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correcting typos

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mhjensen
2019-11-11 04:43:33 +01:00
parent ddec5a4394
commit 2ae3cab126
69 changed files with 300 additions and 300 deletions
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doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html
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@@ -285,7 +285,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 10, 2019</h4></center> <!-- date -->
<center><h4>Nov 11, 2019</h4></center> <!-- date -->
<br>
<p>
doc/pub/DecisionTrees/html/._DecisionTrees-bs001.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs002.html
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doc/pub/DecisionTrees/html/._DecisionTrees-bs003.html
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doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html
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doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs046.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs047.html
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@@ -237,8 +237,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
@@ -278,7 +278,7 @@ The way we proceed is as follows (here we specialize to the squared-error cost f
<ol type="a"></li>
<li> minimize \( \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 \) wrt \( \gamma \) and \( \beta \)</li>
<li> This gives the optimial values \( \beta_m \) and \( \gamma_m \)</li>
<li> This gives the optimal values \( \beta_m \) and \( \gamma_m \)</li>
<li> Determine then the new values \( f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m) \)</li>
</ol>
doc/pub/DecisionTrees/html/._DecisionTrees-bs048.html
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@@ -124,11 +124,11 @@ Automatically generated HTML file from DocOnce source
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@@ -237,8 +237,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
@@ -266,7 +266,7 @@ MathJax.Hub.Config({
<a name="part0048"></a>
<!-- !split -->
<h2 id="___sec47" class="anchor">Squared Error Exampe and Iterative Fitting </h2>
<h2 id="___sec47" class="anchor">Squared-Error Example and Iterative Fitting </h2>
<p>
To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.
@@ -275,7 +275,7 @@ To better understand what happens, let us develop the steps for the iterative fi
For simplicity we assume also that our functions \( b(x;\gamma)=1+\gamma x \).
<p>
This means that for every iteration, we need to optmize
This means that for every iteration, we need to optimize
$$
(\beta_m,\gamma_m) \mathrm{argmin}_{\beta,\lambda}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2=\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(1+\gamma x_i))^2.
@@ -293,7 +293,7 @@ $$
\frac{\partial {\cal C}}{\partial \gamma} =-2\sum_{i}\beta x_i(y_i-\beta(1+\gamma x_i))=0.
$$
We can then rewrite these equations as (defining \( w_i=1+\gamma x_i) \)
We can then rewrite these equations as (defining \( \boldsymbol{w}=\boldsymbol{e}+\gamma x_i) \) with \( \boldsymbol{e} \) being the unit vector)
$$
\gamma \boldsymbol{w}^T(\boldsymbol{y}-\beta\gamma \boldsymbol{w})=0,
$$
@@ -304,7 +304,7 @@ $$
$$
<p>
which leads \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\em{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
which leads to \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\boldsymbol{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
for \( \beta \) gives us an equation for \( \gamma \).
<p>
doc/pub/DecisionTrees/html/._DecisionTrees-bs049.html
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@@ -124,11 +124,11 @@ Automatically generated HTML file from DocOnce source
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@@ -237,8 +237,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
@@ -266,7 +266,7 @@ MathJax.Hub.Config({
<a name="part0049"></a>
<!-- !split -->
<h2 id="___sec48" class="anchor">Iterative Fitting, Classification, AdaBoost </h2>
<h2 id="___sec48" class="anchor">Iterative Fitting, Classification and AdaBoost </h2>
<p>
Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
doc/pub/DecisionTrees/html/._DecisionTrees-bs050.html
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@@ -237,8 +237,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs051.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs052.html
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@@ -237,8 +237,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs053.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs054.html
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@@ -124,11 +124,11 @@ Automatically generated HTML file from DocOnce source
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@@ -237,8 +237,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs055.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
@@ -269,7 +269,7 @@ MathJax.Hub.Config({
<h2 id="___sec54" class="anchor">Gradient boosting: Basics </h2>
<p>
Gradient boosting is again a similar technique to Adapative boosting,
Gradient boosting is again a similar technique to Adaptive boosting,
it combines so-called weak classifiers or regressors into a strong
method via a series of iterations.
doc/pub/DecisionTrees/html/._DecisionTrees-bs056.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs057.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs058.html
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs059.html
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@@ -237,8 +237,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/._DecisionTrees-bs060.html
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@@ -237,8 +237,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
doc/pub/DecisionTrees/html/DecisionTrees-bs.html
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@@ -124,11 +124,11 @@ Automatically generated HTML file from DocOnce source
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@@ -237,8 +237,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared Error Exampe and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
@@ -285,7 +285,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 10, 2019</h4></center> <!-- date -->
<center><h4>Nov 11, 2019</h4></center> <!-- date -->
<br>
<p>
doc/pub/DecisionTrees/html/DecisionTrees-reveal.html
+8 -8
View File
@@ -148,7 +148,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>&nbsp;<br>
<center><h4>Nov 10, 2019</h4></center> <!-- date -->
<center><h4>Nov 11, 2019</h4></center> <!-- date -->
<br>
<p>
@@ -2051,7 +2051,7 @@ The way we proceed is as follows (here we specialize to the squared-error cost f
<ol type="a"></li>
<p><li> minimize \( \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 \) wrt \( \gamma \) and \( \beta \)</li>
<p><li> This gives the optimial values \( \beta_m \) and \( \gamma_m \)</li>
<p><li> This gives the optimal values \( \beta_m \) and \( \gamma_m \)</li>
<p><li> Determine then the new values \( f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m) \)</li>
</ol>
<p>
@@ -2065,7 +2065,7 @@ at the internal nodes, and the predictions at the terminal nodes.
<section>
<h2 id="___sec47">Squared Error Exampe and Iterative Fitting </h2>
<h2 id="___sec47">Squared-Error Example and Iterative Fitting </h2>
<p>
To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.
@@ -2074,7 +2074,7 @@ To better understand what happens, let us develop the steps for the iterative fi
For simplicity we assume also that our functions \( b(x;\gamma)=1+\gamma x \).
<p>
This means that for every iteration, we need to optmize
This means that for every iteration, we need to optimize
<p>&nbsp;<br>
$$
@@ -2098,7 +2098,7 @@ $$
$$
<p>&nbsp;<br>
We can then rewrite these equations as (defining \( w_i=1+\gamma x_i) \)
We can then rewrite these equations as (defining \( \boldsymbol{w}=\boldsymbol{e}+\gamma x_i) \) with \( \boldsymbol{e} \) being the unit vector)
<p>&nbsp;<br>
$$
\gamma \boldsymbol{w}^T(\boldsymbol{y}-\beta\gamma \boldsymbol{w})=0,
@@ -2113,7 +2113,7 @@ $$
<p>&nbsp;<br>
<p>
which leads \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\em{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
which leads to \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\boldsymbol{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
for \( \beta \) gives us an equation for \( \gamma \).
<p>
@@ -2123,7 +2123,7 @@ The solution to these two equations gives us in turn \( \beta_1 \) and \( \gamma
<section>
<h2 id="___sec48">Iterative Fitting, Classification, AdaBoost </h2>
<h2 id="___sec48">Iterative Fitting, Classification and AdaBoost </h2>
<p>
Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
@@ -2358,7 +2358,7 @@ plt.show()
<h2 id="___sec54">Gradient boosting: Basics </h2>
<p>
Gradient boosting is again a similar technique to Adapative boosting,
Gradient boosting is again a similar technique to Adaptive boosting,
it combines so-called weak classifiers or regressors into a strong
method via a series of iterations.
doc/pub/DecisionTrees/html/DecisionTrees-solarized.html
+10 -10
View File
@@ -144,11 +144,11 @@ div { text-align: justify; text-justify: inter-word; }
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'___sec46'),
('Squared Error Exampe and Iterative Fitting',
('Squared-Error Example and Iterative Fitting',
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('Iterative Fitting, Classification and AdaBoost',
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'___sec48'),
@@ -214,7 +214,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 10, 2019</h4></center> <!-- date -->
<center><h4>Nov 11, 2019</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -2054,7 +2054,7 @@ The way we proceed is as follows (here we specialize to the squared-error cost f
<ol type="a"></li>
<li> minimize \( \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 \) wrt \( \gamma \) and \( \beta \)</li>
<li> This gives the optimial values \( \beta_m \) and \( \gamma_m \)</li>
<li> This gives the optimal values \( \beta_m \) and \( \gamma_m \)</li>
<li> Determine then the new values \( f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m) \)</li>
</ol>
@@ -2067,7 +2067,7 @@ at the internal nodes, and the predictions at the terminal nodes.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec47">Squared Error Exampe and Iterative Fitting </h2>
<h2 id="___sec47">Squared-Error Example and Iterative Fitting </h2>
<p>
To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.
@@ -2076,7 +2076,7 @@ To better understand what happens, let us develop the steps for the iterative fi
For simplicity we assume also that our functions \( b(x;\gamma)=1+\gamma x \).
<p>
This means that for every iteration, we need to optmize
This means that for every iteration, we need to optimize
$$
(\beta_m,\gamma_m) \mathrm{argmin}_{\beta,\lambda}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2=\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(1+\gamma x_i))^2.
@@ -2094,7 +2094,7 @@ $$
\frac{\partial {\cal C}}{\partial \gamma} =-2\sum_{i}\beta x_i(y_i-\beta(1+\gamma x_i))=0.
$$
We can then rewrite these equations as (defining \( w_i=1+\gamma x_i) \)
We can then rewrite these equations as (defining \( \boldsymbol{w}=\boldsymbol{e}+\gamma x_i) \) with \( \boldsymbol{e} \) being the unit vector)
$$
\gamma \boldsymbol{w}^T(\boldsymbol{y}-\beta\gamma \boldsymbol{w})=0,
$$
@@ -2105,7 +2105,7 @@ $$
$$
<p>
which leads \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\em{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
which leads to \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\boldsymbol{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
for \( \beta \) gives us an equation for \( \gamma \).
<p>
@@ -2115,7 +2115,7 @@ The solution to these two equations gives us in turn \( \beta_1 \) and \( \gamma
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec48">Iterative Fitting, Classification, AdaBoost </h2>
<h2 id="___sec48">Iterative Fitting, Classification and AdaBoost </h2>
<p>
Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
@@ -2319,7 +2319,7 @@ plt.show()
<h2 id="___sec54">Gradient boosting: Basics </h2>
<p>
Gradient boosting is again a similar technique to Adapative boosting,
Gradient boosting is again a similar technique to Adaptive boosting,
it combines so-called weak classifiers or regressors into a strong
method via a series of iterations.
doc/pub/DecisionTrees/html/DecisionTrees.html
+10 -10
View File
@@ -149,11 +149,11 @@ div { text-align: justify; text-justify: inter-word; }
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@@ -219,7 +219,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 10, 2019</h4></center> <!-- date -->
<center><h4>Nov 11, 2019</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -2059,7 +2059,7 @@ The way we proceed is as follows (here we specialize to the squared-error cost f
<ol type="a"></li>
<li> minimize \( \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 \) wrt \( \gamma \) and \( \beta \)</li>
<li> This gives the optimial values \( \beta_m \) and \( \gamma_m \)</li>
<li> This gives the optimal values \( \beta_m \) and \( \gamma_m \)</li>
<li> Determine then the new values \( f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m) \)</li>
</ol>
@@ -2072,7 +2072,7 @@ at the internal nodes, and the predictions at the terminal nodes.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec47">Squared Error Exampe and Iterative Fitting </h2>
<h2 id="___sec47">Squared-Error Example and Iterative Fitting </h2>
<p>
To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.
@@ -2081,7 +2081,7 @@ To better understand what happens, let us develop the steps for the iterative fi
For simplicity we assume also that our functions \( b(x;\gamma)=1+\gamma x \).
<p>
This means that for every iteration, we need to optmize
This means that for every iteration, we need to optimize
$$
(\beta_m,\gamma_m) \mathrm{argmin}_{\beta,\lambda}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2=\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(1+\gamma x_i))^2.
@@ -2099,7 +2099,7 @@ $$
\frac{\partial {\cal C}}{\partial \gamma} =-2\sum_{i}\beta x_i(y_i-\beta(1+\gamma x_i))=0.
$$
We can then rewrite these equations as (defining \( w_i=1+\gamma x_i) \)
We can then rewrite these equations as (defining \( \boldsymbol{w}=\boldsymbol{e}+\gamma x_i) \) with \( \boldsymbol{e} \) being the unit vector)
$$
\gamma \boldsymbol{w}^T(\boldsymbol{y}-\beta\gamma \boldsymbol{w})=0,
$$
@@ -2110,7 +2110,7 @@ $$
$$
<p>
which leads \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\em{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
which leads to \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\boldsymbol{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
for \( \beta \) gives us an equation for \( \gamma \).
<p>
@@ -2120,7 +2120,7 @@ The solution to these two equations gives us in turn \( \beta_1 \) and \( \gamma
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec48">Iterative Fitting, Classification, AdaBoost </h2>
<h2 id="___sec48">Iterative Fitting, Classification and AdaBoost </h2>
<p>
Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
@@ -2324,7 +2324,7 @@ plt<span style="color: #666666">.</span>show()
<h2 id="___sec54">Gradient boosting: Basics </h2>
<p>
Gradient boosting is again a similar technique to Adapative boosting,
Gradient boosting is again a similar technique to Adaptive boosting,
it combines so-called weak classifiers or regressors into a strong
method via a series of iterations.
doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb
+8 -8
View File
@@ -10,7 +10,7 @@
"<!-- Author: --> \n",
"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
"\n",
"Date: **Nov 10, 2019**\n",
"Date: **Nov 11, 2019**\n",
"\n",
"Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
"\n",
@@ -2107,7 +2107,7 @@
"\n",
"a. minimize $\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2$ wrt $\\gamma$ and $\\beta$\n",
"\n",
"b. This gives the optimial values $\\beta_m$ and $\\gamma_m$\n",
"b. This gives the optimal values $\\beta_m$ and $\\gamma_m$\n",
"\n",
"c. Determine then the new values $f_m(x)=f_{m-1}(x) +\\beta_m b(x;\\gamma_m)$\n",
"\n",
@@ -2117,13 +2117,13 @@
"at the internal nodes, and the predictions at the terminal nodes.\n",
"\n",
"\n",
"## Squared Error Exampe and Iterative Fitting\n",
"## Squared-Error Example and Iterative Fitting\n",
"\n",
"To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.\n",
"\n",
"For simplicity we assume also that our functions $b(x;\\gamma)=1+\\gamma x$. \n",
"\n",
"This means that for every iteration, we need to optmize"
"This means that for every iteration, we need to optimize"
]
},
{
@@ -2172,7 +2172,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"We can then rewrite these equations as (defining $w_i=1+\\gamma x_i)$"
"We can then rewrite these equations as (defining $\\boldsymbol{w}=\\boldsymbol{e}+\\gamma x_i)$ with $\\boldsymbol{e}$ being the unit vector)"
]
},
{
@@ -2204,7 +2204,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"which leads $\\gamma =(\\boldsymbol{x}^T\\boldsymbol{y}-\\beta\\boldsymbol{x}^T\\em{e})/(\\beta\\boldsymbol{x}^T\\boldsymbol{x})$. Inserting\n",
"which leads to $\\gamma =(\\boldsymbol{x}^T\\boldsymbol{y}-\\beta\\boldsymbol{x}^T\\boldsymbol{e})/(\\beta\\boldsymbol{x}^T\\boldsymbol{x})$. Inserting\n",
"for $\\beta$ gives us an equation for $\\gamma$.\n",
"\n",
"The solution to these two equations gives us in turn $\\beta_1$ and $\\gamma_1$ leading to the new expression for $f_1(x)$ as\n",
@@ -2212,7 +2212,7 @@
"\n",
"\n",
"\n",
"## Iterative Fitting, Classification, AdaBoost\n",
"## Iterative Fitting, Classification and AdaBoost\n",
"\n",
"Let us consider a binary classification problem with two outcomes $y_i \\in \\{-1,1\\}$ and $i=0,1,2,\\dots,n-1$ as our set of\n",
"observations. We define a classification function $G(x)$ which produces a prediction taking any of the two values \n",
@@ -2557,7 +2557,7 @@
"source": [
"## Gradient boosting: Basics\n",
"\n",
"Gradient boosting is again a similar technique to Adapative boosting,\n",
"Gradient boosting is again a similar technique to Adaptive boosting,\n",
"it combines so-called weak classifiers or regressors into a strong\n",
"method via a series of iterations.\n",
"\n",
doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz
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doc/pub/DecisionTrees/pdf/DecisionTrees-minted.pdf
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doc/src/DecisionTrees/DecisionTrees.do.txt
+7 -7
View File
@@ -1691,7 +1691,7 @@ o Establish a cost function, here ${\cal C}(\bm{y},\bm{f}) = \frac{1}{n} \sum_{i
o Initialize with a guess $f_0(x)$. It could be one or even zero or some random numbers.
o For $m=1:M$
o minimize $\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2$ wrt $\gamma$ and $\beta$
o This gives the optimial values $\beta_m$ and $\gamma_m$
o This gives the optimal values $\beta_m$ and $\gamma_m$
o Determine then the new values $f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m)$
We could use any of the algorithms we have discussed till now. If we
@@ -1700,13 +1700,13 @@ at the internal nodes, and the predictions at the terminal nodes.
!split
===== Squared Error Exampe and Iterative Fitting =====
===== Squared-Error Example and Iterative Fitting =====
To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.
For simplicity we assume also that our functions $b(x;\gamma)=1+\gamma x$.
This means that for every iteration, we need to optmize
This means that for every iteration, we need to optimize
!bt
\[
@@ -1727,7 +1727,7 @@ and
\frac{\partial {\cal C}}{\partial \gamma} =-2\sum_{i}\beta x_i(y_i-\beta(1+\gamma x_i))=0.
\]
!et
We can then rewrite these equations as (defining $w_i=1+\gamma x_i)$
We can then rewrite these equations as (defining $\bm{w}=\bm{e}+\gamma x_i)$ with $\bm{e}$ being the unit vector)
!bt
\[
\gamma \bm{w}^T(\bm{y}-\beta\gamma \bm{w})=0,
@@ -1740,7 +1740,7 @@ which gives us $\beta = \bm{w}^T\bm{y}/(\bm{w}^T\bm{w})$. Similarly we have
\]
!et
which leads $\gamma =(\bm{x}^T\bm{y}-\beta\bm{x}^T\em{e})/(\beta\bm{x}^T\bm{x})$. Inserting
which leads to $\gamma =(\bm{x}^T\bm{y}-\beta\bm{x}^T\bm{e})/(\beta\bm{x}^T\bm{x})$. Inserting
for $\beta$ gives us an equation for $\gamma$.
The solution to these two equations gives us in turn $\beta_1$ and $\gamma_1$ leading to the new expression for $f_1(x)$ as
@@ -1749,7 +1749,7 @@ $f_1(x) = \beta_1(1+\gamma_1x)$. Doing this $M$ times results in our final estim
!split
===== Iterative Fitting, Classification, AdaBoost =====
===== Iterative Fitting, Classification and AdaBoost =====
Let us consider a binary classification problem with two outcomes $y_i \in \{-1,1\}$ and $i=0,1,2,\dots,n-1$ as our set of
observations. We define a classification function $G(x)$ which produces a prediction taking any of the two values
@@ -1940,7 +1940,7 @@ plt.show()
!split
===== Gradient boosting: Basics =====
Gradient boosting is again a similar technique to Adapative boosting,
Gradient boosting is again a similar technique to Adaptive boosting,
it combines so-called weak classifiers or regressors into a strong
method via a series of iterations.