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took out a slide

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This commit is contained in:
Morten Hjorth-Jensen
2022-09-16 05:33:02 +02:00
parent c6d0149a1e
commit 752205a959
55 changed files with 584 additions and 964 deletions
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doc/pub/week37/html/._week37-bs000.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -309,7 +304,7 @@ MathJax.Hub.Config({
<li><a href="._week37-bs008.html">9</a></li>
<li><a href="._week37-bs009.html">10</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs001.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs001.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -298,7 +293,7 @@ MathJax.Hub.Config({
<li><a href="._week37-bs009.html">10</a></li>
<li><a href="._week37-bs010.html">11</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs002.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs002.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -285,7 +280,7 @@ MathJax.Hub.Config({
<li><a href="._week37-bs010.html">11</a></li>
<li><a href="._week37-bs011.html">12</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs003.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs003.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -306,7 +301,7 @@ $$
<li><a href="._week37-bs011.html">12</a></li>
<li><a href="._week37-bs012.html">13</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs004.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs004.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -318,7 +313,7 @@ $$
<li><a href="._week37-bs012.html">13</a></li>
<li><a href="._week37-bs013.html">14</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs005.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs005.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -313,7 +308,7 @@ is equivalent to the maximization/minimization of the function itself.
<li><a href="._week37-bs013.html">14</a></li>
<li><a href="._week37-bs014.html">15</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs006.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs006.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -312,7 +307,7 @@ $$
<li><a href="._week37-bs014.html">15</a></li>
<li><a href="._week37-bs015.html">16</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs007.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs007.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -303,7 +298,7 @@ $$
<li><a href="._week37-bs015.html">16</a></li>
<li><a href="._week37-bs016.html">17</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs008.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs008.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -299,7 +294,7 @@ necesseraly normalized and is normally called the likelihood function.
<li><a href="._week37-bs016.html">17</a></li>
<li><a href="._week37-bs017.html">18</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs009.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs009.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -388,7 +383,7 @@ plt<span style="color: #666666">.</span>show()
<li><a href="._week37-bs017.html">18</a></li>
<li><a href="._week37-bs018.html">19</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs010.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs010.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -376,7 +371,7 @@ lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</
<li><a href="._week37-bs018.html">19</a></li>
<li><a href="._week37-bs019.html">20</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs011.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs011.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -318,7 +313,7 @@ $$
<li><a href="._week37-bs019.html">20</a></li>
<li><a href="._week37-bs020.html">21</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs012.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs012.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -327,7 +322,7 @@ $$
<li><a href="._week37-bs020.html">21</a></li>
<li><a href="._week37-bs021.html">22</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs013.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs013.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -321,7 +316,7 @@ $$
<li><a href="._week37-bs021.html">22</a></li>
<li><a href="._week37-bs022.html">23</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs014.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs014.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -303,7 +298,7 @@ our regression analysis. In what follows we will
<li><a href="._week37-bs022.html">23</a></li>
<li><a href="._week37-bs023.html">24</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs015.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs015.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -319,7 +314,7 @@ cross-validation and the bootstrap method.
<li><a href="._week37-bs023.html">24</a></li>
<li><a href="._week37-bs024.html">25</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs016.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs016.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -316,7 +311,7 @@ bootstrap is widely used.
<li><a href="._week37-bs024.html">25</a></li>
<li><a href="._week37-bs025.html">26</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs017.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs017.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -305,7 +300,7 @@ MathJax.Hub.Config({
<li><a href="._week37-bs025.html">26</a></li>
<li><a href="._week37-bs026.html">27</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs018.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs018.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -309,7 +304,7 @@ MathJax.Hub.Config({
<li><a href="._week37-bs026.html">27</a></li>
<li><a href="._week37-bs027.html">28</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs019.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs019.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -316,7 +311,7 @@ training error reaches a saturation.
<li><a href="._week37-bs027.html">28</a></li>
<li><a href="._week37-bs028.html">29</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs020.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs020.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -311,7 +306,7 @@ need for bootstrapping.
<li><a href="._week37-bs028.html">29</a></li>
<li><a href="._week37-bs029.html">30</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs021.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs021.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -307,7 +302,7 @@ number \( i \) is left out. Using this notation, define
<li><a href="._week37-bs029.html">30</a></li>
<li><a href="._week37-bs030.html">31</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs022.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs022.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -343,7 +338,7 @@ t <span style="color: #666666">=</span> jackknife(x, stat)
<li><a href="._week37-bs030.html">31</a></li>
<li><a href="._week37-bs031.html">32</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs023.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs023.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -314,7 +309,7 @@ advantages:
<li><a href="._week37-bs031.html">32</a></li>
<li><a href="._week37-bs032.html">33</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs024.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs024.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -309,7 +304,7 @@ $$
<li><a href="._week37-bs032.html">33</a></li>
<li><a href="._week37-bs033.html">34</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs025.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs025.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -309,7 +304,7 @@ product of individual \( p(x_i) \). The independence assumption is important in
<li><a href="._week37-bs033.html">34</a></li>
<li><a href="._week37-bs034.html">35</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs026.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs026.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -318,7 +313,7 @@ $$
<li><a href="._week37-bs034.html">35</a></li>
<li><a href="._week37-bs035.html">36</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs027.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs027.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -320,7 +315,7 @@ and \( \mu \) is also the mean of the PDF \( p(x) \).
<li><a href="._week37-bs035.html">36</a></li>
<li><a href="._week37-bs036.html">37</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs028.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs028.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -332,7 +327,7 @@ finite \( m \), it is not always possible to find a closed form /analytic expres
<li><a href="._week37-bs036.html">37</a></li>
<li><a href="._week37-bs037.html">38</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs029.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs029.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -310,7 +305,7 @@ construct a confidence interval for the estimates.
<li><a href="._week37-bs037.html">38</a></li>
<li><a href="._week37-bs038.html">39</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs030.html">&raquo;</a></li>
</ul>
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doc/pub/week37/html/._week37-bs030.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -317,7 +312,7 @@ Bootstrap method, why it works and various theorems related to it.
<li><a href="._week37-bs038.html">39</a></li>
<li><a href="._week37-bs039.html">40</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs031.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs031.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -304,7 +299,7 @@ estimators.
<li><a href="._week37-bs039.html">40</a></li>
<li><a href="._week37-bs040.html">41</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs032.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs032.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -309,7 +304,7 @@ idea is to use the relative frequency of \( \widehat{\beta}^* \)
<li><a href="._week37-bs040.html">41</a></li>
<li><a href="._week37-bs041.html">42</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs033.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs033.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -306,7 +301,7 @@ result in some asymptotic sense? The answer is yes.
<li><a href="._week37-bs041.html">42</a></li>
<li><a href="._week37-bs042.html">43</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs034.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs034.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -312,7 +307,7 @@ example, if you are interested in estimating the variance of \( \widehat
<li><a href="._week37-bs042.html">43</a></li>
<li><a href="._week37-bs043.html">44</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs035.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs035.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -357,7 +352,7 @@ t <span style="color: #666666">=</span> bootstrap(x, datapoints)
<li><a href="._week37-bs043.html">44</a></li>
<li><a href="._week37-bs044.html">45</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs036.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs036.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -324,7 +319,7 @@ plt<span style="color: #666666">.</span>show()
<li><a href="._week37-bs044.html">45</a></li>
<li><a href="._week37-bs045.html">46</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs037.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs037.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -350,7 +345,7 @@ $$
<li><a href="._week37-bs045.html">46</a></li>
<li><a href="._week37-bs046.html">47</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs038.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs038.html
+4 -11
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -298,8 +293,6 @@ MathJax.Hub.Config({
<li><a href="._week37-bs045.html">46</a></li>
<li><a href="._week37-bs046.html">47</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs039.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs039.html
+4 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -367,7 +362,6 @@ plt<span style="color: #666666">.</span>show()
<li><a href="._week37-bs045.html">46</a></li>
<li><a href="._week37-bs046.html">47</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs040.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs040.html
+4 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -358,7 +353,6 @@ plt<span style="color: #666666">.</span>show()
<li><a href="._week37-bs045.html">46</a></li>
<li><a href="._week37-bs046.html">47</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs041.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs041.html
+4 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -320,7 +315,6 @@ flexible statistical methods have higher variance.
<li><a href="._week37-bs045.html">46</a></li>
<li><a href="._week37-bs046.html">47</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs042.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs042.html
+4 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -381,7 +376,6 @@ plt<span style="color: #666666">.</span>show()
<li><a href="._week37-bs045.html">46</a></li>
<li><a href="._week37-bs046.html">47</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs043.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs043.html
+4 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -303,7 +298,6 @@ cross-validation (LOOCV).
<li><a href="._week37-bs045.html">46</a></li>
<li><a href="._week37-bs046.html">47</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs044.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs044.html
+19 -37
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -265,35 +260,23 @@ MathJax.Hub.Config({
<div class="container">
<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
<a name="part0044"></a>
<!-- !split -->
<h2 id="how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" class="anchor">How to set up the cross-validation for Ridge and/or Lasso </h2>
<ul>
<li> Define a range of interest for the penalty parameter.</li>
<li> Divide the data set into training and test set comprising samples \( \{1, \ldots, n\} \setminus i \) and \( \{ i \} \), respectively.</li>
<li> Fit the linear regression model by means of ridge estimation for each \( \lambda \) in the grid using the training set, and the corresponding estimate of the error variance \( \boldsymbol{\sigma}_{-i}^2(\lambda) \), as</li>
</ul>
$$
\begin{align*}
\boldsymbol{\beta}_{-i}(\lambda) & = ( \boldsymbol{X}_{-i, \ast}^{T}
\boldsymbol{X}_{-i, \ast} + \lambda \boldsymbol{I}_{pp})^{-1}
\boldsymbol{X}_{-i, \ast}^{T} \boldsymbol{y}_{-i}
\end{align*}
$$
<ul>
<li> Evaluate the prediction performance of these models on the test set by \( [y_i, \boldsymbol{X}_{i, \ast}; \boldsymbol{\beta}_{-i}(\lambda), \boldsymbol{\sigma}_{-i}^2(\lambda)] \). Or, by the prediction error \( |y_i - \boldsymbol{X}_{i, \ast} \boldsymbol{\beta}_{-i}(\lambda)| \), the relative error, the error squared or the R2 score function.</li>
<li> Repeat the first three steps such that each sample plays the role of the test set once.</li>
<li> Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as</li>
</ul>
$$
\begin{align*}
\frac{1}{n} \sum_{i = 1}^n \log\{L[y_i, \mathbf{X}_{i, \ast}; \boldsymbol{\beta}_{-i}(\lambda), \boldsymbol{\sigma}_{-i}^2(\lambda)]\}.
\end{align*}
$$
<!-- !split -->
<h2 id="cross-validation-in-brief" class="anchor">Cross-validation in brief </h2>
<p>For the various values of \( k \)</p>
<ol>
<li> shuffle the dataset randomly.</li>
<li> Split the dataset into \( k \) groups.</li>
<li> For each unique group:
<ol type="a"></li>
<li> Decide which group to use as set for test data</li>
<li> Take the remaining groups as a training data set</li>
<li> Fit a model on the training set and evaluate it on the test set</li>
<li> Retain the evaluation score and discard the model</li>
</ol>
<li> Summarize the model using the sample of model evaluation scores</li>
</ol>
<p>
<!-- navigation buttons at the bottom of the page -->
<ul class="pagination">
@@ -312,7 +295,6 @@ $$
<li><a href="._week37-bs045.html">46</a></li>
<li><a href="._week37-bs046.html">47</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs045.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs045.html
+117 -24
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -266,22 +261,121 @@ MathJax.Hub.Config({
<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
<a name="part0045"></a>
<!-- !split -->
<h2 id="cross-validation-in-brief" class="anchor">Cross-validation in brief </h2>
<h2 id="code-example-for-cross-validation-and-k-fold-cross-validation" class="anchor">Code Example for Cross-validation and \( k \)-fold Cross-validation </h2>
<p>The code here uses Ridge regression with cross-validation (CV) resampling and \( k \)-fold CV in order to fit a specific polynomial. </p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="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">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> KFold
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> Ridge
<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_val_score
<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> PolynomialFeatures
<span style="color: #408080; font-style: italic"># A seed just to ensure that the random numbers are the same for every run.</span>
<span style="color: #408080; font-style: italic"># Useful for eventual debugging.</span>
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">3155</span>)
<span style="color: #408080; font-style: italic"># Generate the data.</span>
nsamples <span style="color: #666666">=</span> <span style="color: #666666">100</span>
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(nsamples)
y <span style="color: #666666">=</span> <span style="color: #666666">3*</span>x<span style="color: #666666">**2</span> <span style="color: #666666">+</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(nsamples)
<span style="color: #408080; font-style: italic">## Cross-validation on Ridge regression using KFold only</span>
<span style="color: #408080; font-style: italic"># Decide degree on polynomial to fit</span>
poly <span style="color: #666666">=</span> PolynomialFeatures(degree <span style="color: #666666">=</span> <span style="color: #666666">6</span>)
<span style="color: #408080; font-style: italic"># Decide which values of lambda to use</span>
nlambdas <span style="color: #666666">=</span> <span style="color: #666666">500</span>
lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-3</span>, <span style="color: #666666">5</span>, nlambdas)
<span style="color: #408080; font-style: italic"># Initialize a KFold instance</span>
k <span style="color: #666666">=</span> <span style="color: #666666">5</span>
kfold <span style="color: #666666">=</span> KFold(n_splits <span style="color: #666666">=</span> k)
<span style="color: #408080; font-style: italic"># Perform the cross-validation to estimate MSE</span>
scores_KFold <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((nlambdas, k))
i <span style="color: #666666">=</span> <span style="color: #666666">0</span>
<span style="color: #008000; font-weight: bold">for</span> lmb <span style="color: #AA22FF; font-weight: bold">in</span> lambdas:
ridge <span style="color: #666666">=</span> Ridge(alpha <span style="color: #666666">=</span> lmb)
j <span style="color: #666666">=</span> <span style="color: #666666">0</span>
<span style="color: #008000; font-weight: bold">for</span> train_inds, test_inds <span style="color: #AA22FF; font-weight: bold">in</span> kfold<span style="color: #666666">.</span>split(x):
xtrain <span style="color: #666666">=</span> x[train_inds]
ytrain <span style="color: #666666">=</span> y[train_inds]
xtest <span style="color: #666666">=</span> x[test_inds]
ytest <span style="color: #666666">=</span> y[test_inds]
Xtrain <span style="color: #666666">=</span> poly<span style="color: #666666">.</span>fit_transform(xtrain[:, np<span style="color: #666666">.</span>newaxis])
ridge<span style="color: #666666">.</span>fit(Xtrain, ytrain[:, np<span style="color: #666666">.</span>newaxis])
Xtest <span style="color: #666666">=</span> poly<span style="color: #666666">.</span>fit_transform(xtest[:, np<span style="color: #666666">.</span>newaxis])
ypred <span style="color: #666666">=</span> ridge<span style="color: #666666">.</span>predict(Xtest)
scores_KFold[i,j] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>sum((ypred <span style="color: #666666">-</span> ytest[:, np<span style="color: #666666">.</span>newaxis])<span style="color: #666666">**2</span>)<span style="color: #666666">/</span>np<span style="color: #666666">.</span>size(ypred)
j <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
i <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
estimated_mse_KFold <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean(scores_KFold, axis <span style="color: #666666">=</span> <span style="color: #666666">1</span>)
<span style="color: #408080; font-style: italic">## Cross-validation using cross_val_score from sklearn along with KFold</span>
<span style="color: #408080; font-style: italic"># kfold is an instance initialized above as:</span>
<span style="color: #408080; font-style: italic"># kfold = KFold(n_splits = k)</span>
estimated_mse_sklearn <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(nlambdas)
i <span style="color: #666666">=</span> <span style="color: #666666">0</span>
<span style="color: #008000; font-weight: bold">for</span> lmb <span style="color: #AA22FF; font-weight: bold">in</span> lambdas:
ridge <span style="color: #666666">=</span> Ridge(alpha <span style="color: #666666">=</span> lmb)
X <span style="color: #666666">=</span> poly<span style="color: #666666">.</span>fit_transform(x[:, np<span style="color: #666666">.</span>newaxis])
estimated_mse_folds <span style="color: #666666">=</span> cross_val_score(ridge, X, y[:, np<span style="color: #666666">.</span>newaxis], scoring<span style="color: #666666">=</span><span style="color: #BA2121">&#39;neg_mean_squared_error&#39;</span>, cv<span style="color: #666666">=</span>kfold)
<span style="color: #408080; font-style: italic"># cross_val_score return an array containing the estimated negative mse for every fold.</span>
<span style="color: #408080; font-style: italic"># we have to the the mean of every array in order to get an estimate of the mse of the model</span>
estimated_mse_sklearn[i] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean(<span style="color: #666666">-</span>estimated_mse_folds)
i <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
<span style="color: #408080; font-style: italic">## Plot and compare the slightly different ways to perform cross-validation</span>
plt<span style="color: #666666">.</span>figure()
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), estimated_mse_sklearn, label <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;cross_val_score&#39;</span>)
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), estimated_mse_KFold, <span style="color: #BA2121">&#39;r--&#39;</span>, label <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;KFold&#39;</span>)
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&#39;log10(lambda)&#39;</span>)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&#39;mse&#39;</span>)
plt<span style="color: #666666">.</span>legend()
plt<span style="color: #666666">.</span>show()
</pre>
</div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area">
<div class="output_subarea output_stream output_stdout output_text">
</div>
</div>
</div>
</div>
</div>
<p>For the various values of \( k \)</p>
<ol>
<li> shuffle the dataset randomly.</li>
<li> Split the dataset into \( k \) groups.</li>
<li> For each unique group:
<ol type="a"></li>
<li> Decide which group to use as set for test data</li>
<li> Take the remaining groups as a training data set</li>
<li> Fit a model on the training set and evaluate it on the test set</li>
<li> Retain the evaluation score and discard the model</li>
</ol>
<li> Summarize the model using the sample of model evaluation scores</li>
</ol>
<p>
<!-- navigation buttons at the bottom of the page -->
<ul class="pagination">
@@ -299,7 +393,6 @@ MathJax.Hub.Config({
<li class="active"><a href="._week37-bs045.html">46</a></li>
<li><a href="._week37-bs046.html">47</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs046.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs046.html
+68 -85
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -266,9 +261,8 @@ MathJax.Hub.Config({
<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
<a name="part0046"></a>
<!-- !split -->
<h2 id="code-example-for-cross-validation-and-k-fold-cross-validation" class="anchor">Code Example for Cross-validation and \( k \)-fold Cross-validation </h2>
<h2 id="more-examples-on-bootstrap-and-cross-validation-and-errors" class="anchor">More examples on bootstrap and cross-validation and errors </h2>
<p>The code here uses Ridge regression with cross-validation (CV) resampling and \( k \)-fold CV in order to fit a specific polynomial. </p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="cell border-box-sizing code_cell rendered">
@@ -276,94 +270,83 @@ MathJax.Hub.Config({
<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>
<pre style="line-height: 125%;"><span style="color: #408080; font-style: italic"># Common imports</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">os</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> KFold
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> Ridge
<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_val_score
<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> PolynomialFeatures
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LinearRegression, Ridge, Lasso
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.utils</span> <span style="color: #008000; font-weight: bold">import</span> resample
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.metrics</span> <span style="color: #008000; font-weight: bold">import</span> mean_squared_error
<span style="color: #408080; font-style: italic"># Where to save the figures and data files</span>
PROJECT_ROOT_DIR <span style="color: #666666">=</span> <span style="color: #BA2121">&quot;Results&quot;</span>
FIGURE_ID <span style="color: #666666">=</span> <span style="color: #BA2121">&quot;Results/FigureFiles&quot;</span>
DATA_ID <span style="color: #666666">=</span> <span style="color: #BA2121">&quot;DataFiles/&quot;</span>
<span style="color: #408080; font-style: italic"># A seed just to ensure that the random numbers are the same for every run.</span>
<span style="color: #408080; font-style: italic"># Useful for eventual debugging.</span>
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">3155</span>)
<span style="color: #008000; font-weight: bold">if</span> <span style="color: #AA22FF; font-weight: bold">not</span> os<span style="color: #666666">.</span>path<span style="color: #666666">.</span>exists(PROJECT_ROOT_DIR):
os<span style="color: #666666">.</span>mkdir(PROJECT_ROOT_DIR)
<span style="color: #408080; font-style: italic"># Generate the data.</span>
nsamples <span style="color: #666666">=</span> <span style="color: #666666">100</span>
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(nsamples)
y <span style="color: #666666">=</span> <span style="color: #666666">3*</span>x<span style="color: #666666">**2</span> <span style="color: #666666">+</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(nsamples)
<span style="color: #008000; font-weight: bold">if</span> <span style="color: #AA22FF; font-weight: bold">not</span> os<span style="color: #666666">.</span>path<span style="color: #666666">.</span>exists(FIGURE_ID):
os<span style="color: #666666">.</span>makedirs(FIGURE_ID)
<span style="color: #408080; font-style: italic">## Cross-validation on Ridge regression using KFold only</span>
<span style="color: #008000; font-weight: bold">if</span> <span style="color: #AA22FF; font-weight: bold">not</span> os<span style="color: #666666">.</span>path<span style="color: #666666">.</span>exists(DATA_ID):
os<span style="color: #666666">.</span>makedirs(DATA_ID)
<span style="color: #408080; font-style: italic"># Decide degree on polynomial to fit</span>
poly <span style="color: #666666">=</span> PolynomialFeatures(degree <span style="color: #666666">=</span> <span style="color: #666666">6</span>)
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">image_path</span>(fig_id):
<span style="color: #008000; font-weight: bold">return</span> os<span style="color: #666666">.</span>path<span style="color: #666666">.</span>join(FIGURE_ID, fig_id)
<span style="color: #408080; font-style: italic"># Decide which values of lambda to use</span>
nlambdas <span style="color: #666666">=</span> <span style="color: #666666">500</span>
lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-3</span>, <span style="color: #666666">5</span>, nlambdas)
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">data_path</span>(dat_id):
<span style="color: #008000; font-weight: bold">return</span> os<span style="color: #666666">.</span>path<span style="color: #666666">.</span>join(DATA_ID, dat_id)
<span style="color: #408080; font-style: italic"># Initialize a KFold instance</span>
k <span style="color: #666666">=</span> <span style="color: #666666">5</span>
kfold <span style="color: #666666">=</span> KFold(n_splits <span style="color: #666666">=</span> k)
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">save_fig</span>(fig_id):
plt<span style="color: #666666">.</span>savefig(image_path(fig_id) <span style="color: #666666">+</span> <span style="color: #BA2121">&quot;.png&quot;</span>, <span style="color: #008000">format</span><span style="color: #666666">=</span><span style="color: #BA2121">&#39;png&#39;</span>)
<span style="color: #408080; font-style: italic"># Perform the cross-validation to estimate MSE</span>
scores_KFold <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((nlambdas, k))
infile <span style="color: #666666">=</span> <span style="color: #008000">open</span>(data_path(<span style="color: #BA2121">&quot;EoS.csv&quot;</span>),<span style="color: #BA2121">&#39;r&#39;</span>)
i <span style="color: #666666">=</span> <span style="color: #666666">0</span>
<span style="color: #008000; font-weight: bold">for</span> lmb <span style="color: #AA22FF; font-weight: bold">in</span> lambdas:
ridge <span style="color: #666666">=</span> Ridge(alpha <span style="color: #666666">=</span> lmb)
j <span style="color: #666666">=</span> <span style="color: #666666">0</span>
<span style="color: #008000; font-weight: bold">for</span> train_inds, test_inds <span style="color: #AA22FF; font-weight: bold">in</span> kfold<span style="color: #666666">.</span>split(x):
xtrain <span style="color: #666666">=</span> x[train_inds]
ytrain <span style="color: #666666">=</span> y[train_inds]
<span style="color: #408080; font-style: italic"># Read the EoS data as csv file and organize the data into two arrays with density and energies</span>
EoS <span style="color: #666666">=</span> pd<span style="color: #666666">.</span>read_csv(infile, names<span style="color: #666666">=</span>(<span style="color: #BA2121">&#39;Density&#39;</span>, <span style="color: #BA2121">&#39;Energy&#39;</span>))
EoS[<span style="color: #BA2121">&#39;Energy&#39;</span>] <span style="color: #666666">=</span> pd<span style="color: #666666">.</span>to_numeric(EoS[<span style="color: #BA2121">&#39;Energy&#39;</span>], errors<span style="color: #666666">=</span><span style="color: #BA2121">&#39;coerce&#39;</span>)
EoS <span style="color: #666666">=</span> EoS<span style="color: #666666">.</span>dropna()
Energies <span style="color: #666666">=</span> EoS[<span style="color: #BA2121">&#39;Energy&#39;</span>]
Density <span style="color: #666666">=</span> EoS[<span style="color: #BA2121">&#39;Density&#39;</span>]
<span style="color: #408080; font-style: italic"># The design matrix now as function of various polytrops</span>
xtest <span style="color: #666666">=</span> x[test_inds]
ytest <span style="color: #666666">=</span> y[test_inds]
Maxpolydegree <span style="color: #666666">=</span> <span style="color: #666666">30</span>
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(Density),Maxpolydegree))
X[:,<span style="color: #666666">0</span>] <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
testerror <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(Maxpolydegree)
trainingerror <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(Maxpolydegree)
polynomial <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(Maxpolydegree)
Xtrain <span style="color: #666666">=</span> poly<span style="color: #666666">.</span>fit_transform(xtrain[:, np<span style="color: #666666">.</span>newaxis])
ridge<span style="color: #666666">.</span>fit(Xtrain, ytrain[:, np<span style="color: #666666">.</span>newaxis])
trials <span style="color: #666666">=</span> <span style="color: #666666">100</span>
<span style="color: #008000; font-weight: bold">for</span> polydegree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>, Maxpolydegree):
polynomial[polydegree] <span style="color: #666666">=</span> polydegree
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(polydegree):
X[:,degree] <span style="color: #666666">=</span> Density<span style="color: #666666">**</span>(degree<span style="color: #666666">/3.0</span>)
Xtest <span style="color: #666666">=</span> poly<span style="color: #666666">.</span>fit_transform(xtest[:, np<span style="color: #666666">.</span>newaxis])
ypred <span style="color: #666666">=</span> ridge<span style="color: #666666">.</span>predict(Xtest)
<span style="color: #408080; font-style: italic"># loop over trials in order to estimate the expectation value of the MSE</span>
testerror[polydegree] <span style="color: #666666">=</span> <span style="color: #666666">0.0</span>
trainingerror[polydegree] <span style="color: #666666">=</span> <span style="color: #666666">0.0</span>
<span style="color: #008000; font-weight: bold">for</span> samples <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(trials):
x_train, x_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(X, Energies, test_size<span style="color: #666666">=0.2</span>)
model <span style="color: #666666">=</span> LinearRegression(fit_intercept<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>)<span style="color: #666666">.</span>fit(x_train, y_train)
ypred <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(x_train)
ytilde <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(x_test)
testerror[polydegree] <span style="color: #666666">+=</span> mean_squared_error(y_test, ytilde)
trainingerror[polydegree] <span style="color: #666666">+=</span> mean_squared_error(y_train, ypred)
scores_KFold[i,j] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>sum((ypred <span style="color: #666666">-</span> ytest[:, np<span style="color: #666666">.</span>newaxis])<span style="color: #666666">**2</span>)<span style="color: #666666">/</span>np<span style="color: #666666">.</span>size(ypred)
j <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
i <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
estimated_mse_KFold <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean(scores_KFold, axis <span style="color: #666666">=</span> <span style="color: #666666">1</span>)
<span style="color: #408080; font-style: italic">## Cross-validation using cross_val_score from sklearn along with KFold</span>
<span style="color: #408080; font-style: italic"># kfold is an instance initialized above as:</span>
<span style="color: #408080; font-style: italic"># kfold = KFold(n_splits = k)</span>
estimated_mse_sklearn <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(nlambdas)
i <span style="color: #666666">=</span> <span style="color: #666666">0</span>
<span style="color: #008000; font-weight: bold">for</span> lmb <span style="color: #AA22FF; font-weight: bold">in</span> lambdas:
ridge <span style="color: #666666">=</span> Ridge(alpha <span style="color: #666666">=</span> lmb)
X <span style="color: #666666">=</span> poly<span style="color: #666666">.</span>fit_transform(x[:, np<span style="color: #666666">.</span>newaxis])
estimated_mse_folds <span style="color: #666666">=</span> cross_val_score(ridge, X, y[:, np<span style="color: #666666">.</span>newaxis], scoring<span style="color: #666666">=</span><span style="color: #BA2121">&#39;neg_mean_squared_error&#39;</span>, cv<span style="color: #666666">=</span>kfold)
<span style="color: #408080; font-style: italic"># cross_val_score return an array containing the estimated negative mse for every fold.</span>
<span style="color: #408080; font-style: italic"># we have to the the mean of every array in order to get an estimate of the mse of the model</span>
estimated_mse_sklearn[i] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean(<span style="color: #666666">-</span>estimated_mse_folds)
i <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
<span style="color: #408080; font-style: italic">## Plot and compare the slightly different ways to perform cross-validation</span>
plt<span style="color: #666666">.</span>figure()
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), estimated_mse_sklearn, label <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;cross_val_score&#39;</span>)
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), estimated_mse_KFold, <span style="color: #BA2121">&#39;r--&#39;</span>, label <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;KFold&#39;</span>)
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&#39;log10(lambda)&#39;</span>)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&#39;mse&#39;</span>)
testerror[polydegree] <span style="color: #666666">/=</span> trials
trainingerror[polydegree] <span style="color: #666666">/=</span> trials
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Degree of polynomial: </span><span style="color: #BB6688; font-weight: bold">%3d</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span> polynomial[polydegree])
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Mean squared error on training data: </span><span style="color: #BB6688; font-weight: bold">%.8f</span><span style="color: #BA2121">&quot;</span> <span style="color: #666666">%</span> trainingerror[polydegree])
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Mean squared error on test data: </span><span style="color: #BB6688; font-weight: bold">%.8f</span><span style="color: #BA2121">&quot;</span> <span style="color: #666666">%</span> testerror[polydegree])
plt<span style="color: #666666">.</span>plot(polynomial, np<span style="color: #666666">.</span>log10(trainingerror), label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Training Error&#39;</span>)
plt<span style="color: #666666">.</span>plot(polynomial, np<span style="color: #666666">.</span>log10(testerror), label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Test Error&#39;</span>)
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&#39;Polynomial degree&#39;</span>)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&#39;log10[MSE]&#39;</span>)
plt<span style="color: #666666">.</span>legend()
plt<span style="color: #666666">.</span>show()
</pre>
</div>
@@ -380,6 +363,7 @@ plt<span style="color: #666666">.</span>show()
</div>
</div>
<p>Note that we kept the intercept column in the fitting here. This means that we need to set the <b>intercept</b> in the call to the <b>Scikit-Learn</b> function as <b>False</b>. Alternatively, we could have set up the design matrix \( X \) without the first column of ones.</p>
<p>
<!-- navigation buttons at the bottom of the page -->
@@ -397,7 +381,6 @@ plt<span style="color: #666666">.</span>show()
<li><a href="._week37-bs045.html">46</a></li>
<li class="active"><a href="._week37-bs046.html">47</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/._week37-bs047.html
+19 -38
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -265,9 +260,10 @@ MathJax.Hub.Config({
<div class="container">
<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
<a name="part0047"></a>
<!-- !split -->
<h2 id="more-examples-on-bootstrap-and-cross-validation-and-errors" class="anchor">More examples on bootstrap and cross-validation and errors </h2>
<!-- !split -->
<h2 id="the-same-example-but-now-with-cross-validation" class="anchor">The same example but now with cross-validation </h2>
<p>In this example we keep the intercept column again but add cross-validation in order to estimate the best possible value of the means squared error.</p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="cell border-box-sizing code_cell rendered">
@@ -281,9 +277,11 @@ MathJax.Hub.Config({
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LinearRegression, Ridge, Lasso
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.utils</span> <span style="color: #008000; font-weight: bold">import</span> resample
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.metrics</span> <span style="color: #008000; font-weight: bold">import</span> mean_squared_error
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> KFold
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> cross_val_score
<span style="color: #408080; font-style: italic"># Where to save the figures and data files</span>
PROJECT_ROOT_DIR <span style="color: #666666">=</span> <span style="color: #BA2121">&quot;Results&quot;</span>
FIGURE_ID <span style="color: #666666">=</span> <span style="color: #BA2121">&quot;Results/FigureFiles&quot;</span>
@@ -320,35 +318,22 @@ Density <span style="color: #666666">=</span> EoS[<span style="color: #BA2121">&
Maxpolydegree <span style="color: #666666">=</span> <span style="color: #666666">30</span>
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(Density),Maxpolydegree))
X[:,<span style="color: #666666">0</span>] <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
testerror <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(Maxpolydegree)
trainingerror <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(Maxpolydegree)
estimated_mse_sklearn <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(Maxpolydegree)
polynomial <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(Maxpolydegree)
k <span style="color: #666666">=5</span>
kfold <span style="color: #666666">=</span> KFold(n_splits <span style="color: #666666">=</span> k)
trials <span style="color: #666666">=</span> <span style="color: #666666">100</span>
<span style="color: #008000; font-weight: bold">for</span> polydegree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>, Maxpolydegree):
polynomial[polydegree] <span style="color: #666666">=</span> polydegree
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(polydegree):
X[:,degree] <span style="color: #666666">=</span> Density<span style="color: #666666">**</span>(degree<span style="color: #666666">/3.0</span>)
OLS <span style="color: #666666">=</span> LinearRegression(fit_intercept<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>)
<span style="color: #408080; font-style: italic"># loop over trials in order to estimate the expectation value of the MSE</span>
testerror[polydegree] <span style="color: #666666">=</span> <span style="color: #666666">0.0</span>
trainingerror[polydegree] <span style="color: #666666">=</span> <span style="color: #666666">0.0</span>
<span style="color: #008000; font-weight: bold">for</span> samples <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(trials):
x_train, x_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(X, Energies, test_size<span style="color: #666666">=0.2</span>)
model <span style="color: #666666">=</span> LinearRegression(fit_intercept<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>)<span style="color: #666666">.</span>fit(x_train, y_train)
ypred <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(x_train)
ytilde <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(x_test)
testerror[polydegree] <span style="color: #666666">+=</span> mean_squared_error(y_test, ytilde)
trainingerror[polydegree] <span style="color: #666666">+=</span> mean_squared_error(y_train, ypred)
estimated_mse_folds <span style="color: #666666">=</span> cross_val_score(OLS, X, Energies, scoring<span style="color: #666666">=</span><span style="color: #BA2121">&#39;neg_mean_squared_error&#39;</span>, cv<span style="color: #666666">=</span>kfold)
<span style="color: #408080; font-style: italic">#[:, np.newaxis]</span>
estimated_mse_sklearn[polydegree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean(<span style="color: #666666">-</span>estimated_mse_folds)
testerror[polydegree] <span style="color: #666666">/=</span> trials
trainingerror[polydegree] <span style="color: #666666">/=</span> trials
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Degree of polynomial: </span><span style="color: #BB6688; font-weight: bold">%3d</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span> polynomial[polydegree])
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Mean squared error on training data: </span><span style="color: #BB6688; font-weight: bold">%.8f</span><span style="color: #BA2121">&quot;</span> <span style="color: #666666">%</span> trainingerror[polydegree])
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Mean squared error on test data: </span><span style="color: #BB6688; font-weight: bold">%.8f</span><span style="color: #BA2121">&quot;</span> <span style="color: #666666">%</span> testerror[polydegree])
plt<span style="color: #666666">.</span>plot(polynomial, np<span style="color: #666666">.</span>log10(trainingerror), label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Training Error&#39;</span>)
plt<span style="color: #666666">.</span>plot(polynomial, np<span style="color: #666666">.</span>log10(testerror), label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Test Error&#39;</span>)
plt<span style="color: #666666">.</span>plot(polynomial, np<span style="color: #666666">.</span>log10(estimated_mse_sklearn), label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Test Error&#39;</span>)
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&#39;Polynomial degree&#39;</span>)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&#39;log10[MSE]&#39;</span>)
plt<span style="color: #666666">.</span>legend()
@@ -368,8 +353,6 @@ plt<span style="color: #666666">.</span>show()
</div>
</div>
<p>Note that we kept the intercept column in the fitting here. This means that we need to set the <b>intercept</b> in the call to the <b>Scikit-Learn</b> function as <b>False</b>. Alternatively, we could have set up the design matrix \( X \) without the first column of ones.</p>
<p>
<!-- navigation buttons at the bottom of the page -->
<ul class="pagination">
@@ -385,8 +368,6 @@ plt<span style="color: #666666">.</span>show()
<li><a href="._week37-bs045.html">46</a></li>
<li><a href="._week37-bs046.html">47</a></li>
<li class="active"><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs048.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
</div> <!-- end container -->
doc/pub/week37/html/week37-bs.html
+5 -10
View File
@@ -152,10 +152,6 @@ doconce format html week37.do.txt --html_style=bootstrap --pygments_html_style=d
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -250,11 +246,10 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week37-bs041.html#summing-up" style="font-size: 80%;">Summing up</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs042.html#another-example-from-scikit-learn-s-repository" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs043.html#various-steps-in-cross-validation" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs048.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs044.html#cross-validation-in-brief" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs045.html#code-example-for-cross-validation-and-k-fold-cross-validation" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs046.html#more-examples-on-bootstrap-and-cross-validation-and-errors" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
<!-- navigation toc: --> <li><a href="._week37-bs047.html#the-same-example-but-now-with-cross-validation" style="font-size: 80%;">The same example but now with cross-validation</a></li>
</ul>
</li>
@@ -309,7 +304,7 @@ MathJax.Hub.Config({
<li><a href="._week37-bs008.html">9</a></li>
<li><a href="._week37-bs009.html">10</a></li>
<li><a href="">...</a></li>
<li><a href="._week37-bs048.html">49</a></li>
<li><a href="._week37-bs047.html">48</a></li>
<li><a href="._week37-bs001.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/week37/html/week37-reveal.html
-35
View File
@@ -1721,41 +1721,6 @@ cross-validation (LOOCV).
</p>
</section>
<section>
<h2 id="how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">How to set up the cross-validation for Ridge and/or Lasso </h2>
<ul>
<p><li> Define a range of interest for the penalty parameter.</li>
<p><li> Divide the data set into training and test set comprising samples \( \{1, \ldots, n\} \setminus i \) and \( \{ i \} \), respectively.</li>
<p><li> Fit the linear regression model by means of ridge estimation for each \( \lambda \) in the grid using the training set, and the corresponding estimate of the error variance \( \boldsymbol{\sigma}_{-i}^2(\lambda) \), as</li>
</ul>
<p>
<p>&nbsp;<br>
$$
\begin{align*}
\boldsymbol{\beta}_{-i}(\lambda) & = ( \boldsymbol{X}_{-i, \ast}^{T}
\boldsymbol{X}_{-i, \ast} + \lambda \boldsymbol{I}_{pp})^{-1}
\boldsymbol{X}_{-i, \ast}^{T} \boldsymbol{y}_{-i}
\end{align*}
$$
<p>&nbsp;<br>
<ul>
<p><li> Evaluate the prediction performance of these models on the test set by \( [y_i, \boldsymbol{X}_{i, \ast}; \boldsymbol{\beta}_{-i}(\lambda), \boldsymbol{\sigma}_{-i}^2(\lambda)] \). Or, by the prediction error \( |y_i - \boldsymbol{X}_{i, \ast} \boldsymbol{\beta}_{-i}(\lambda)| \), the relative error, the error squared or the R2 score function.</li>
<p><li> Repeat the first three steps such that each sample plays the role of the test set once.</li>
<p><li> Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as</li>
</ul>
<p>
<p>&nbsp;<br>
$$
\begin{align*}
\frac{1}{n} \sum_{i = 1}^n \log\{L[y_i, \mathbf{X}_{i, \ast}; \boldsymbol{\beta}_{-i}(\lambda), \boldsymbol{\sigma}_{-i}^2(\lambda)]\}.
\end{align*}
$$
<p>&nbsp;<br>
</section>
<section>
<h2 id="cross-validation-in-brief">Cross-validation in brief </h2>
doc/pub/week37/html/week37-solarized.html
-33
View File
@@ -179,10 +179,6 @@ div.toc p,a {
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -1643,35 +1639,6 @@ choosing \( k=n \). This particular case is referred to as leave-one-out
cross-validation (LOOCV).
</p>
<!-- !split -->
<h2 id="how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">How to set up the cross-validation for Ridge and/or Lasso </h2>
<ul>
<li> Define a range of interest for the penalty parameter.</li>
<li> Divide the data set into training and test set comprising samples \( \{1, \ldots, n\} \setminus i \) and \( \{ i \} \), respectively.</li>
<li> Fit the linear regression model by means of ridge estimation for each \( \lambda \) in the grid using the training set, and the corresponding estimate of the error variance \( \boldsymbol{\sigma}_{-i}^2(\lambda) \), as</li>
</ul>
$$
\begin{align*}
\boldsymbol{\beta}_{-i}(\lambda) & = ( \boldsymbol{X}_{-i, \ast}^{T}
\boldsymbol{X}_{-i, \ast} + \lambda \boldsymbol{I}_{pp})^{-1}
\boldsymbol{X}_{-i, \ast}^{T} \boldsymbol{y}_{-i}
\end{align*}
$$
<ul>
<li> Evaluate the prediction performance of these models on the test set by \( [y_i, \boldsymbol{X}_{i, \ast}; \boldsymbol{\beta}_{-i}(\lambda), \boldsymbol{\sigma}_{-i}^2(\lambda)] \). Or, by the prediction error \( |y_i - \boldsymbol{X}_{i, \ast} \boldsymbol{\beta}_{-i}(\lambda)| \), the relative error, the error squared or the R2 score function.</li>
<li> Repeat the first three steps such that each sample plays the role of the test set once.</li>
<li> Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as</li>
</ul>
$$
\begin{align*}
\frac{1}{n} \sum_{i = 1}^n \log\{L[y_i, \mathbf{X}_{i, \ast}; \boldsymbol{\beta}_{-i}(\lambda), \boldsymbol{\sigma}_{-i}^2(\lambda)]\}.
\end{align*}
$$
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="cross-validation-in-brief">Cross-validation in brief </h2>
doc/pub/week37/html/week37.html
-33
View File
@@ -256,10 +256,6 @@ div.toc p,a {
2,
None,
'various-steps-in-cross-validation'),
('How to set up the cross-validation for Ridge and/or Lasso',
2,
None,
'how-to-set-up-the-cross-validation-for-ridge-and-or-lasso'),
('Cross-validation in brief',
2,
None,
@@ -1720,35 +1716,6 @@ choosing \( k=n \). This particular case is referred to as leave-one-out
cross-validation (LOOCV).
</p>
<!-- !split -->
<h2 id="how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">How to set up the cross-validation for Ridge and/or Lasso </h2>
<ul>
<li> Define a range of interest for the penalty parameter.</li>
<li> Divide the data set into training and test set comprising samples \( \{1, \ldots, n\} \setminus i \) and \( \{ i \} \), respectively.</li>
<li> Fit the linear regression model by means of ridge estimation for each \( \lambda \) in the grid using the training set, and the corresponding estimate of the error variance \( \boldsymbol{\sigma}_{-i}^2(\lambda) \), as</li>
</ul>
$$
\begin{align*}
\boldsymbol{\beta}_{-i}(\lambda) & = ( \boldsymbol{X}_{-i, \ast}^{T}
\boldsymbol{X}_{-i, \ast} + \lambda \boldsymbol{I}_{pp})^{-1}
\boldsymbol{X}_{-i, \ast}^{T} \boldsymbol{y}_{-i}
\end{align*}
$$
<ul>
<li> Evaluate the prediction performance of these models on the test set by \( [y_i, \boldsymbol{X}_{i, \ast}; \boldsymbol{\beta}_{-i}(\lambda), \boldsymbol{\sigma}_{-i}^2(\lambda)] \). Or, by the prediction error \( |y_i - \boldsymbol{X}_{i, \ast} \boldsymbol{\beta}_{-i}(\lambda)| \), the relative error, the error squared or the R2 score function.</li>
<li> Repeat the first three steps such that each sample plays the role of the test set once.</li>
<li> Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as</li>
</ul>
$$
\begin{align*}
\frac{1}{n} \sum_{i = 1}^n \log\{L[y_i, \mathbf{X}_{i, \ast}; \boldsymbol{\beta}_{-i}(\lambda), \boldsymbol{\sigma}_{-i}^2(\lambda)]\}.
\end{align*}
$$
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="cross-validation-in-brief">Cross-validation in brief </h2>
doc/pub/week37/ipynb/ipynb-week37-src.tar.gz
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doc/pub/week37/ipynb/week37.ipynb
+142 -202
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doc/src/week37/week37.do.txt
-26
View File
@@ -1278,32 +1278,6 @@ involves a degree of randomness. This may be fully excluded when
choosing $k=n$. This particular case is referred to as leave-one-out
cross-validation (LOOCV).
!split
===== How to set up the cross-validation for Ridge and/or Lasso =====
* Define a range of interest for the penalty parameter.
* Divide the data set into training and test set comprising samples $\{1, \ldots, n\} \setminus i$ and $\{ i \}$, respectively.
* Fit the linear regression model by means of ridge estimation for each $\lambda$ in the grid using the training set, and the corresponding estimate of the error variance $\bm{\sigma}_{-i}^2(\lambda)$, as
!bt
\begin{align*}
\bm{\beta}_{-i}(\lambda) & = ( \bm{X}_{-i, \ast}^{T}
\bm{X}_{-i, \ast} + \lambda \bm{I}_{pp})^{-1}
\bm{X}_{-i, \ast}^{T} \bm{y}_{-i}
\end{align*}
!et
* Evaluate the prediction performance of these models on the test set by $[y_i, \bm{X}_{i, \ast}; \bm{\beta}_{-i}(\lambda), \bm{\sigma}_{-i}^2(\lambda)]$. Or, by the prediction error $|y_i - \bm{X}_{i, \ast} \bm{\beta}_{-i}(\lambda)|$, the relative error, the error squared or the R2 score function.
* Repeat the first three steps such that each sample plays the role of the test set once.
* Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as
!bt
\begin{align*}
\frac{1}{n} \sum_{i = 1}^n \log\{L[y_i, \mathbf{X}_{i, \ast}; \bm{\beta}_{-i}(\lambda), \bm{\sigma}_{-i}^2(\lambda)]\}.
\end{align*}
!et
!split
===== Cross-validation in brief =====