \( y_i \) with a given
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs015.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -414,7 +359,7 @@ $$
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs016.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -475,7 +420,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs017.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
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||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
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|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -412,7 +357,7 @@ $$
|
||||
<li><a href="._week38-bs025.html">26</a></li>
|
||||
<li><a href="._week38-bs026.html">27</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs018.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -415,7 +360,7 @@ $$
|
||||
<li><a href="._week38-bs026.html">27</a></li>
|
||||
<li><a href="._week38-bs027.html">28</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs019.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -412,7 +357,7 @@ in practice we often supplement the cross-entropy with additional regularization
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs020.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -414,7 +359,7 @@ $$
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs021.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -415,7 +360,7 @@ $$
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs022.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -407,7 +352,7 @@ $$
|
||||
<li><a href="._week38-bs030.html">31</a></li>
|
||||
<li><a href="._week38-bs031.html">32</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs023.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -419,7 +364,7 @@ $$
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs024.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -431,7 +376,7 @@ methods</a>.
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs025.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -396,7 +341,7 @@ MathJax.Hub.Config({
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs026.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -475,7 +420,7 @@ This becomes however less functional in the long run.
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs027.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -473,7 +418,7 @@ contains more information on how to set the different parameters.
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs028.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -472,7 +417,7 @@ ypredictRidge <span style="color: #666666">=</span> gridsearch<span style="color
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs029.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -440,7 +385,7 @@ logreg<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs030.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -456,7 +401,7 @@ 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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs031.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -464,7 +409,7 @@ applications. This will be discussed later this semester (<a href="https://compp
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs032.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -392,8 +337,6 @@ X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_tes
|
||||
<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)))
|
||||
|
||||
|
||||
<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
|
||||
@@ -402,7 +345,6 @@ accuracy <span style="color: #666666">=</span> cross_validate(logreg,X_test,y_te
|
||||
<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>)
|
||||
@@ -453,7 +395,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs033.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -408,7 +353,7 @@ some approximative/numerical method to compute the minimum.
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs034.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -413,7 +358,7 @@ $$
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs035.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -417,7 +362,7 @@ $$
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs036.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -414,7 +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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs037.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -407,7 +352,7 @@ normally discourage the use of this method.
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs038.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -427,7 +372,7 @@ $$
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs039.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -409,7 +354,7 @@ vanishes, then Newton-Raphson may fail totally
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs040.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -447,7 +392,7 @@ more than two non-linear equations. In our case, the Jacobian matrix is given by
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs041.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -414,7 +359,7 @@ we are always moving towards smaller function values, i.e a minimum.
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs042.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -410,7 +355,7 @@ the learning rate within the context of Machine Learning.
|
||||
<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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs043.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -169,47 +169,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -332,32 +291,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs050.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs051.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs052.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs054.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs056.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs063.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs066.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs067.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs069.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-bs070.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs071.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs072.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs073.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-bs074.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs075.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-bs076.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-bs077.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs078.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs053.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs055.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-bs056.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs057.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs058.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs059.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-bs060.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs061.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-bs062.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-bs063.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs064.html#challenge-yourself-this-weekend" style="font-size: 80%;">Challenge yourself this weekend</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -412,7 +357,7 @@ 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-bs078.html">79</a></li>
|
||||
<li><a href="._week38-bs064.html">65</a></li>
|
||||
<li><a href="._week38-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -1517,8 +1517,6 @@ X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,ra
|
||||
<span style="color: #228B22"># Logistic Regression</span>
|
||||
logreg = LogisticRegression(solver=<span style="color: #CD5555">'lbfgs'</span>)
|
||||
logreg.fit(X_train, y_train)
|
||||
<span style="color: #658b00">print</span>(<span style="color: #CD5555">"Test set accuracy with Logistic Regression: {:.2f}"</span>.format(logreg.score(X_test,y_test)))
|
||||
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.preprocessing</span> <span style="color: #8B008B; font-weight: bold">import</span> LabelEncoder
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> cross_validate
|
||||
@@ -1527,7 +1525,6 @@ accuracy = cross_validate(logreg,X_test,y_test,cv=<span style="color: #B452CD">1
|
||||
<span style="color: #658b00">print</span>(accuracy)
|
||||
<span style="color: #658b00">print</span>(<span style="color: #CD5555">"Test set accuracy with Logistic Regression: {:.2f}"</span>.format(logreg.score(X_test,y_test)))
|
||||
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">scikitplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">skplt</span>
|
||||
y_pred = logreg.predict(X_test)
|
||||
skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=<span style="color: #8B008B; font-weight: bold">True</span>)
|
||||
@@ -2069,593 +2066,6 @@ is minimal, where \( f \) is convex and differentiable. Then, any point
|
||||
<p>Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this).</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="standard-steepest-descent">Standard steepest descent </h2>
|
||||
|
||||
<p>Before we proceed, we would like to discuss the approach called the
|
||||
<b>standard Steepest descent</b> (different from the above steepest descent discussion), which again leads to us having to be able
|
||||
to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).
|
||||
</p>
|
||||
|
||||
<a href="https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf" target="_blank">The success of the CG method</a>
|
||||
<p>for finding solutions of non-linear problems is based on the theory
|
||||
of conjugate gradients for linear systems of equations. It belongs to
|
||||
the class of iterative methods for solving problems from linear
|
||||
algebra of the type
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{x} = \boldsymbol{b}.
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>In the iterative process we end up with a problem like</p>
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}= \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x},
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>where \( \boldsymbol{r} \) is the so-called residual or error in the iterative process.</p>
|
||||
|
||||
<p>When we have found the exact solution, \( \boldsymbol{r}=0 \).</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="gradient-method">Gradient method </h2>
|
||||
|
||||
<p>The residual is zero when we reach the minimum of the quadratic equation</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
P(\boldsymbol{x})=\frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T\boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>with the constraint that the matrix \( \boldsymbol{A} \) is positive definite and
|
||||
symmetric. This defines also the Hessian and we want it to be positive definite.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="steepest-descent-method">Steepest descent method </h2>
|
||||
|
||||
<p>We denote the initial guess for \( \boldsymbol{x} \) as \( \boldsymbol{x}_0 \).
|
||||
We can assume without loss of generality that
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_0=0,
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>or consider the system</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{z} = \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_0,
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>instead.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="steepest-descent-method">Steepest descent method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>One can show that the solution \( \boldsymbol{x} \) is also the unique minimizer of the quadratic form</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
f(\boldsymbol{x}) = \frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T \boldsymbol{x} , \quad \boldsymbol{x}\in\mathbf{R}^n.
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>This suggests taking the first basis vector \( \boldsymbol{r}_1 \) (see below for definition)
|
||||
to be the gradient of \( f \) at \( \boldsymbol{x}=\boldsymbol{x}_0 \),
|
||||
which equals
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{x}_0-\boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>and
|
||||
\( \boldsymbol{x}_0=0 \) it is equal \( -\boldsymbol{b} \).
|
||||
</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="final-expressions">Final expressions </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>We can compute the residual iteratively as</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_{k+1}=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_{k+1},
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>which equals</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{b}-\boldsymbol{A}(\boldsymbol{x}_k+\alpha_k\boldsymbol{r}_k),
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>or</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
(\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k)-\alpha_k\boldsymbol{A}\boldsymbol{r}_k,
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>which gives</p>
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
\alpha_k = \frac{\boldsymbol{r}_k^T\boldsymbol{r}_k}{\boldsymbol{r}_k^T\boldsymbol{A}\boldsymbol{r}_k}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>leading to the iterative scheme</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_{k+1}=\boldsymbol{x}_k-\alpha_k\boldsymbol{r}_{k},
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="steepest-descent-example">Steepest descent example </h2>
|
||||
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<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: #eeeedd">
|
||||
<pre style="font-size: 80%; line-height: 125%;"><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy.linalg</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">la</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">scipy.optimize</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sopt</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pt</span>
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">mpl_toolkits.mplot3d</span> <span style="color: #8B008B; font-weight: bold">import</span> axes3d
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">f</span>(x):
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> x[<span style="color: #B452CD">0</span>]**<span style="color: #B452CD">2</span> + <span style="color: #B452CD">3.0</span>*x[<span style="color: #B452CD">1</span>]**<span style="color: #B452CD">2</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">df</span>(x):
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> np.array([<span style="color: #B452CD">2</span>*x[<span style="color: #B452CD">0</span>], <span style="color: #B452CD">6</span>*x[<span style="color: #B452CD">1</span>]])
|
||||
|
||||
fig = pt.figure()
|
||||
ax = fig.gca(projection=<span style="color: #CD5555">"3d"</span>)
|
||||
|
||||
xmesh, ymesh = np.mgrid[-<span style="color: #B452CD">3</span>:<span style="color: #B452CD">3</span>:<span style="color: #B452CD">50</span>j,-<span style="color: #B452CD">3</span>:<span style="color: #B452CD">3</span>:<span style="color: #B452CD">50</span>j]
|
||||
fmesh = f(np.array([xmesh, ymesh]))
|
||||
ax.plot_surface(xmesh, ymesh, fmesh)
|
||||
</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>And then as countor plot</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<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: #eeeedd">
|
||||
<pre style="font-size: 80%; line-height: 125%;">pt.axis(<span style="color: #CD5555">"equal"</span>)
|
||||
pt.contour(xmesh, ymesh, fmesh)
|
||||
guesses = [np.array([<span style="color: #B452CD">2</span>, <span style="color: #B452CD">2.</span>/<span style="color: #B452CD">5</span>])]
|
||||
</pre>
|
||||
</div>
|
||||
</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>Find guesses</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<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: #eeeedd">
|
||||
<pre style="font-size: 80%; line-height: 125%;">x = guesses[-<span style="color: #B452CD">1</span>]
|
||||
s = -df(x)
|
||||
</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>Run it!</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<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: #eeeedd">
|
||||
<pre style="font-size: 80%; line-height: 125%;"><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">f1d</span>(alpha):
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> f(x + alpha*s)
|
||||
|
||||
alpha_opt = sopt.golden(f1d)
|
||||
next_guess = x + alpha_opt * s
|
||||
guesses.append(next_guess)
|
||||
<span style="color: #658b00">print</span>(next_guess)
|
||||
</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>What happened?</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<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: #eeeedd">
|
||||
<pre style="font-size: 80%; line-height: 125%;">pt.axis(<span style="color: #CD5555">"equal"</span>)
|
||||
pt.contour(xmesh, ymesh, fmesh, <span style="color: #B452CD">50</span>)
|
||||
it_array = np.array(guesses)
|
||||
pt.plot(it_array.T[<span style="color: #B452CD">0</span>], it_array.T[<span style="color: #B452CD">1</span>], <span style="color: #CD5555">"x-"</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>Note that we did only one iteration here. We can easily add more using our previous guesses.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>In the CG method we define so-called conjugate directions and two vectors
|
||||
\( \boldsymbol{s} \) and \( \boldsymbol{t} \)
|
||||
are said to be
|
||||
conjugate if
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{s}^T\boldsymbol{A}\boldsymbol{t}= 0.
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>The philosophy of the CG method is to perform searches in various conjugate directions
|
||||
of our vectors \( \boldsymbol{x}_i \) obeying the above criterion, namely
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_i^T\boldsymbol{A}\boldsymbol{x}_j= 0.
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>Two vectors are conjugate if they are orthogonal with respect to
|
||||
this inner product. Being conjugate is a symmetric relation: if \( \boldsymbol{s} \) is conjugate to \( \boldsymbol{t} \), then \( \boldsymbol{t} \) is conjugate to \( \boldsymbol{s} \).
|
||||
</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>An example is given by the eigenvectors of the matrix</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{v}_i^T\boldsymbol{A}\boldsymbol{v}_j= \lambda\boldsymbol{v}_i^T\boldsymbol{v}_j,
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>which is zero unless \( i=j \). </p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>Assume now that we have a symmetric positive-definite matrix \( \boldsymbol{A} \) of size
|
||||
\( n\times n \). At each iteration \( i+1 \) we obtain the conjugate direction of a vector
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_{i+1}=\boldsymbol{x}_{i}+\alpha_i\boldsymbol{p}_{i}.
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>We assume that \( \boldsymbol{p}_{i} \) is a sequence of \( n \) mutually conjugate directions.
|
||||
Then the \( \boldsymbol{p}_{i} \) form a basis of \( R^n \) and we can expand the solution
|
||||
$ \boldsymbol{A}\boldsymbol{x} = \boldsymbol{b}$ in this basis, namely
|
||||
</p>
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x} = \sum^{n}_{i=1} \alpha_i \boldsymbol{p}_i.
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>The coefficients are given by</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\mathbf{A}\mathbf{x} = \sum^{n}_{i=1} \alpha_i \mathbf{A} \mathbf{p}_i = \mathbf{b}.
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>Multiplying with \( \boldsymbol{p}_k^T \) from the left gives</p>
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{x} = \sum^{n}_{i=1} \alpha_i\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{p}_i= \boldsymbol{p}_k^T \boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>and we can define the coefficients \( \alpha_k \) as</p>
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\alpha_k = \frac{\boldsymbol{p}_k^T \boldsymbol{b}}{\boldsymbol{p}_k^T \boldsymbol{A} \boldsymbol{p}_k}
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="conjugate-gradient-method-and-iterations">Conjugate gradient method and iterations </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
|
||||
<p>If we choose the conjugate vectors \( \boldsymbol{p}_k \) carefully,
|
||||
then we may not need all of them to obtain a good approximation to the solution
|
||||
\( \boldsymbol{x} \).
|
||||
We want to regard the conjugate gradient method as an iterative method.
|
||||
This will us to solve systems where \( n \) is so large that the direct
|
||||
method would take too much time.
|
||||
</p>
|
||||
|
||||
<p>We denote the initial guess for \( \boldsymbol{x} \) as \( \boldsymbol{x}_0 \).
|
||||
We can assume without loss of generality that
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_0=0,
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>or consider the system</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{z} = \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_0,
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>instead.</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>One can show that the solution \( \boldsymbol{x} \) is also the unique minimizer of the quadratic form</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
f(\boldsymbol{x}) = \frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T \boldsymbol{x} , \quad \boldsymbol{x}\in\mathbf{R}^n.
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>This suggests taking the first basis vector \( \boldsymbol{p}_1 \)
|
||||
to be the gradient of \( f \) at \( \boldsymbol{x}=\boldsymbol{x}_0 \),
|
||||
which equals
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{x}_0-\boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>and
|
||||
\( \boldsymbol{x}_0=0 \) it is equal \( -\boldsymbol{b} \).
|
||||
The other vectors in the basis will be conjugate to the gradient,
|
||||
hence the name conjugate gradient method.
|
||||
</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>Let \( \boldsymbol{r}_k \) be the residual at the \( k \)-th step:</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_k=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k.
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>Note that \( \boldsymbol{r}_k \) is the negative gradient of \( f \) at
|
||||
\( \boldsymbol{x}=\boldsymbol{x}_k \),
|
||||
so the gradient descent method would be to move in the direction \( \boldsymbol{r}_k \).
|
||||
Here, we insist that the directions \( \boldsymbol{p}_k \) are conjugate to each other,
|
||||
so we take the direction closest to the gradient \( \boldsymbol{r}_k \)
|
||||
under the conjugacy constraint.
|
||||
This gives the following expression
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{p}_{k+1}=\boldsymbol{r}_k-\frac{\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{r}_k}{\boldsymbol{p}_k^T\boldsymbol{A}\boldsymbol{p}_k} \boldsymbol{p}_k.
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>We can also compute the residual iteratively as</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_{k+1}=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_{k+1},
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>which equals</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{b}-\boldsymbol{A}(\boldsymbol{x}_k+\alpha_k\boldsymbol{p}_k),
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>or</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
(\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k)-\alpha_k\boldsymbol{A}\boldsymbol{p}_k,
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>which gives</p>
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_{k+1}=\boldsymbol{r}_k-\boldsymbol{A}\boldsymbol{p}_{k},
|
||||
\end{equation*}
|
||||
$$
|
||||
<p> <br>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="revisiting-our-first-homework">Revisiting our first homework </h2>
|
||||
|
||||
|
||||
@@ -196,47 +196,6 @@ div.toc p,a {
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -1555,8 +1514,6 @@ X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,ra
|
||||
<span style="color: #228B22"># Logistic Regression</span>
|
||||
logreg = LogisticRegression(solver=<span style="color: #CD5555">'lbfgs'</span>)
|
||||
logreg.fit(X_train, y_train)
|
||||
<span style="color: #658b00">print</span>(<span style="color: #CD5555">"Test set accuracy with Logistic Regression: {:.2f}"</span>.format(logreg.score(X_test,y_test)))
|
||||
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.preprocessing</span> <span style="color: #8B008B; font-weight: bold">import</span> LabelEncoder
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> cross_validate
|
||||
@@ -1565,7 +1522,6 @@ accuracy = cross_validate(logreg,X_test,y_test,cv=<span style="color: #B452CD">1
|
||||
<span style="color: #658b00">print</span>(accuracy)
|
||||
<span style="color: #658b00">print</span>(<span style="color: #CD5555">"Test set accuracy with Logistic Regression: {:.2f}"</span>.format(logreg.score(X_test,y_test)))
|
||||
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">scikitplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">skplt</span>
|
||||
y_pred = logreg.predict(X_test)
|
||||
skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=<span style="color: #8B008B; font-weight: bold">True</span>)
|
||||
@@ -2041,529 +1997,6 @@ is minimal, where \( f \) is convex and differentiable. Then, any point
|
||||
</ol>
|
||||
<p>Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this).</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="standard-steepest-descent">Standard steepest descent </h2>
|
||||
|
||||
<p>Before we proceed, we would like to discuss the approach called the
|
||||
<b>standard Steepest descent</b> (different from the above steepest descent discussion), which again leads to us having to be able
|
||||
to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).
|
||||
</p>
|
||||
|
||||
<a href="https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf" target="_blank">The success of the CG method</a>
|
||||
<p>for finding solutions of non-linear problems is based on the theory
|
||||
of conjugate gradients for linear systems of equations. It belongs to
|
||||
the class of iterative methods for solving problems from linear
|
||||
algebra of the type
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{x} = \boldsymbol{b}.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>In the iterative process we end up with a problem like</p>
|
||||
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}= \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>where \( \boldsymbol{r} \) is the so-called residual or error in the iterative process.</p>
|
||||
|
||||
<p>When we have found the exact solution, \( \boldsymbol{r}=0 \).</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="gradient-method">Gradient method </h2>
|
||||
|
||||
<p>The residual is zero when we reach the minimum of the quadratic equation</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
P(\boldsymbol{x})=\frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T\boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>with the constraint that the matrix \( \boldsymbol{A} \) is positive definite and
|
||||
symmetric. This defines also the Hessian and we want it to be positive definite.
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="steepest-descent-method">Steepest descent method </h2>
|
||||
|
||||
<p>We denote the initial guess for \( \boldsymbol{x} \) as \( \boldsymbol{x}_0 \).
|
||||
We can assume without loss of generality that
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_0=0,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>or consider the system</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{z} = \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_0,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>instead.</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="steepest-descent-method">Steepest descent method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>One can show that the solution \( \boldsymbol{x} \) is also the unique minimizer of the quadratic form</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
f(\boldsymbol{x}) = \frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T \boldsymbol{x} , \quad \boldsymbol{x}\in\mathbf{R}^n.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>This suggests taking the first basis vector \( \boldsymbol{r}_1 \) (see below for definition)
|
||||
to be the gradient of \( f \) at \( \boldsymbol{x}=\boldsymbol{x}_0 \),
|
||||
which equals
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{x}_0-\boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>and
|
||||
\( \boldsymbol{x}_0=0 \) it is equal \( -\boldsymbol{b} \).
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="final-expressions">Final expressions </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>We can compute the residual iteratively as</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_{k+1}=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_{k+1},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>which equals</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{b}-\boldsymbol{A}(\boldsymbol{x}_k+\alpha_k\boldsymbol{r}_k),
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>or</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
(\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k)-\alpha_k\boldsymbol{A}\boldsymbol{r}_k,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>which gives</p>
|
||||
|
||||
$$
|
||||
\alpha_k = \frac{\boldsymbol{r}_k^T\boldsymbol{r}_k}{\boldsymbol{r}_k^T\boldsymbol{A}\boldsymbol{r}_k}
|
||||
$$
|
||||
|
||||
<p>leading to the iterative scheme</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_{k+1}=\boldsymbol{x}_k-\alpha_k\boldsymbol{r}_{k},
|
||||
\end{equation*}
|
||||
$$
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="steepest-descent-example">Steepest descent example </h2>
|
||||
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<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: #eeeedd">
|
||||
<pre style="line-height: 125%;"><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy.linalg</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">la</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">scipy.optimize</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sopt</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pt</span>
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">mpl_toolkits.mplot3d</span> <span style="color: #8B008B; font-weight: bold">import</span> axes3d
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">f</span>(x):
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> x[<span style="color: #B452CD">0</span>]**<span style="color: #B452CD">2</span> + <span style="color: #B452CD">3.0</span>*x[<span style="color: #B452CD">1</span>]**<span style="color: #B452CD">2</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">df</span>(x):
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> np.array([<span style="color: #B452CD">2</span>*x[<span style="color: #B452CD">0</span>], <span style="color: #B452CD">6</span>*x[<span style="color: #B452CD">1</span>]])
|
||||
|
||||
fig = pt.figure()
|
||||
ax = fig.gca(projection=<span style="color: #CD5555">"3d"</span>)
|
||||
|
||||
xmesh, ymesh = np.mgrid[-<span style="color: #B452CD">3</span>:<span style="color: #B452CD">3</span>:<span style="color: #B452CD">50</span>j,-<span style="color: #B452CD">3</span>:<span style="color: #B452CD">3</span>:<span style="color: #B452CD">50</span>j]
|
||||
fmesh = f(np.array([xmesh, ymesh]))
|
||||
ax.plot_surface(xmesh, ymesh, fmesh)
|
||||
</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>And then as countor plot</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<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: #eeeedd">
|
||||
<pre style="line-height: 125%;">pt.axis(<span style="color: #CD5555">"equal"</span>)
|
||||
pt.contour(xmesh, ymesh, fmesh)
|
||||
guesses = [np.array([<span style="color: #B452CD">2</span>, <span style="color: #B452CD">2.</span>/<span style="color: #B452CD">5</span>])]
|
||||
</pre>
|
||||
</div>
|
||||
</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>Find guesses</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<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: #eeeedd">
|
||||
<pre style="line-height: 125%;">x = guesses[-<span style="color: #B452CD">1</span>]
|
||||
s = -df(x)
|
||||
</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>Run it!</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<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: #eeeedd">
|
||||
<pre style="line-height: 125%;"><span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">f1d</span>(alpha):
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> f(x + alpha*s)
|
||||
|
||||
alpha_opt = sopt.golden(f1d)
|
||||
next_guess = x + alpha_opt * s
|
||||
guesses.append(next_guess)
|
||||
<span style="color: #658b00">print</span>(next_guess)
|
||||
</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>What happened?</p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<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: #eeeedd">
|
||||
<pre style="line-height: 125%;">pt.axis(<span style="color: #CD5555">"equal"</span>)
|
||||
pt.contour(xmesh, ymesh, fmesh, <span style="color: #B452CD">50</span>)
|
||||
it_array = np.array(guesses)
|
||||
pt.plot(it_array.T[<span style="color: #B452CD">0</span>], it_array.T[<span style="color: #B452CD">1</span>], <span style="color: #CD5555">"x-"</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>Note that we did only one iteration here. We can easily add more using our previous guesses.</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>In the CG method we define so-called conjugate directions and two vectors
|
||||
\( \boldsymbol{s} \) and \( \boldsymbol{t} \)
|
||||
are said to be
|
||||
conjugate if
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{s}^T\boldsymbol{A}\boldsymbol{t}= 0.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>The philosophy of the CG method is to perform searches in various conjugate directions
|
||||
of our vectors \( \boldsymbol{x}_i \) obeying the above criterion, namely
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_i^T\boldsymbol{A}\boldsymbol{x}_j= 0.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>Two vectors are conjugate if they are orthogonal with respect to
|
||||
this inner product. Being conjugate is a symmetric relation: if \( \boldsymbol{s} \) is conjugate to \( \boldsymbol{t} \), then \( \boldsymbol{t} \) is conjugate to \( \boldsymbol{s} \).
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>An example is given by the eigenvectors of the matrix</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{v}_i^T\boldsymbol{A}\boldsymbol{v}_j= \lambda\boldsymbol{v}_i^T\boldsymbol{v}_j,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>which is zero unless \( i=j \). </p>
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>Assume now that we have a symmetric positive-definite matrix \( \boldsymbol{A} \) of size
|
||||
\( n\times n \). At each iteration \( i+1 \) we obtain the conjugate direction of a vector
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_{i+1}=\boldsymbol{x}_{i}+\alpha_i\boldsymbol{p}_{i}.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>We assume that \( \boldsymbol{p}_{i} \) is a sequence of \( n \) mutually conjugate directions.
|
||||
Then the \( \boldsymbol{p}_{i} \) form a basis of \( R^n \) and we can expand the solution
|
||||
$ \boldsymbol{A}\boldsymbol{x} = \boldsymbol{b}$ in this basis, namely
|
||||
</p>
|
||||
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x} = \sum^{n}_{i=1} \alpha_i \boldsymbol{p}_i.
|
||||
\end{equation*}
|
||||
$$
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>The coefficients are given by</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\mathbf{A}\mathbf{x} = \sum^{n}_{i=1} \alpha_i \mathbf{A} \mathbf{p}_i = \mathbf{b}.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>Multiplying with \( \boldsymbol{p}_k^T \) from the left gives</p>
|
||||
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{x} = \sum^{n}_{i=1} \alpha_i\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{p}_i= \boldsymbol{p}_k^T \boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>and we can define the coefficients \( \alpha_k \) as</p>
|
||||
|
||||
$$
|
||||
\begin{equation*}
|
||||
\alpha_k = \frac{\boldsymbol{p}_k^T \boldsymbol{b}}{\boldsymbol{p}_k^T \boldsymbol{A} \boldsymbol{p}_k}
|
||||
\end{equation*}
|
||||
$$
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method-and-iterations">Conjugate gradient method and iterations </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
|
||||
<p>If we choose the conjugate vectors \( \boldsymbol{p}_k \) carefully,
|
||||
then we may not need all of them to obtain a good approximation to the solution
|
||||
\( \boldsymbol{x} \).
|
||||
We want to regard the conjugate gradient method as an iterative method.
|
||||
This will us to solve systems where \( n \) is so large that the direct
|
||||
method would take too much time.
|
||||
</p>
|
||||
|
||||
<p>We denote the initial guess for \( \boldsymbol{x} \) as \( \boldsymbol{x}_0 \).
|
||||
We can assume without loss of generality that
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_0=0,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>or consider the system</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{z} = \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_0,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>instead.</p>
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>One can show that the solution \( \boldsymbol{x} \) is also the unique minimizer of the quadratic form</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
f(\boldsymbol{x}) = \frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T \boldsymbol{x} , \quad \boldsymbol{x}\in\mathbf{R}^n.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>This suggests taking the first basis vector \( \boldsymbol{p}_1 \)
|
||||
to be the gradient of \( f \) at \( \boldsymbol{x}=\boldsymbol{x}_0 \),
|
||||
which equals
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{x}_0-\boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>and
|
||||
\( \boldsymbol{x}_0=0 \) it is equal \( -\boldsymbol{b} \).
|
||||
The other vectors in the basis will be conjugate to the gradient,
|
||||
hence the name conjugate gradient method.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>Let \( \boldsymbol{r}_k \) be the residual at the \( k \)-th step:</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_k=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>Note that \( \boldsymbol{r}_k \) is the negative gradient of \( f \) at
|
||||
\( \boldsymbol{x}=\boldsymbol{x}_k \),
|
||||
so the gradient descent method would be to move in the direction \( \boldsymbol{r}_k \).
|
||||
Here, we insist that the directions \( \boldsymbol{p}_k \) are conjugate to each other,
|
||||
so we take the direction closest to the gradient \( \boldsymbol{r}_k \)
|
||||
under the conjugacy constraint.
|
||||
This gives the following expression
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{p}_{k+1}=\boldsymbol{r}_k-\frac{\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{r}_k}{\boldsymbol{p}_k^T\boldsymbol{A}\boldsymbol{p}_k} \boldsymbol{p}_k.
|
||||
\end{equation*}
|
||||
$$
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>We can also compute the residual iteratively as</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_{k+1}=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_{k+1},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>which equals</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{b}-\boldsymbol{A}(\boldsymbol{x}_k+\alpha_k\boldsymbol{p}_k),
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>or</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
(\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k)-\alpha_k\boldsymbol{A}\boldsymbol{p}_k,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>which gives</p>
|
||||
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_{k+1}=\boldsymbol{r}_k-\boldsymbol{A}\boldsymbol{p}_{k},
|
||||
\end{equation*}
|
||||
$$
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split -->
|
||||
<h2 id="revisiting-our-first-homework">Revisiting our first homework </h2>
|
||||
|
||||
|
||||
@@ -273,47 +273,6 @@ div.toc p,a {
|
||||
'conditions-on-convex-functions'),
|
||||
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
||||
('Some simple problems', 2, None, 'some-simple-problems'),
|
||||
('Standard steepest descent',
|
||||
2,
|
||||
None,
|
||||
'standard-steepest-descent'),
|
||||
('Gradient method', 2, None, 'gradient-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Steepest descent method', 2, None, 'steepest-descent-method'),
|
||||
('Final expressions', 2, None, 'final-expressions'),
|
||||
('Steepest descent example', 2, None, 'steepest-descent-example'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method and iterations',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method-and-iterations'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Conjugate gradient method',
|
||||
2,
|
||||
None,
|
||||
'conjugate-gradient-method'),
|
||||
('Revisiting our first homework',
|
||||
2,
|
||||
None,
|
||||
@@ -1632,8 +1591,6 @@ X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_tes
|
||||
<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)))
|
||||
|
||||
|
||||
<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
|
||||
@@ -1642,7 +1599,6 @@ accuracy <span style="color: #666666">=</span> cross_validate(logreg,X_test,y_te
|
||||
<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>)
|
||||
@@ -2118,529 +2074,6 @@ is minimal, where \( f \) is convex and differentiable. Then, any point
|
||||
</ol>
|
||||
<p>Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this).</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="standard-steepest-descent">Standard steepest descent </h2>
|
||||
|
||||
<p>Before we proceed, we would like to discuss the approach called the
|
||||
<b>standard Steepest descent</b> (different from the above steepest descent discussion), which again leads to us having to be able
|
||||
to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).
|
||||
</p>
|
||||
|
||||
<a href="https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf" target="_blank">The success of the CG method</a>
|
||||
<p>for finding solutions of non-linear problems is based on the theory
|
||||
of conjugate gradients for linear systems of equations. It belongs to
|
||||
the class of iterative methods for solving problems from linear
|
||||
algebra of the type
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{x} = \boldsymbol{b}.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>In the iterative process we end up with a problem like</p>
|
||||
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}= \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>where \( \boldsymbol{r} \) is the so-called residual or error in the iterative process.</p>
|
||||
|
||||
<p>When we have found the exact solution, \( \boldsymbol{r}=0 \).</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="gradient-method">Gradient method </h2>
|
||||
|
||||
<p>The residual is zero when we reach the minimum of the quadratic equation</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
P(\boldsymbol{x})=\frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T\boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>with the constraint that the matrix \( \boldsymbol{A} \) is positive definite and
|
||||
symmetric. This defines also the Hessian and we want it to be positive definite.
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="steepest-descent-method">Steepest descent method </h2>
|
||||
|
||||
<p>We denote the initial guess for \( \boldsymbol{x} \) as \( \boldsymbol{x}_0 \).
|
||||
We can assume without loss of generality that
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_0=0,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>or consider the system</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{z} = \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_0,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>instead.</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="steepest-descent-method">Steepest descent method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>One can show that the solution \( \boldsymbol{x} \) is also the unique minimizer of the quadratic form</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
f(\boldsymbol{x}) = \frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T \boldsymbol{x} , \quad \boldsymbol{x}\in\mathbf{R}^n.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>This suggests taking the first basis vector \( \boldsymbol{r}_1 \) (see below for definition)
|
||||
to be the gradient of \( f \) at \( \boldsymbol{x}=\boldsymbol{x}_0 \),
|
||||
which equals
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{x}_0-\boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>and
|
||||
\( \boldsymbol{x}_0=0 \) it is equal \( -\boldsymbol{b} \).
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="final-expressions">Final expressions </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>We can compute the residual iteratively as</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_{k+1}=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_{k+1},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>which equals</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{b}-\boldsymbol{A}(\boldsymbol{x}_k+\alpha_k\boldsymbol{r}_k),
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>or</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
(\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k)-\alpha_k\boldsymbol{A}\boldsymbol{r}_k,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>which gives</p>
|
||||
|
||||
$$
|
||||
\alpha_k = \frac{\boldsymbol{r}_k^T\boldsymbol{r}_k}{\boldsymbol{r}_k^T\boldsymbol{A}\boldsymbol{r}_k}
|
||||
$$
|
||||
|
||||
<p>leading to the iterative scheme</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_{k+1}=\boldsymbol{x}_k-\alpha_k\boldsymbol{r}_{k},
|
||||
\end{equation*}
|
||||
$$
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="steepest-descent-example">Steepest descent example </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">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy.linalg</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">la</span>
|
||||
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scipy.optimize</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sopt</span>
|
||||
|
||||
<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">pt</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">mpl_toolkits.mplot3d</span> <span style="color: #008000; font-weight: bold">import</span> axes3d
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f</span>(x):
|
||||
<span style="color: #008000; font-weight: bold">return</span> x[<span style="color: #666666">0</span>]<span style="color: #666666">**2</span> <span style="color: #666666">+</span> <span style="color: #666666">3.0*</span>x[<span style="color: #666666">1</span>]<span style="color: #666666">**2</span>
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">df</span>(x):
|
||||
<span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">2*</span>x[<span style="color: #666666">0</span>], <span style="color: #666666">6*</span>x[<span style="color: #666666">1</span>]])
|
||||
|
||||
fig <span style="color: #666666">=</span> pt<span style="color: #666666">.</span>figure()
|
||||
ax <span style="color: #666666">=</span> fig<span style="color: #666666">.</span>gca(projection<span style="color: #666666">=</span><span style="color: #BA2121">"3d"</span>)
|
||||
|
||||
xmesh, ymesh <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mgrid[<span style="color: #666666">-3</span>:<span style="color: #666666">3</span>:<span style="color: #666666">50</span>j,<span style="color: #666666">-3</span>:<span style="color: #666666">3</span>:<span style="color: #666666">50</span>j]
|
||||
fmesh <span style="color: #666666">=</span> f(np<span style="color: #666666">.</span>array([xmesh, ymesh]))
|
||||
ax<span style="color: #666666">.</span>plot_surface(xmesh, ymesh, fmesh)
|
||||
</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>And then as countor plot</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%;">pt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">"equal"</span>)
|
||||
pt<span style="color: #666666">.</span>contour(xmesh, ymesh, fmesh)
|
||||
guesses <span style="color: #666666">=</span> [np<span style="color: #666666">.</span>array([<span style="color: #666666">2</span>, <span style="color: #666666">2./5</span>])]
|
||||
</pre>
|
||||
</div>
|
||||
</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>Find guesses</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%;">x <span style="color: #666666">=</span> guesses[<span style="color: #666666">-1</span>]
|
||||
s <span style="color: #666666">=</span> <span style="color: #666666">-</span>df(x)
|
||||
</pre>
|
||||
</div>
|
||||
</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>Run it!</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">def</span> <span style="color: #0000FF">f1d</span>(alpha):
|
||||
<span style="color: #008000; font-weight: bold">return</span> f(x <span style="color: #666666">+</span> alpha<span style="color: #666666">*</span>s)
|
||||
|
||||
alpha_opt <span style="color: #666666">=</span> sopt<span style="color: #666666">.</span>golden(f1d)
|
||||
next_guess <span style="color: #666666">=</span> x <span style="color: #666666">+</span> alpha_opt <span style="color: #666666">*</span> s
|
||||
guesses<span style="color: #666666">.</span>append(next_guess)
|
||||
<span style="color: #008000">print</span>(next_guess)
|
||||
</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>What happened?</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%;">pt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">"equal"</span>)
|
||||
pt<span style="color: #666666">.</span>contour(xmesh, ymesh, fmesh, <span style="color: #666666">50</span>)
|
||||
it_array <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array(guesses)
|
||||
pt<span style="color: #666666">.</span>plot(it_array<span style="color: #666666">.</span>T[<span style="color: #666666">0</span>], it_array<span style="color: #666666">.</span>T[<span style="color: #666666">1</span>], <span style="color: #BA2121">"x-"</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>Note that we did only one iteration here. We can easily add more using our previous guesses.</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>In the CG method we define so-called conjugate directions and two vectors
|
||||
\( \boldsymbol{s} \) and \( \boldsymbol{t} \)
|
||||
are said to be
|
||||
conjugate if
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{s}^T\boldsymbol{A}\boldsymbol{t}= 0.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>The philosophy of the CG method is to perform searches in various conjugate directions
|
||||
of our vectors \( \boldsymbol{x}_i \) obeying the above criterion, namely
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_i^T\boldsymbol{A}\boldsymbol{x}_j= 0.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>Two vectors are conjugate if they are orthogonal with respect to
|
||||
this inner product. Being conjugate is a symmetric relation: if \( \boldsymbol{s} \) is conjugate to \( \boldsymbol{t} \), then \( \boldsymbol{t} \) is conjugate to \( \boldsymbol{s} \).
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>An example is given by the eigenvectors of the matrix</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{v}_i^T\boldsymbol{A}\boldsymbol{v}_j= \lambda\boldsymbol{v}_i^T\boldsymbol{v}_j,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>which is zero unless \( i=j \). </p>
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>Assume now that we have a symmetric positive-definite matrix \( \boldsymbol{A} \) of size
|
||||
\( n\times n \). At each iteration \( i+1 \) we obtain the conjugate direction of a vector
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_{i+1}=\boldsymbol{x}_{i}+\alpha_i\boldsymbol{p}_{i}.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>We assume that \( \boldsymbol{p}_{i} \) is a sequence of \( n \) mutually conjugate directions.
|
||||
Then the \( \boldsymbol{p}_{i} \) form a basis of \( R^n \) and we can expand the solution
|
||||
$ \boldsymbol{A}\boldsymbol{x} = \boldsymbol{b}$ in this basis, namely
|
||||
</p>
|
||||
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x} = \sum^{n}_{i=1} \alpha_i \boldsymbol{p}_i.
|
||||
\end{equation*}
|
||||
$$
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>The coefficients are given by</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\mathbf{A}\mathbf{x} = \sum^{n}_{i=1} \alpha_i \mathbf{A} \mathbf{p}_i = \mathbf{b}.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>Multiplying with \( \boldsymbol{p}_k^T \) from the left gives</p>
|
||||
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{x} = \sum^{n}_{i=1} \alpha_i\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{p}_i= \boldsymbol{p}_k^T \boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>and we can define the coefficients \( \alpha_k \) as</p>
|
||||
|
||||
$$
|
||||
\begin{equation*}
|
||||
\alpha_k = \frac{\boldsymbol{p}_k^T \boldsymbol{b}}{\boldsymbol{p}_k^T \boldsymbol{A} \boldsymbol{p}_k}
|
||||
\end{equation*}
|
||||
$$
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method-and-iterations">Conjugate gradient method and iterations </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
|
||||
<p>If we choose the conjugate vectors \( \boldsymbol{p}_k \) carefully,
|
||||
then we may not need all of them to obtain a good approximation to the solution
|
||||
\( \boldsymbol{x} \).
|
||||
We want to regard the conjugate gradient method as an iterative method.
|
||||
This will us to solve systems where \( n \) is so large that the direct
|
||||
method would take too much time.
|
||||
</p>
|
||||
|
||||
<p>We denote the initial guess for \( \boldsymbol{x} \) as \( \boldsymbol{x}_0 \).
|
||||
We can assume without loss of generality that
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{x}_0=0,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>or consider the system</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{z} = \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_0,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>instead.</p>
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>One can show that the solution \( \boldsymbol{x} \) is also the unique minimizer of the quadratic form</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
f(\boldsymbol{x}) = \frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T \boldsymbol{x} , \quad \boldsymbol{x}\in\mathbf{R}^n.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>This suggests taking the first basis vector \( \boldsymbol{p}_1 \)
|
||||
to be the gradient of \( f \) at \( \boldsymbol{x}=\boldsymbol{x}_0 \),
|
||||
which equals
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{A}\boldsymbol{x}_0-\boldsymbol{b},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>and
|
||||
\( \boldsymbol{x}_0=0 \) it is equal \( -\boldsymbol{b} \).
|
||||
The other vectors in the basis will be conjugate to the gradient,
|
||||
hence the name conjugate gradient method.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>Let \( \boldsymbol{r}_k \) be the residual at the \( k \)-th step:</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_k=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k.
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>Note that \( \boldsymbol{r}_k \) is the negative gradient of \( f \) at
|
||||
\( \boldsymbol{x}=\boldsymbol{x}_k \),
|
||||
so the gradient descent method would be to move in the direction \( \boldsymbol{r}_k \).
|
||||
Here, we insist that the directions \( \boldsymbol{p}_k \) are conjugate to each other,
|
||||
so we take the direction closest to the gradient \( \boldsymbol{r}_k \)
|
||||
under the conjugacy constraint.
|
||||
This gives the following expression
|
||||
</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{p}_{k+1}=\boldsymbol{r}_k-\frac{\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{r}_k}{\boldsymbol{p}_k^T\boldsymbol{A}\boldsymbol{p}_k} \boldsymbol{p}_k.
|
||||
\end{equation*}
|
||||
$$
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="conjugate-gradient-method">Conjugate gradient method </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<p>We can also compute the residual iteratively as</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_{k+1}=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_{k+1},
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>which equals</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{b}-\boldsymbol{A}(\boldsymbol{x}_k+\alpha_k\boldsymbol{p}_k),
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>or</p>
|
||||
$$
|
||||
\begin{equation*}
|
||||
(\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k)-\alpha_k\boldsymbol{A}\boldsymbol{p}_k,
|
||||
\end{equation*}
|
||||
$$
|
||||
|
||||
<p>which gives</p>
|
||||
|
||||
$$
|
||||
\begin{equation*}
|
||||
\boldsymbol{r}_{k+1}=\boldsymbol{r}_k-\boldsymbol{A}\boldsymbol{p}_{k},
|
||||
\end{equation*}
|
||||
$$
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split -->
|
||||
<h2 id="revisiting-our-first-homework">Revisiting our first homework </h2>
|
||||
|
||||
|
||||
Binary file not shown.
+204
-1162
File diff suppressed because it is too large
Load Diff
@@ -1050,8 +1050,6 @@ print(X_test.shape)
|
||||
# Logistic Regression
|
||||
logreg = LogisticRegression(solver='lbfgs')
|
||||
logreg.fit(X_train, y_train)
|
||||
print("Test set accuracy with Logistic Regression: {:.2f}".format(logreg.score(X_test,y_test)))
|
||||
|
||||
|
||||
from sklearn.preprocessing import LabelEncoder
|
||||
from sklearn.model_selection import cross_validate
|
||||
@@ -1060,7 +1058,6 @@ accuracy = cross_validate(logreg,X_test,y_test,cv=10)['test_score']
|
||||
print(accuracy)
|
||||
print("Test set accuracy with Logistic Regression: {:.2f}".format(logreg.score(X_test,y_test)))
|
||||
|
||||
|
||||
import scikitplot as skplt
|
||||
y_pred = logreg.predict(X_test)
|
||||
skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
|
||||
@@ -1527,374 +1524,6 @@ Using the definition of convexity, try to show that a function satisfying the pr
|
||||
|
||||
|
||||
|
||||
!split
|
||||
===== Standard steepest descent =====
|
||||
|
||||
|
||||
Before we proceed, we would like to discuss the approach called the
|
||||
_standard Steepest descent_ (different from the above steepest descent discussion), which again leads to us having to be able
|
||||
to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).
|
||||
|
||||
"The success of the CG method":"https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf"
|
||||
for finding solutions of non-linear problems is based on the theory
|
||||
of conjugate gradients for linear systems of equations. It belongs to
|
||||
the class of iterative methods for solving problems from linear
|
||||
algebra of the type
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{A}\bm{x} = \bm{b}.
|
||||
\end{equation*}
|
||||
!et
|
||||
|
||||
In the iterative process we end up with a problem like
|
||||
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{r}= \bm{b}-\bm{A}\bm{x},
|
||||
\end{equation*}
|
||||
!et
|
||||
where $\bm{r}$ is the so-called residual or error in the iterative process.
|
||||
|
||||
When we have found the exact solution, $\bm{r}=0$.
|
||||
|
||||
!split
|
||||
===== Gradient method =====
|
||||
|
||||
The residual is zero when we reach the minimum of the quadratic equation
|
||||
!bt
|
||||
\begin{equation*}
|
||||
P(\bm{x})=\frac{1}{2}\bm{x}^T\bm{A}\bm{x} - \bm{x}^T\bm{b},
|
||||
\end{equation*}
|
||||
!et
|
||||
|
||||
with the constraint that the matrix $\bm{A}$ is positive definite and
|
||||
symmetric. This defines also the Hessian and we want it to be positive definite.
|
||||
|
||||
|
||||
!split
|
||||
===== Steepest descent method =====
|
||||
|
||||
We denote the initial guess for $\bm{x}$ as $\bm{x}_0$.
|
||||
We can assume without loss of generality that
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{x}_0=0,
|
||||
\end{equation*}
|
||||
!et
|
||||
or consider the system
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{A}\bm{z} = \bm{b}-\bm{A}\bm{x}_0,
|
||||
\end{equation*}
|
||||
!et
|
||||
instead.
|
||||
|
||||
|
||||
!split
|
||||
===== Steepest descent method =====
|
||||
!bblock
|
||||
One can show that the solution $\bm{x}$ is also the unique minimizer of the quadratic form
|
||||
!bt
|
||||
\begin{equation*}
|
||||
f(\bm{x}) = \frac{1}{2}\bm{x}^T\bm{A}\bm{x} - \bm{x}^T \bm{x} , \quad \bm{x}\in\mathbf{R}^n.
|
||||
\end{equation*}
|
||||
!et
|
||||
This suggests taking the first basis vector $\bm{r}_1$ (see below for definition)
|
||||
to be the gradient of $f$ at $\bm{x}=\bm{x}_0$,
|
||||
which equals
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{A}\bm{x}_0-\bm{b},
|
||||
\end{equation*}
|
||||
!et
|
||||
and
|
||||
$\bm{x}_0=0$ it is equal $-\bm{b}$.
|
||||
|
||||
!eblock
|
||||
|
||||
!split
|
||||
===== Final expressions =====
|
||||
!bblock
|
||||
We can compute the residual iteratively as
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{r}_{k+1}=\bm{b}-\bm{A}\bm{x}_{k+1},
|
||||
\end{equation*}
|
||||
!et
|
||||
which equals
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{b}-\bm{A}(\bm{x}_k+\alpha_k\bm{r}_k),
|
||||
\end{equation*}
|
||||
!et
|
||||
or
|
||||
!bt
|
||||
\begin{equation*}
|
||||
(\bm{b}-\bm{A}\bm{x}_k)-\alpha_k\bm{A}\bm{r}_k,
|
||||
\end{equation*}
|
||||
!et
|
||||
which gives
|
||||
|
||||
!bt
|
||||
\[
|
||||
\alpha_k = \frac{\bm{r}_k^T\bm{r}_k}{\bm{r}_k^T\bm{A}\bm{r}_k}
|
||||
\]
|
||||
!et
|
||||
leading to the iterative scheme
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{x}_{k+1}=\bm{x}_k-\alpha_k\bm{r}_{k},
|
||||
\end{equation*}
|
||||
!et
|
||||
!eblock
|
||||
|
||||
|
||||
|
||||
!split
|
||||
===== Steepest descent example =====
|
||||
|
||||
!bc pycod
|
||||
import numpy as np
|
||||
import numpy.linalg as la
|
||||
|
||||
import scipy.optimize as sopt
|
||||
|
||||
import matplotlib.pyplot as pt
|
||||
from mpl_toolkits.mplot3d import axes3d
|
||||
|
||||
def f(x):
|
||||
return x[0]**2 + 3.0*x[1]**2
|
||||
|
||||
def df(x):
|
||||
return np.array([2*x[0], 6*x[1]])
|
||||
|
||||
fig = pt.figure()
|
||||
ax = fig.gca(projection="3d")
|
||||
|
||||
xmesh, ymesh = np.mgrid[-3:3:50j,-3:3:50j]
|
||||
fmesh = f(np.array([xmesh, ymesh]))
|
||||
ax.plot_surface(xmesh, ymesh, fmesh)
|
||||
!ec
|
||||
And then as countor plot
|
||||
!bc pycod
|
||||
pt.axis("equal")
|
||||
pt.contour(xmesh, ymesh, fmesh)
|
||||
guesses = [np.array([2, 2./5])]
|
||||
!ec
|
||||
Find guesses
|
||||
!bc pycod
|
||||
x = guesses[-1]
|
||||
s = -df(x)
|
||||
!ec
|
||||
Run it!
|
||||
!bc pycod
|
||||
def f1d(alpha):
|
||||
return f(x + alpha*s)
|
||||
|
||||
alpha_opt = sopt.golden(f1d)
|
||||
next_guess = x + alpha_opt * s
|
||||
guesses.append(next_guess)
|
||||
print(next_guess)
|
||||
!ec
|
||||
What happened?
|
||||
!bc pycod
|
||||
pt.axis("equal")
|
||||
pt.contour(xmesh, ymesh, fmesh, 50)
|
||||
it_array = np.array(guesses)
|
||||
pt.plot(it_array.T[0], it_array.T[1], "x-")
|
||||
!ec
|
||||
|
||||
Note that we did only one iteration here. We can easily add more using our previous guesses.
|
||||
|
||||
!split
|
||||
===== Conjugate gradient method =====
|
||||
!bblock
|
||||
In the CG method we define so-called conjugate directions and two vectors
|
||||
$\bm{s}$ and $\bm{t}$
|
||||
are said to be
|
||||
conjugate if
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{s}^T\bm{A}\bm{t}= 0.
|
||||
\end{equation*}
|
||||
!et
|
||||
The philosophy of the CG method is to perform searches in various conjugate directions
|
||||
of our vectors $\bm{x}_i$ obeying the above criterion, namely
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{x}_i^T\bm{A}\bm{x}_j= 0.
|
||||
\end{equation*}
|
||||
!et
|
||||
Two vectors are conjugate if they are orthogonal with respect to
|
||||
this inner product. Being conjugate is a symmetric relation: if $\bm{s}$ is conjugate to $\bm{t}$, then $\bm{t}$ is conjugate to $\bm{s}$.
|
||||
!eblock
|
||||
|
||||
!split
|
||||
===== Conjugate gradient method =====
|
||||
!bblock
|
||||
An example is given by the eigenvectors of the matrix
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{v}_i^T\bm{A}\bm{v}_j= \lambda\bm{v}_i^T\bm{v}_j,
|
||||
\end{equation*}
|
||||
!et
|
||||
which is zero unless $i=j$.
|
||||
!eblock
|
||||
|
||||
|
||||
!split
|
||||
===== Conjugate gradient method =====
|
||||
!bblock
|
||||
Assume now that we have a symmetric positive-definite matrix $\bm{A}$ of size
|
||||
$n\times n$. At each iteration $i+1$ we obtain the conjugate direction of a vector
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{x}_{i+1}=\bm{x}_{i}+\alpha_i\bm{p}_{i}.
|
||||
\end{equation*}
|
||||
!et
|
||||
We assume that $\bm{p}_{i}$ is a sequence of $n$ mutually conjugate directions.
|
||||
Then the $\bm{p}_{i}$ form a basis of $R^n$ and we can expand the solution
|
||||
$ \bm{A}\bm{x} = \bm{b}$ in this basis, namely
|
||||
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{x} = \sum^{n}_{i=1} \alpha_i \bm{p}_i.
|
||||
\end{equation*}
|
||||
!et
|
||||
!eblock
|
||||
|
||||
!split
|
||||
===== Conjugate gradient method =====
|
||||
!bblock
|
||||
The coefficients are given by
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\mathbf{A}\mathbf{x} = \sum^{n}_{i=1} \alpha_i \mathbf{A} \mathbf{p}_i = \mathbf{b}.
|
||||
\end{equation*}
|
||||
!et
|
||||
Multiplying with $\bm{p}_k^T$ from the left gives
|
||||
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{p}_k^T \bm{A}\bm{x} = \sum^{n}_{i=1} \alpha_i\bm{p}_k^T \bm{A}\bm{p}_i= \bm{p}_k^T \bm{b},
|
||||
\end{equation*}
|
||||
!et
|
||||
and we can define the coefficients $\alpha_k$ as
|
||||
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\alpha_k = \frac{\bm{p}_k^T \bm{b}}{\bm{p}_k^T \bm{A} \bm{p}_k}
|
||||
\end{equation*}
|
||||
!et
|
||||
!eblock
|
||||
|
||||
!split
|
||||
===== Conjugate gradient method and iterations =====
|
||||
!bblock
|
||||
|
||||
If we choose the conjugate vectors $\bm{p}_k$ carefully,
|
||||
then we may not need all of them to obtain a good approximation to the solution
|
||||
$\bm{x}$.
|
||||
We want to regard the conjugate gradient method as an iterative method.
|
||||
This will us to solve systems where $n$ is so large that the direct
|
||||
method would take too much time.
|
||||
|
||||
We denote the initial guess for $\bm{x}$ as $\bm{x}_0$.
|
||||
We can assume without loss of generality that
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{x}_0=0,
|
||||
\end{equation*}
|
||||
!et
|
||||
or consider the system
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{A}\bm{z} = \bm{b}-\bm{A}\bm{x}_0,
|
||||
\end{equation*}
|
||||
!et
|
||||
instead.
|
||||
!eblock
|
||||
|
||||
|
||||
!split
|
||||
===== Conjugate gradient method =====
|
||||
!bblock
|
||||
One can show that the solution $\bm{x}$ is also the unique minimizer of the quadratic form
|
||||
!bt
|
||||
\begin{equation*}
|
||||
f(\bm{x}) = \frac{1}{2}\bm{x}^T\bm{A}\bm{x} - \bm{x}^T \bm{x} , \quad \bm{x}\in\mathbf{R}^n.
|
||||
\end{equation*}
|
||||
!et
|
||||
This suggests taking the first basis vector $\bm{p}_1$
|
||||
to be the gradient of $f$ at $\bm{x}=\bm{x}_0$,
|
||||
which equals
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{A}\bm{x}_0-\bm{b},
|
||||
\end{equation*}
|
||||
!et
|
||||
and
|
||||
$\bm{x}_0=0$ it is equal $-\bm{b}$.
|
||||
The other vectors in the basis will be conjugate to the gradient,
|
||||
hence the name conjugate gradient method.
|
||||
!eblock
|
||||
|
||||
|
||||
!split
|
||||
===== Conjugate gradient method =====
|
||||
!bblock
|
||||
Let $\bm{r}_k$ be the residual at the $k$-th step:
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{r}_k=\bm{b}-\bm{A}\bm{x}_k.
|
||||
\end{equation*}
|
||||
!et
|
||||
Note that $\bm{r}_k$ is the negative gradient of $f$ at
|
||||
$\bm{x}=\bm{x}_k$,
|
||||
so the gradient descent method would be to move in the direction $\bm{r}_k$.
|
||||
Here, we insist that the directions $\bm{p}_k$ are conjugate to each other,
|
||||
so we take the direction closest to the gradient $\bm{r}_k$
|
||||
under the conjugacy constraint.
|
||||
This gives the following expression
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{p}_{k+1}=\bm{r}_k-\frac{\bm{p}_k^T \bm{A}\bm{r}_k}{\bm{p}_k^T\bm{A}\bm{p}_k} \bm{p}_k.
|
||||
\end{equation*}
|
||||
!et
|
||||
!eblock
|
||||
|
||||
!split
|
||||
===== Conjugate gradient method =====
|
||||
!bblock
|
||||
We can also compute the residual iteratively as
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{r}_{k+1}=\bm{b}-\bm{A}\bm{x}_{k+1},
|
||||
\end{equation*}
|
||||
!et
|
||||
which equals
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{b}-\bm{A}(\bm{x}_k+\alpha_k\bm{p}_k),
|
||||
\end{equation*}
|
||||
!et
|
||||
or
|
||||
!bt
|
||||
\begin{equation*}
|
||||
(\bm{b}-\bm{A}\bm{x}_k)-\alpha_k\bm{A}\bm{p}_k,
|
||||
\end{equation*}
|
||||
!et
|
||||
which gives
|
||||
|
||||
!bt
|
||||
\begin{equation*}
|
||||
\bm{r}_{k+1}=\bm{r}_k-\bm{A}\bm{p}_{k},
|
||||
\end{equation*}
|
||||
!et
|
||||
!eblock
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
!split
|
||||
|
||||
Reference in New Issue
Block a user