more cleaning
This commit is contained in:
mhjensen
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
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||||
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||||
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||||
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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||||
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||||
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||||
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
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||||
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||||
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||||
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<li><a href="._DecisionTrees-bs008.html">9</a></li>
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<li><a href="._DecisionTrees-bs009.html">10</a></li>
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<li><a href="">...</a></li>
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<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
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<li><a href="._DecisionTrees-bs001.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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@@ -228,16 +229,17 @@ MathJax.Hub.Config({
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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>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" 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%;">Basic Steps of AdaBoost</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" 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%;">Basic Steps of AdaBoost</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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||||
</ul>
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||||
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@@ -301,7 +303,7 @@ given some assumptions, make predictions about the target feature value
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<li><a href="._DecisionTrees-bs009.html">10</a></li>
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||||
<li><a href="._DecisionTrees-bs010.html">11</a></li>
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||||
<li><a href="">...</a></li>
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
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||||
<li><a href="._DecisionTrees-bs002.html">»</a></li>
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||||
</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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@@ -228,16 +229,17 @@ MathJax.Hub.Config({
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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>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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||||
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||||
</ul>
|
||||
</li>
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||||
@@ -279,7 +281,7 @@ This tree was produced using the Wisconsin cancer data (discussed here as well,
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<li><a href="._DecisionTrees-bs010.html">11</a></li>
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<li><a href="._DecisionTrees-bs011.html">12</a></li>
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<li><a href="">...</a></li>
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<li><a href="._DecisionTrees-bs059.html">60</a></li>
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<li><a href="._DecisionTrees-bs060.html">61</a></li>
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||||
<li><a href="._DecisionTrees-bs003.html">»</a></li>
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||||
</ul>
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||||
<!-- ------------------- end of main content --------------- -->
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@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
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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>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -287,7 +289,7 @@ node.
|
||||
<li><a href="._DecisionTrees-bs011.html">12</a></li>
|
||||
<li><a href="._DecisionTrees-bs012.html">13</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs004.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
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|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -288,7 +290,7 @@ Then we are essentially done!
|
||||
<li><a href="._DecisionTrees-bs012.html">13</a></li>
|
||||
<li><a href="._DecisionTrees-bs013.html">14</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs005.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -367,7 +369,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._DecisionTrees-bs013.html">14</a></li>
|
||||
<li><a href="._DecisionTrees-bs014.html">15</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs006.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -300,7 +302,7 @@ within box \( j \).
|
||||
<li><a href="._DecisionTrees-bs014.html">15</a></li>
|
||||
<li><a href="._DecisionTrees-bs015.html">16</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs007.html">»</a></li>
|
||||
</ul>
|
||||
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|
||||
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||||
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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>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
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|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -292,7 +294,7 @@ better tree in some future step.
|
||||
<li><a href="._DecisionTrees-bs015.html">16</a></li>
|
||||
<li><a href="._DecisionTrees-bs016.html">17</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs008.html">»</a></li>
|
||||
</ul>
|
||||
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|
||||
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||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -325,7 +327,7 @@ region contains more than five observations.
|
||||
<li><a href="._DecisionTrees-bs016.html">17</a></li>
|
||||
<li><a href="._DecisionTrees-bs017.html">18</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs009.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
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@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -294,7 +296,7 @@ parameter \( \alpha \).
|
||||
<li><a href="._DecisionTrees-bs017.html">18</a></li>
|
||||
<li><a href="._DecisionTrees-bs018.html">19</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs010.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
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|
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|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
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||||
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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||||
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||||
</ul>
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@@ -307,7 +309,7 @@ subtree corresponding to \( \alpha \).
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<li><a href="._DecisionTrees-bs018.html">19</a></li>
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<li><a href="._DecisionTrees-bs019.html">20</a></li>
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<li><a href="">...</a></li>
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<li><a href="._DecisionTrees-bs059.html">60</a></li>
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<li><a href="._DecisionTrees-bs060.html">61</a></li>
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<li><a href="._DecisionTrees-bs011.html">»</a></li>
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@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
||||
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|
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||||
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||||
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|
||||
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||||
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|
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|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -303,7 +305,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._DecisionTrees-bs019.html">20</a></li>
|
||||
<li><a href="._DecisionTrees-bs020.html">21</a></li>
|
||||
<li><a href="">...</a></li>
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
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<li><a href="._DecisionTrees-bs012.html">»</a></li>
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||||
</ul>
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||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
||||
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|
||||
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||||
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|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
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|
||||
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|
||||
'___sec49'),
|
||||
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|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
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|
||||
'___sec50'),
|
||||
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|
||||
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|
||||
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|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -295,7 +297,7 @@ fall into that region.
|
||||
<li><a href="._DecisionTrees-bs020.html">21</a></li>
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||||
<li><a href="._DecisionTrees-bs021.html">22</a></li>
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||||
<li><a href="">...</a></li>
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs013.html">»</a></li>
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||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
||||
'___sec47'),
|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
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|
||||
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||||
('Regression Case', 2, None, '___sec58'),
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||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
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|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -300,7 +302,7 @@ than is the classification error rate.
|
||||
<li><a href="._DecisionTrees-bs021.html">22</a></li>
|
||||
<li><a href="._DecisionTrees-bs022.html">23</a></li>
|
||||
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
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||||
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||||
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|
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
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|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
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|
||||
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|
||||
@@ -326,7 +328,7 @@ $$
|
||||
<li><a href="._DecisionTrees-bs022.html">23</a></li>
|
||||
<li><a href="._DecisionTrees-bs023.html">24</a></li>
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||||
<li><a href="">...</a></li>
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
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<li><a href="._DecisionTrees-bs015.html">»</a></li>
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</ul>
|
||||
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|
||||
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||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
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||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
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|
||||
@@ -317,7 +319,7 @@ os<span style="color: #666666">.</span>system(cmd)
|
||||
<li><a href="._DecisionTrees-bs023.html">24</a></li>
|
||||
<li><a href="._DecisionTrees-bs024.html">25</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs016.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -308,7 +310,7 @@ os<span style="color: #666666">.</span>system(cmd)
|
||||
<li><a href="._DecisionTrees-bs024.html">25</a></li>
|
||||
<li><a href="._DecisionTrees-bs025.html">26</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs017.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
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|
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|
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
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||||
@@ -291,7 +293,7 @@ We discuss both algorithms with applications here. The popular library <b>Scikit
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||||
<li><a href="._DecisionTrees-bs025.html">26</a></li>
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||||
<li><a href="._DecisionTrees-bs026.html">27</a></li>
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||||
<li><a href="">...</a></li>
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<li><a href="._DecisionTrees-bs059.html">60</a></li>
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<li><a href="._DecisionTrees-bs060.html">61</a></li>
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<li><a href="._DecisionTrees-bs018.html">»</a></li>
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||||
</ul>
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||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
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('Xgboost on the Cancer Data', 2, None, '___sec59')]}
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|
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<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -281,7 +283,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._DecisionTrees-bs026.html">27</a></li>
|
||||
<li><a href="._DecisionTrees-bs027.html">28</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs019.html">»</a></li>
|
||||
</ul>
|
||||
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|
||||
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||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
||||
'___sec47'),
|
||||
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|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
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|
||||
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|
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|
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|
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|
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|
||||
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
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|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -281,7 +283,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._DecisionTrees-bs027.html">28</a></li>
|
||||
<li><a href="._DecisionTrees-bs028.html">29</a></li>
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||||
<li><a href="">...</a></li>
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs020.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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('Regression Case', 2, None, '___sec58'),
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('Xgboost on the Cancer Data', 2, None, '___sec59')]}
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|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,7 +323,7 @@ The table here summarizes the various attributes and
|
||||
<li><a href="._DecisionTrees-bs028.html">29</a></li>
|
||||
<li><a href="._DecisionTrees-bs029.html">30</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs021.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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||||
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|
||||
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|
||||
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|
||||
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|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
||||
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|
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|
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|
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|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -352,7 +354,7 @@ os<span style="color: #666666">.</span>system(cmd)
|
||||
<li><a href="._DecisionTrees-bs029.html">30</a></li>
|
||||
<li><a href="._DecisionTrees-bs030.html">31</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs022.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
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|
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|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -354,7 +356,7 @@ split <span style="color: #666666">=</span> get_split(dataset)
|
||||
<li><a href="._DecisionTrees-bs030.html">31</a></li>
|
||||
<li><a href="._DecisionTrees-bs031.html">32</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs023.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
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|
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|
||||
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||||
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|
||||
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|
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|
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|
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||||
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|
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|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -312,7 +314,7 @@ attributes at each step while growing the tree.
|
||||
<li><a href="._DecisionTrees-bs031.html">32</a></li>
|
||||
<li><a href="._DecisionTrees-bs032.html">33</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs024.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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||||
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|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
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||||
@@ -472,7 +474,7 @@ MathJax.Hub.Config({
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||||
<li><a href="._DecisionTrees-bs032.html">33</a></li>
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||||
<li><a href="._DecisionTrees-bs033.html">34</a></li>
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||||
<li><a href="">...</a></li>
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<li><a href="._DecisionTrees-bs059.html">60</a></li>
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<li><a href="._DecisionTrees-bs060.html">61</a></li>
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<li><a href="._DecisionTrees-bs025.html">»</a></li>
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||||
</ul>
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||||
<!-- ------------------- end of main content --------------- -->
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||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
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|
||||
|
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<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -325,7 +327,7 @@ deep_tree_clf<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
<li><a href="._DecisionTrees-bs033.html">34</a></li>
|
||||
<li><a href="._DecisionTrees-bs034.html">35</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs026.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
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|
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|
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|
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('Adaptive boosting: AdaBoost, Basic Algorithm',
|
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|
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|
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|
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|
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|
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|
||||
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|
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|
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|
||||
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|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
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('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
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|
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|
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<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -348,7 +350,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._DecisionTrees-bs034.html">35</a></li>
|
||||
<li><a href="._DecisionTrees-bs035.html">36</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs027.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
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|
||||
'___sec50'),
|
||||
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|
||||
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|
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<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -304,7 +306,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._DecisionTrees-bs035.html">36</a></li>
|
||||
<li><a href="._DecisionTrees-bs036.html">37</a></li>
|
||||
<li><a href="">...</a></li>
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs028.html">»</a></li>
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||||
</ul>
|
||||
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|
||||
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||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
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|
||||
@@ -298,7 +300,7 @@ tree_reg<span style="color: #666666">.</span>fit(X, y)
|
||||
<li><a href="._DecisionTrees-bs036.html">37</a></li>
|
||||
<li><a href="._DecisionTrees-bs037.html">38</a></li>
|
||||
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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<li><a href="._DecisionTrees-bs060.html">61</a></li>
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<li><a href="._DecisionTrees-bs029.html">»</a></li>
|
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|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
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||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" 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%;">Basic Steps of AdaBoost</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
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|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
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|
||||
@@ -354,7 +356,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._DecisionTrees-bs037.html">38</a></li>
|
||||
<li><a href="._DecisionTrees-bs038.html">39</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs030.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
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|
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|
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<li><a href="._DecisionTrees-bs038.html">39</a></li>
|
||||
<li><a href="._DecisionTrees-bs039.html">40</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs031.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
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||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -293,7 +295,7 @@ However, by aggregating many decision trees, using methods like bagging, random
|
||||
<li><a href="._DecisionTrees-bs039.html">40</a></li>
|
||||
<li><a href="._DecisionTrees-bs040.html">41</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs032.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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||||
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|
||||
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|
||||
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|
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|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -300,7 +302,7 @@ We discuss these methods here.
|
||||
<li><a href="._DecisionTrees-bs040.html">41</a></li>
|
||||
<li><a href="._DecisionTrees-bs041.html">42</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs033.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
'___sec47'),
|
||||
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|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
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|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
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|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
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|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
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|
||||
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|
||||
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|
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('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
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|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -284,7 +286,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._DecisionTrees-bs041.html">42</a></li>
|
||||
<li><a href="._DecisionTrees-bs042.html">43</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs034.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
||||
'___sec47'),
|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
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|
||||
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|
||||
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('Xgboost on the Cancer Data', 2, None, '___sec59')]}
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|
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<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
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|
||||
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|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -295,7 +297,7 @@ learning method.
|
||||
<li><a href="._DecisionTrees-bs042.html">43</a></li>
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||||
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||||
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||||
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||||
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<li><a href="._DecisionTrees-bs035.html">»</a></li>
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||||
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||||
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||||
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||||
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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>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -305,7 +307,7 @@ predictor, averaged over all \( B \) trees.
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||||
<li><a href="._DecisionTrees-bs043.html">44</a></li>
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||||
<li><a href="._DecisionTrees-bs044.html">45</a></li>
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||||
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
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||||
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|
||||
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|
||||
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||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
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|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
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|
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|
||||
@@ -296,7 +298,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._DecisionTrees-bs044.html">45</a></li>
|
||||
<li><a href="._DecisionTrees-bs045.html">46</a></li>
|
||||
<li><a href="">...</a></li>
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs037.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
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|
||||
</li>
|
||||
@@ -327,7 +329,7 @@ voting_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<li><a href="._DecisionTrees-bs045.html">46</a></li>
|
||||
<li><a href="._DecisionTrees-bs046.html">47</a></li>
|
||||
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
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||||
</ul>
|
||||
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||||
|
||||
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('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
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|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -334,7 +336,7 @@ voting_clf<span style="color: #666666">.</span>fit(X_train, y_train)
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||||
<li><a href="._DecisionTrees-bs046.html">47</a></li>
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||||
<li><a href="._DecisionTrees-bs047.html">48</a></li>
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<li><a href="._DecisionTrees-bs059.html">60</a></li>
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<li><a href="._DecisionTrees-bs060.html">61</a></li>
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<li><a href="._DecisionTrees-bs039.html">»</a></li>
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</ul>
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||||
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||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
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|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
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|
||||
@@ -337,7 +339,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._DecisionTrees-bs047.html">48</a></li>
|
||||
<li><a href="._DecisionTrees-bs048.html">49</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs040.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
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|
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@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
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|
||||
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|
||||
@@ -335,7 +337,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._DecisionTrees-bs048.html">49</a></li>
|
||||
<li><a href="._DecisionTrees-bs049.html">50</a></li>
|
||||
<li><a href="">...</a></li>
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs041.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -320,7 +322,7 @@ this setting.
|
||||
<li><a href="._DecisionTrees-bs049.html">50</a></li>
|
||||
<li><a href="._DecisionTrees-bs050.html">51</a></li>
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||||
<li><a href="">...</a></li>
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
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||||
<li><a href="._DecisionTrees-bs042.html">»</a></li>
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||||
</ul>
|
||||
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|
||||
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||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
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@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -302,7 +304,7 @@ We will grow of forest of say \( M \) trees.
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||||
<li><a href="._DecisionTrees-bs050.html">51</a></li>
|
||||
<li><a href="._DecisionTrees-bs051.html">52</a></li>
|
||||
<li><a href="">...</a></li>
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||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs043.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
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|
||||
@@ -349,7 +351,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._DecisionTrees-bs051.html">52</a></li>
|
||||
<li><a href="._DecisionTrees-bs052.html">53</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs044.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
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@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -298,7 +300,7 @@ np<span style="color: #666666">.</span>sum(y_pred <span style="color: #666666">=
|
||||
<li><a href="._DecisionTrees-bs052.html">53</a></li>
|
||||
<li><a href="._DecisionTrees-bs053.html">54</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
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||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs045.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
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|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
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|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -293,7 +295,7 @@ them with a factor.
|
||||
<li><a href="._DecisionTrees-bs053.html">54</a></li>
|
||||
<li><a href="._DecisionTrees-bs054.html">55</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs046.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
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||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
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|
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|
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|
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|
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<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -316,7 +318,7 @@ In iterative fitting or additive modeling, we minimize the cost function with re
|
||||
<li><a href="._DecisionTrees-bs054.html">55</a></li>
|
||||
<li><a href="._DecisionTrees-bs055.html">56</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs047.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
'___sec47'),
|
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
'___sec50'),
|
||||
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|
||||
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|
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|
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|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
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|
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|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -264,9 +266,9 @@ The way we proceed is as follows (here we specialize to the squared-error cost f
|
||||
<li> For \( m=1:M \)
|
||||
|
||||
<ol type="a"></li>
|
||||
<li> minmize $\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 wrt \( \gamma \) and $\beta$$</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> Determine then the new values $f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m)</li>
|
||||
<li> Determine then the new values \( f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m) \)</li>
|
||||
</ol>
|
||||
|
||||
</ol>
|
||||
@@ -299,7 +301,7 @@ We could use any of the algorithms we have discussed till now. If we use trees,
|
||||
<li><a href="._DecisionTrees-bs055.html">56</a></li>
|
||||
<li><a href="._DecisionTrees-bs056.html">57</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs048.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
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|
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|
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|
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('Regression Case', 2, None, '___sec58'),
|
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('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
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|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -310,7 +312,7 @@ $$
|
||||
<li><a href="._DecisionTrees-bs056.html">57</a></li>
|
||||
<li><a href="._DecisionTrees-bs057.html">58</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs049.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
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|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -265,9 +267,19 @@ $$
|
||||
The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the
|
||||
exponential cost/loss function defined as
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1(x_i)+\beta G(x_i})}
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1}(x_i)+\beta G(x_i))}.
|
||||
$$
|
||||
|
||||
<p>
|
||||
We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in the regression case.
|
||||
This is normally done in two steps. Let us however first rewrite the cost function as
|
||||
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{-(y_i\beta G(x_i))},
|
||||
$$
|
||||
|
||||
where we have defined \( w_i^m= \exp{-(y_if_{m-1}(x_i))} \).
|
||||
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -294,7 +306,7 @@ $$
|
||||
<li><a href="._DecisionTrees-bs057.html">58</a></li>
|
||||
<li><a href="._DecisionTrees-bs058.html">59</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs050.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
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|
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|
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|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -253,26 +255,32 @@ MathJax.Hub.Config({
|
||||
<a name="part0050"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec49" class="anchor">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
<h2 id="___sec49" class="anchor">Building up AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
The algorithm here is rather straightforward. Assume that our weak
|
||||
classifier is a decision tree and we consider a binary set of outputs
|
||||
with \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
|
||||
observations. Our design matrix is given in terms of the
|
||||
feature/predictor vectors
|
||||
\( \boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1} \). Finally, we define also a
|
||||
classifier determined by our data via a function \( G(\boldsymbol{X}) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \).
|
||||
|
||||
<p>
|
||||
We can then define the misclassification error \( \mathrm{err} \) as
|
||||
First, for any \( \beta > 0 \), we optimize \( G \) by setting
|
||||
$$
|
||||
\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(\boldsymbol{X}_{i*}),
|
||||
G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)),
|
||||
$$
|
||||
|
||||
where the function \( I() \) is one if we misclassify and zero if we classify correctly.
|
||||
which is the classifier that minimizes the weighted error rate in predicting \( y \).
|
||||
|
||||
<p>
|
||||
We can do this by rewriting
|
||||
$$
|
||||
\exp{-\beta}\sum_{y_i=G(x_i)}w_i^m+\exp{\beta}\sum_{y_i\ne G(x_i)}w_i^m,
|
||||
$$
|
||||
|
||||
which can be rewritten as
|
||||
$$
|
||||
(\exp{\beta}-\exp{-\beta})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{-\beta}\sum_{i=0}^{n-1}w_i^m=0,
|
||||
$$
|
||||
|
||||
which leads to
|
||||
$$
|
||||
\beta_m = frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}},
|
||||
$$
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -297,6 +305,8 @@ where the function \( I() \) is one if we misclassify and zero if we classify co
|
||||
<li><a href="._DecisionTrees-bs057.html">58</a></li>
|
||||
<li><a href="._DecisionTrees-bs058.html">59</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs051.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
'___sec47'),
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
||||
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|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
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|
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|
||||
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|
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('Gradient Boosting, Examples', 2, None, '___sec55'),
|
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('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -253,42 +255,24 @@ MathJax.Hub.Config({
|
||||
<a name="part0051"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec50" class="anchor">Basic Steps of AdaBoost </h2>
|
||||
<h2 id="___sec50" class="anchor">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
|
||||
<p>
|
||||
With the above definitions we are now ready to set up the algorithm for AdaBoost.
|
||||
The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.
|
||||
|
||||
<ol>
|
||||
<li> We start by initializing all weights to \( w_i = 1/n \), with \( i=0,1,2,\dots n-1 \). It is to see then that \( \sum_{i=0}^{n-1}w_i = 1 \).</li>
|
||||
<li> We rewrite the misclassification error as</li>
|
||||
</ol>
|
||||
The algorithm here is rather straightforward. Assume that our weak
|
||||
classifier is a decision tree and we consider a binary set of outputs
|
||||
with \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
|
||||
observations. Our design matrix is given in terms of the
|
||||
feature/predictor vectors
|
||||
\( \boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1} \). Finally, we define also a
|
||||
classifier determined by our data via a function \( G(\boldsymbol{X}) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \).
|
||||
|
||||
<p>
|
||||
We can then define the misclassification error \( \mathrm{err} \) as
|
||||
$$
|
||||
\mathrm{err}=\frac{\sum_{i=0}^{n-1}w_iI(y_i\ne G(\boldsymbol{X}_{i*})}{\sum_{i=0}^{n-1}w_i},
|
||||
\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(\boldsymbol{X}_{i*}),
|
||||
$$
|
||||
|
||||
|
||||
<ol>
|
||||
<li> Then we start looping over all attempts at classifying, namely we start an iterative process for \( m=1:M \), where \( M \) is the final number of classifications. Our given classifier could for example be a plain decision tree.
|
||||
|
||||
<ol type="a"></li>
|
||||
<li> Fit then a given classifier to the training using the weights \( w_i \).</li>
|
||||
<li> Compute then \( \mathrm{err} \) and figure out which events are classified properly and which are classified wrongly.</li>
|
||||
<li> Define a quantity \( \alpha_{m} = \log{(1-\mathrm{err})/\mathrm{err}} \)</li>
|
||||
<li> Set the new weights to \( w_i = w_i\times \exp{(\alpha_m I(y_i\ne G(\boldsymbol{X}_{i*})} \).</li>
|
||||
</ol>
|
||||
|
||||
<li> Compute the new classifier \( G(\boldsymbol{X})= \sum_{i=0}^{n-1}\alpha_m I(y_i\ne G(\boldsymbol{X}_{i*}) \).</li>
|
||||
</ol>
|
||||
|
||||
For the iterations with \( m \le 2 \) the weights are modified
|
||||
individually at each steps. The obersvations which were misclassified
|
||||
at iteration \( m-1 \) have a weight which is larger than those which were
|
||||
classified properly. As this proceeds, the observations which were
|
||||
difficult to classifiy correctly are given a larger influence. Each
|
||||
new classification step \( m \) is then forced to concentrate on those
|
||||
observations that are missed in the previous iterations.
|
||||
where the function \( I() \) is one if we misclassify and zero if we classify correctly.
|
||||
|
||||
<p>
|
||||
<p>
|
||||
@@ -314,6 +298,7 @@ observations that are missed in the previous iterations.
|
||||
<li><a href="._DecisionTrees-bs057.html">58</a></li>
|
||||
<li><a href="._DecisionTrees-bs058.html">59</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs052.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -253,36 +255,43 @@ MathJax.Hub.Config({
|
||||
<a name="part0052"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec51" class="anchor">AdaBoost Examples </h2>
|
||||
<h2 id="___sec51" class="anchor">Basic Steps of AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
Using <b>Scikit-Learn</b> it is easy to appply the adaptive boosting algorithm, as done here.
|
||||
With the above definitions we are now ready to set up the algorithm for AdaBoost.
|
||||
The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.
|
||||
|
||||
<p>
|
||||
<ol>
|
||||
<li> We start by initializing all weights to \( w_i = 1/n \), with \( i=0,1,2,\dots n-1 \). It is to see then that \( \sum_{i=0}^{n-1}w_i = 1 \).</li>
|
||||
<li> We rewrite the misclassification error as</li>
|
||||
</ol>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> AdaBoostClassifier
|
||||
$$
|
||||
\mathrm{err}=\frac{\sum_{i=0}^{n-1}w_iI(y_i\ne G(\boldsymbol{X}_{i*})}{\sum_{i=0}^{n-1}w_i},
|
||||
$$
|
||||
|
||||
ada_clf <span style="color: #666666">=</span> AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth<span style="color: #666666">=1</span>), n_estimators<span style="color: #666666">=200</span>,
|
||||
algorithm<span style="color: #666666">=</span><span style="color: #BA2121">"SAMME.R"</span>, learning_rate<span style="color: #666666">=0.5</span>, random_state<span style="color: #666666">=42</span>)
|
||||
ada_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> AdaBoostClassifier
|
||||
<ol>
|
||||
<li> Then we start looping over all attempts at classifying, namely we start an iterative process for \( m=1:M \), where \( M \) is the final number of classifications. Our given classifier could for example be a plain decision tree.
|
||||
|
||||
<ol type="a"></li>
|
||||
<li> Fit then a given classifier to the training using the weights \( w_i \).</li>
|
||||
<li> Compute then \( \mathrm{err} \) and figure out which events are classified properly and which are classified wrongly.</li>
|
||||
<li> Define a quantity \( \alpha_{m} = \log{(1-\mathrm{err})/\mathrm{err}} \)</li>
|
||||
<li> Set the new weights to \( w_i = w_i\times \exp{(\alpha_m I(y_i\ne G(\boldsymbol{X}_{i*})} \).</li>
|
||||
</ol>
|
||||
|
||||
<li> Compute the new classifier \( G(\boldsymbol{X})= \sum_{i=0}^{n-1}\alpha_m I(y_i\ne G(\boldsymbol{X}_{i*}) \).</li>
|
||||
</ol>
|
||||
|
||||
For the iterations with \( m \le 2 \) the weights are modified
|
||||
individually at each steps. The obersvations which were misclassified
|
||||
at iteration \( m-1 \) have a weight which is larger than those which were
|
||||
classified properly. As this proceeds, the observations which were
|
||||
difficult to classifiy correctly are given a larger influence. Each
|
||||
new classification step \( m \) is then forced to concentrate on those
|
||||
observations that are missed in the previous iterations.
|
||||
|
||||
ada_clf <span style="color: #666666">=</span> AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth<span style="color: #666666">=1</span>), n_estimators<span style="color: #666666">=200</span>,
|
||||
algorithm<span style="color: #666666">=</span><span style="color: #BA2121">"SAMME.R"</span>, learning_rate<span style="color: #666666">=0.5</span>, random_state<span style="color: #666666">=42</span>)
|
||||
ada_clf<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
y_pred <span style="color: #666666">=</span> ada_clf<span style="color: #666666">.</span>predict(X_test_scaled)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_confusion_matrix(y_test, y_pred, normalize<span style="color: #666666">=</span><span style="color: #008000">True</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
y_probas <span style="color: #666666">=</span> ada_clf<span style="color: #666666">.</span>predict_proba(X_test_scaled)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_roc(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_cumulative_gain(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -306,6 +315,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._DecisionTrees-bs057.html">58</a></li>
|
||||
<li><a href="._DecisionTrees-bs058.html">59</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs053.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -253,18 +255,36 @@ MathJax.Hub.Config({
|
||||
<a name="part0053"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec52" class="anchor">Gradient boosting: Basics </h2>
|
||||
<h2 id="___sec52" class="anchor">AdaBoost Examples </h2>
|
||||
|
||||
<p>
|
||||
Gradient boosting is again a similar technique to Adapative boosting,
|
||||
it combines so-called weak classifiers or regressors into a strong
|
||||
method via a series of iterations.
|
||||
Using <b>Scikit-Learn</b> it is easy to appply the adaptive boosting algorithm, as done here.
|
||||
|
||||
<p>
|
||||
In order to understand the method, let us illustrate its basics by
|
||||
bringing back the essential steps in linear regression, where our cost
|
||||
function was the least squares function.
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> AdaBoostClassifier
|
||||
|
||||
ada_clf <span style="color: #666666">=</span> AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth<span style="color: #666666">=1</span>), n_estimators<span style="color: #666666">=200</span>,
|
||||
algorithm<span style="color: #666666">=</span><span style="color: #BA2121">"SAMME.R"</span>, learning_rate<span style="color: #666666">=0.5</span>, random_state<span style="color: #666666">=42</span>)
|
||||
ada_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> AdaBoostClassifier
|
||||
|
||||
ada_clf <span style="color: #666666">=</span> AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth<span style="color: #666666">=1</span>), n_estimators<span style="color: #666666">=200</span>,
|
||||
algorithm<span style="color: #666666">=</span><span style="color: #BA2121">"SAMME.R"</span>, learning_rate<span style="color: #666666">=0.5</span>, random_state<span style="color: #666666">=42</span>)
|
||||
ada_clf<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
y_pred <span style="color: #666666">=</span> ada_clf<span style="color: #666666">.</span>predict(X_test_scaled)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_confusion_matrix(y_test, y_pred, normalize<span style="color: #666666">=</span><span style="color: #008000">True</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
y_probas <span style="color: #666666">=</span> ada_clf<span style="color: #666666">.</span>predict_proba(X_test_scaled)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_roc(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_cumulative_gain(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -287,6 +307,7 @@ function was the least squares function.
|
||||
<li><a href="._DecisionTrees-bs057.html">58</a></li>
|
||||
<li><a href="._DecisionTrees-bs058.html">59</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs054.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -253,30 +255,19 @@ MathJax.Hub.Config({
|
||||
<a name="part0054"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec53" class="anchor">Gradient Boosting, algorithm </h2>
|
||||
<h2 id="___sec53" class="anchor">Gradient boosting: Basics </h2>
|
||||
|
||||
<p>
|
||||
Suppose we have a cost function \( C(f)=\sum_{i=0}^{n-1}L(y_i, f(x_i)) \) where \( y_i \) is our target and \( f(x_i) \) the function which is meant to model \( y_i \). The above cost function could be our standard least squares function
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f})=\frac{1}{n}\sum_{i=0}^{n-1}(y_i-f(x_i))^2.
|
||||
$$
|
||||
Gradient boosting is again a similar technique to Adapative boosting,
|
||||
it combines so-called weak classifiers or regressors into a strong
|
||||
method via a series of iterations.
|
||||
|
||||
<p>
|
||||
The way we proceed in an iterative fashion is to
|
||||
|
||||
<ol>
|
||||
<li> Initialize our estimate by \( f_0(x)=0 \).</li>
|
||||
<li> For \( m=1:M \), we
|
||||
|
||||
<ol type="a"></li>
|
||||
<li> compute the negative gradient vector \( \boldsymbol{u}_m = -\partial C(\boldsymbol{y},\boldsymbol{f})/\partial \boldsymbol{f}(x) \) at $f(x) = f_{m-1}(x);</li>
|
||||
<li> fit the so-called base-learner to the negative gradient \( h_m(u_m,x) \);</li>
|
||||
<li> update the estimate \( f_m(x) = f_{m-1}(x)+\nu h_m(u_m,x) \);</li>
|
||||
</ol>
|
||||
|
||||
<li> The final estimate is then \( f_M(x) = \sum_{m=1}^M\nu h_m(u_m,x) \).</li>
|
||||
</ol>
|
||||
In order to understand the method, let us illustrate its basics by
|
||||
bringing back the essential steps in linear regression, where our cost
|
||||
function was the least squares function.
|
||||
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -297,6 +288,7 @@ The way we proceed in an iterative fashion is to
|
||||
<li><a href="._DecisionTrees-bs057.html">58</a></li>
|
||||
<li><a href="._DecisionTrees-bs058.html">59</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs055.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -253,94 +255,30 @@ MathJax.Hub.Config({
|
||||
<a name="part0055"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec54" class="anchor">Gradient Boosting, Examples </h2>
|
||||
<h2 id="___sec54" class="anchor">Gradient Boosting, algorithm </h2>
|
||||
|
||||
<p>
|
||||
Suppose we have a cost function \( C(f)=\sum_{i=0}^{n-1}L(y_i, f(x_i)) \) where \( y_i \) is our target and \( f(x_i) \) the function which is meant to model \( y_i \). The above cost function could be our standard least squares function
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f})=\frac{1}{n}\sum_{i=0}^{n-1}(y_i-f(x_i))^2.
|
||||
$$
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">42</span>)
|
||||
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(<span style="color: #666666">100</span>, <span style="color: #666666">1</span>) <span style="color: #666666">-</span> <span style="color: #666666">0.5</span>
|
||||
y <span style="color: #666666">=</span> <span style="color: #666666">3*</span>X[:, <span style="color: #666666">0</span>]<span style="color: #666666">**2</span> <span style="color: #666666">+</span> <span style="color: #666666">0.05</span> <span style="color: #666666">*</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">100</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.tree</span> <span style="color: #008000; font-weight: bold">import</span> DecisionTreeRegressor
|
||||
|
||||
tree_reg1 <span style="color: #666666">=</span> DecisionTreeRegressor(max_depth<span style="color: #666666">=2</span>, random_state<span style="color: #666666">=42</span>)
|
||||
tree_reg1<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
y2 <span style="color: #666666">=</span> y <span style="color: #666666">-</span> tree_reg1<span style="color: #666666">.</span>predict(X)
|
||||
tree_reg2 <span style="color: #666666">=</span> DecisionTreeRegressor(max_depth<span style="color: #666666">=2</span>, random_state<span style="color: #666666">=42</span>)
|
||||
tree_reg2<span style="color: #666666">.</span>fit(X, y2)
|
||||
|
||||
y3 <span style="color: #666666">=</span> y2 <span style="color: #666666">-</span> tree_reg2<span style="color: #666666">.</span>predict(X)
|
||||
tree_reg3 <span style="color: #666666">=</span> DecisionTreeRegressor(max_depth<span style="color: #666666">=2</span>, random_state<span style="color: #666666">=42</span>)
|
||||
tree_reg3<span style="color: #666666">.</span>fit(X, y3)
|
||||
|
||||
X_new <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([[<span style="color: #666666">0.8</span>]])
|
||||
y_pred <span style="color: #666666">=</span> <span style="color: #008000">sum</span>(tree<span style="color: #666666">.</span>predict(X_new) <span style="color: #008000; font-weight: bold">for</span> tree <span style="color: #AA22FF; font-weight: bold">in</span> (tree_reg1, tree_reg2, tree_reg3))
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">plot_predictions</span>(regressors, X, y, axes, label<span style="color: #666666">=</span><span style="color: #008000">None</span>, style<span style="color: #666666">=</span><span style="color: #BA2121">"r-"</span>, data_style<span style="color: #666666">=</span><span style="color: #BA2121">"b."</span>, data_label<span style="color: #666666">=</span><span style="color: #008000">None</span>):
|
||||
x1 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(axes[<span style="color: #666666">0</span>], axes[<span style="color: #666666">1</span>], <span style="color: #666666">500</span>)
|
||||
y_pred <span style="color: #666666">=</span> <span style="color: #008000">sum</span>(regressor<span style="color: #666666">.</span>predict(x1<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)) <span style="color: #008000; font-weight: bold">for</span> regressor <span style="color: #AA22FF; font-weight: bold">in</span> regressors)
|
||||
plt<span style="color: #666666">.</span>plot(X[:, <span style="color: #666666">0</span>], y, data_style, label<span style="color: #666666">=</span>data_label)
|
||||
plt<span style="color: #666666">.</span>plot(x1, y_pred, style, linewidth<span style="color: #666666">=2</span>, label<span style="color: #666666">=</span>label)
|
||||
<span style="color: #008000; font-weight: bold">if</span> label <span style="color: #AA22FF; font-weight: bold">or</span> data_label:
|
||||
plt<span style="color: #666666">.</span>legend(loc<span style="color: #666666">=</span><span style="color: #BA2121">"upper center"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
plt<span style="color: #666666">.</span>axis(axes)
|
||||
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>,<span style="color: #666666">11</span>))
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">321</span>)
|
||||
plot_predictions([tree_reg1], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h_1(x_1)$"</span>, style<span style="color: #666666">=</span><span style="color: #BA2121">"g-"</span>, data_label<span style="color: #666666">=</span><span style="color: #BA2121">"Training set"</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y$"</span>, fontsize<span style="color: #666666">=16</span>, rotation<span style="color: #666666">=0</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Residuals and tree predictions"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">322</span>)
|
||||
plot_predictions([tree_reg1], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h(x_1) = h_1(x_1)$"</span>, data_label<span style="color: #666666">=</span><span style="color: #BA2121">"Training set"</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y$"</span>, fontsize<span style="color: #666666">=16</span>, rotation<span style="color: #666666">=0</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Ensemble predictions"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">323</span>)
|
||||
plot_predictions([tree_reg2], X, y2, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h_2(x_1)$"</span>, style<span style="color: #666666">=</span><span style="color: #BA2121">"g-"</span>, data_style<span style="color: #666666">=</span><span style="color: #BA2121">"k+"</span>, data_label<span style="color: #666666">=</span><span style="color: #BA2121">"Residuals"</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y - h_1(x_1)$"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">324</span>)
|
||||
plot_predictions([tree_reg1, tree_reg2], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h(x_1) = h_1(x_1) + h_2(x_1)$"</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y$"</span>, fontsize<span style="color: #666666">=16</span>, rotation<span style="color: #666666">=0</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">325</span>)
|
||||
plot_predictions([tree_reg3], X, y3, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h_3(x_1)$"</span>, style<span style="color: #666666">=</span><span style="color: #BA2121">"g-"</span>, data_style<span style="color: #666666">=</span><span style="color: #BA2121">"k+"</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y - h_1(x_1) - h_2(x_1)$"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">"$x_1$"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">326</span>)
|
||||
plot_predictions([tree_reg1, tree_reg2, tree_reg3], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h(x_1) = h_1(x_1) + h_2(x_1) + h_3(x_1)$"</span>)
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">"$x_1$"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y$"</span>, fontsize<span style="color: #666666">=16</span>, rotation<span style="color: #666666">=0</span>)
|
||||
|
||||
save_fig(<span style="color: #BA2121">"gradient_boosting_plot"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> GradientBoostingRegressor
|
||||
|
||||
gbrt <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=2</span>, n_estimators<span style="color: #666666">=3</span>, learning_rate<span style="color: #666666">=1.0</span>, random_state<span style="color: #666666">=42</span>)
|
||||
gbrt<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
gbrt_slow <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=2</span>, n_estimators<span style="color: #666666">=200</span>, learning_rate<span style="color: #666666">=0.1</span>, random_state<span style="color: #666666">=42</span>)
|
||||
gbrt_slow<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>,<span style="color: #666666">4</span>))
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">121</span>)
|
||||
plot_predictions([gbrt], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"Ensemble predictions"</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"learning_rate={}, n_estimators={}"</span><span style="color: #666666">.</span>format(gbrt<span style="color: #666666">.</span>learning_rate, gbrt<span style="color: #666666">.</span>n_estimators), fontsize<span style="color: #666666">=14</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">122</span>)
|
||||
plot_predictions([gbrt_slow], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>])
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"learning_rate={}, n_estimators={}"</span><span style="color: #666666">.</span>format(gbrt_slow<span style="color: #666666">.</span>learning_rate, gbrt_slow<span style="color: #666666">.</span>n_estimators), fontsize<span style="color: #666666">=14</span>)
|
||||
|
||||
save_fig(<span style="color: #BA2121">"gbrt_learning_rate_plot"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
The way we proceed in an iterative fashion is to
|
||||
|
||||
<ol>
|
||||
<li> Initialize our estimate by \( f_0(x)=0 \).</li>
|
||||
<li> For \( m=1:M \), we
|
||||
|
||||
<ol type="a"></li>
|
||||
<li> compute the negative gradient vector \( \boldsymbol{u}_m = -\partial C(\boldsymbol{y},\boldsymbol{f})/\partial \boldsymbol{f}(x) \) at $f(x) = f_{m-1}(x);</li>
|
||||
<li> fit the so-called base-learner to the negative gradient \( h_m(u_m,x) \);</li>
|
||||
<li> update the estimate \( f_m(x) = f_{m-1}(x)+\nu h_m(u_m,x) \);</li>
|
||||
</ol>
|
||||
|
||||
<li> The final estimate is then \( f_M(x) = \sum_{m=1}^M\nu h_m(u_m,x) \).</li>
|
||||
</ol>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -360,6 +298,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._DecisionTrees-bs057.html">58</a></li>
|
||||
<li><a href="._DecisionTrees-bs058.html">59</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs056.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -253,66 +255,92 @@ MathJax.Hub.Config({
|
||||
<a name="part0056"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec55" class="anchor">Gradient Boots with Early Stopping </h2>
|
||||
<h2 id="___sec55" class="anchor">Gradient Boosting, Examples </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">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.metrics</span> <span style="color: #008000; font-weight: bold">import</span> mean_squared_error
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">42</span>)
|
||||
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(<span style="color: #666666">100</span>, <span style="color: #666666">1</span>) <span style="color: #666666">-</span> <span style="color: #666666">0.5</span>
|
||||
y <span style="color: #666666">=</span> <span style="color: #666666">3*</span>X[:, <span style="color: #666666">0</span>]<span style="color: #666666">**2</span> <span style="color: #666666">+</span> <span style="color: #666666">0.05</span> <span style="color: #666666">*</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">100</span>)
|
||||
|
||||
X_train, X_val, y_train, y_val <span style="color: #666666">=</span> train_test_split(X, y, random_state<span style="color: #666666">=49</span>)
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.tree</span> <span style="color: #008000; font-weight: bold">import</span> DecisionTreeRegressor
|
||||
|
||||
gbrt <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=2</span>, n_estimators<span style="color: #666666">=120</span>, random_state<span style="color: #666666">=42</span>)
|
||||
gbrt<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
tree_reg1 <span style="color: #666666">=</span> DecisionTreeRegressor(max_depth<span style="color: #666666">=2</span>, random_state<span style="color: #666666">=42</span>)
|
||||
tree_reg1<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
errors <span style="color: #666666">=</span> [mean_squared_error(y_val, y_pred)
|
||||
<span style="color: #008000; font-weight: bold">for</span> y_pred <span style="color: #AA22FF; font-weight: bold">in</span> gbrt<span style="color: #666666">.</span>staged_predict(X_val)]
|
||||
bst_n_estimators <span style="color: #666666">=</span> np<span style="color: #666666">.</span>argmin(errors) <span style="color: #666666">+</span> <span style="color: #666666">1</span>
|
||||
y2 <span style="color: #666666">=</span> y <span style="color: #666666">-</span> tree_reg1<span style="color: #666666">.</span>predict(X)
|
||||
tree_reg2 <span style="color: #666666">=</span> DecisionTreeRegressor(max_depth<span style="color: #666666">=2</span>, random_state<span style="color: #666666">=42</span>)
|
||||
tree_reg2<span style="color: #666666">.</span>fit(X, y2)
|
||||
|
||||
gbrt_best <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=2</span>,n_estimators<span style="color: #666666">=</span>bst_n_estimators, random_state<span style="color: #666666">=42</span>)
|
||||
gbrt_best<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
y3 <span style="color: #666666">=</span> y2 <span style="color: #666666">-</span> tree_reg2<span style="color: #666666">.</span>predict(X)
|
||||
tree_reg3 <span style="color: #666666">=</span> DecisionTreeRegressor(max_depth<span style="color: #666666">=2</span>, random_state<span style="color: #666666">=42</span>)
|
||||
tree_reg3<span style="color: #666666">.</span>fit(X, y3)
|
||||
|
||||
min_error <span style="color: #666666">=</span> np<span style="color: #666666">.</span>min(errors)
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>, <span style="color: #666666">4</span>))
|
||||
X_new <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([[<span style="color: #666666">0.8</span>]])
|
||||
y_pred <span style="color: #666666">=</span> <span style="color: #008000">sum</span>(tree<span style="color: #666666">.</span>predict(X_new) <span style="color: #008000; font-weight: bold">for</span> tree <span style="color: #AA22FF; font-weight: bold">in</span> (tree_reg1, tree_reg2, tree_reg3))
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">121</span>)
|
||||
plt<span style="color: #666666">.</span>plot(errors, <span style="color: #BA2121">"b.-"</span>)
|
||||
plt<span style="color: #666666">.</span>plot([bst_n_estimators, bst_n_estimators], [<span style="color: #666666">0</span>, min_error], <span style="color: #BA2121">"k--"</span>)
|
||||
plt<span style="color: #666666">.</span>plot([<span style="color: #666666">0</span>, <span style="color: #666666">120</span>], [min_error, min_error], <span style="color: #BA2121">"k--"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(bst_n_estimators, min_error, <span style="color: #BA2121">"ko"</span>)
|
||||
plt<span style="color: #666666">.</span>text(bst_n_estimators, min_error<span style="color: #666666">*1.2</span>, <span style="color: #BA2121">"Minimum"</span>, ha<span style="color: #666666">=</span><span style="color: #BA2121">"center"</span>, fontsize<span style="color: #666666">=14</span>)
|
||||
plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0</span>, <span style="color: #666666">120</span>, <span style="color: #666666">0</span>, <span style="color: #666666">0.01</span>])
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">"Number of trees"</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Validation error"</span>, fontsize<span style="color: #666666">=14</span>)
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">plot_predictions</span>(regressors, X, y, axes, label<span style="color: #666666">=</span><span style="color: #008000">None</span>, style<span style="color: #666666">=</span><span style="color: #BA2121">"r-"</span>, data_style<span style="color: #666666">=</span><span style="color: #BA2121">"b."</span>, data_label<span style="color: #666666">=</span><span style="color: #008000">None</span>):
|
||||
x1 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(axes[<span style="color: #666666">0</span>], axes[<span style="color: #666666">1</span>], <span style="color: #666666">500</span>)
|
||||
y_pred <span style="color: #666666">=</span> <span style="color: #008000">sum</span>(regressor<span style="color: #666666">.</span>predict(x1<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)) <span style="color: #008000; font-weight: bold">for</span> regressor <span style="color: #AA22FF; font-weight: bold">in</span> regressors)
|
||||
plt<span style="color: #666666">.</span>plot(X[:, <span style="color: #666666">0</span>], y, data_style, label<span style="color: #666666">=</span>data_label)
|
||||
plt<span style="color: #666666">.</span>plot(x1, y_pred, style, linewidth<span style="color: #666666">=2</span>, label<span style="color: #666666">=</span>label)
|
||||
<span style="color: #008000; font-weight: bold">if</span> label <span style="color: #AA22FF; font-weight: bold">or</span> data_label:
|
||||
plt<span style="color: #666666">.</span>legend(loc<span style="color: #666666">=</span><span style="color: #BA2121">"upper center"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
plt<span style="color: #666666">.</span>axis(axes)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">122</span>)
|
||||
plot_predictions([gbrt_best], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>])
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Best model (</span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121"> trees)"</span> <span style="color: #666666">%</span> bst_n_estimators, fontsize<span style="color: #666666">=14</span>)
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>,<span style="color: #666666">11</span>))
|
||||
|
||||
save_fig(<span style="color: #BA2121">"early_stopping_gbrt_plot"</span>)
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">321</span>)
|
||||
plot_predictions([tree_reg1], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h_1(x_1)$"</span>, style<span style="color: #666666">=</span><span style="color: #BA2121">"g-"</span>, data_label<span style="color: #666666">=</span><span style="color: #BA2121">"Training set"</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y$"</span>, fontsize<span style="color: #666666">=16</span>, rotation<span style="color: #666666">=0</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Residuals and tree predictions"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">322</span>)
|
||||
plot_predictions([tree_reg1], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h(x_1) = h_1(x_1)$"</span>, data_label<span style="color: #666666">=</span><span style="color: #BA2121">"Training set"</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y$"</span>, fontsize<span style="color: #666666">=16</span>, rotation<span style="color: #666666">=0</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Ensemble predictions"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">323</span>)
|
||||
plot_predictions([tree_reg2], X, y2, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h_2(x_1)$"</span>, style<span style="color: #666666">=</span><span style="color: #BA2121">"g-"</span>, data_style<span style="color: #666666">=</span><span style="color: #BA2121">"k+"</span>, data_label<span style="color: #666666">=</span><span style="color: #BA2121">"Residuals"</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y - h_1(x_1)$"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">324</span>)
|
||||
plot_predictions([tree_reg1, tree_reg2], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h(x_1) = h_1(x_1) + h_2(x_1)$"</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y$"</span>, fontsize<span style="color: #666666">=16</span>, rotation<span style="color: #666666">=0</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">325</span>)
|
||||
plot_predictions([tree_reg3], X, y3, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h_3(x_1)$"</span>, style<span style="color: #666666">=</span><span style="color: #BA2121">"g-"</span>, data_style<span style="color: #666666">=</span><span style="color: #BA2121">"k+"</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y - h_1(x_1) - h_2(x_1)$"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">"$x_1$"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">326</span>)
|
||||
plot_predictions([tree_reg1, tree_reg2, tree_reg3], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"$h(x_1) = h_1(x_1) + h_2(x_1) + h_3(x_1)$"</span>)
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">"$x_1$"</span>, fontsize<span style="color: #666666">=16</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"$y$"</span>, fontsize<span style="color: #666666">=16</span>, rotation<span style="color: #666666">=0</span>)
|
||||
|
||||
save_fig(<span style="color: #BA2121">"gradient_boosting_plot"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> GradientBoostingRegressor
|
||||
|
||||
gbrt <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=2</span>, warm_start<span style="color: #666666">=</span><span style="color: #008000">True</span>, random_state<span style="color: #666666">=42</span>)
|
||||
gbrt <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=2</span>, n_estimators<span style="color: #666666">=3</span>, learning_rate<span style="color: #666666">=1.0</span>, random_state<span style="color: #666666">=42</span>)
|
||||
gbrt<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
min_val_error <span style="color: #666666">=</span> <span style="color: #008000">float</span>(<span style="color: #BA2121">"inf"</span>)
|
||||
error_going_up <span style="color: #666666">=</span> <span style="color: #666666">0</span>
|
||||
<span style="color: #008000; font-weight: bold">for</span> n_estimators <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>, <span style="color: #666666">120</span>):
|
||||
gbrt<span style="color: #666666">.</span>n_estimators <span style="color: #666666">=</span> n_estimators
|
||||
gbrt<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
y_pred <span style="color: #666666">=</span> gbrt<span style="color: #666666">.</span>predict(X_val)
|
||||
val_error <span style="color: #666666">=</span> mean_squared_error(y_val, y_pred)
|
||||
<span style="color: #008000; font-weight: bold">if</span> val_error <span style="color: #666666"><</span> min_val_error:
|
||||
min_val_error <span style="color: #666666">=</span> val_error
|
||||
error_going_up <span style="color: #666666">=</span> <span style="color: #666666">0</span>
|
||||
<span style="color: #008000; font-weight: bold">else</span>:
|
||||
error_going_up <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
|
||||
<span style="color: #008000; font-weight: bold">if</span> error_going_up <span style="color: #666666">==</span> <span style="color: #666666">5</span>:
|
||||
<span style="color: #008000; font-weight: bold">break</span> <span style="color: #408080; font-style: italic"># early stopping</span>
|
||||
gbrt_slow <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=2</span>, n_estimators<span style="color: #666666">=200</span>, learning_rate<span style="color: #666666">=0.1</span>, random_state<span style="color: #666666">=42</span>)
|
||||
gbrt_slow<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>,<span style="color: #666666">4</span>))
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span>(gbrt<span style="color: #666666">.</span>n_estimators)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Minimum validation MSE:"</span>, min_val_error)
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">121</span>)
|
||||
plot_predictions([gbrt], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">"Ensemble predictions"</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"learning_rate={}, n_estimators={}"</span><span style="color: #666666">.</span>format(gbrt<span style="color: #666666">.</span>learning_rate, gbrt<span style="color: #666666">.</span>n_estimators), fontsize<span style="color: #666666">=14</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">122</span>)
|
||||
plot_predictions([gbrt_slow], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>])
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"learning_rate={}, n_estimators={}"</span><span style="color: #666666">.</span>format(gbrt_slow<span style="color: #666666">.</span>learning_rate, gbrt_slow<span style="color: #666666">.</span>n_estimators), fontsize<span style="color: #666666">=14</span>)
|
||||
|
||||
save_fig(<span style="color: #BA2121">"gbrt_learning_rate_plot"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
|
||||
@@ -333,6 +361,7 @@ error_going_up <span style="color: #666666">=</span> <span style="color: #666666
|
||||
<li><a href="._DecisionTrees-bs057.html">58</a></li>
|
||||
<li><a href="._DecisionTrees-bs058.html">59</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs057.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -253,24 +255,67 @@ MathJax.Hub.Config({
|
||||
<a name="part0057"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec56" class="anchor">XGBoost: Extreme Gradient Boosting </h2>
|
||||
|
||||
<h2 id="___sec56" class="anchor">Gradient Boots with Early Stopping </h2>
|
||||
<p>
|
||||
<a href="https://github.com/dmlc/xgboost" target="_self">XGBoost</a> or Extreme Gradient
|
||||
Boosting, is an optimized distributed gradient boosting library
|
||||
designed to be highly efficient, flexible and portable. It implements
|
||||
machine learning algorithms under the Gradient Boosting
|
||||
framework. XGBoost provides a parallel tree boosting that solve many
|
||||
data science problems in a fast and accurate way. See the <a href="https://arxiv.org/abs/1603.02754" target="_self">article by Chen and Guestrin</a>.
|
||||
|
||||
<p>
|
||||
The authors design and build a highly scalable end-to-end tree
|
||||
boosting system. It has a theoretically justified weighted quantile
|
||||
sketch for efficient proposal calculation. It introduces a novel sparsity-aware algorithm for parallel tree learning and an effective cache-aware block structure for out-of-core tree learning.
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">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.metrics</span> <span style="color: #008000; font-weight: bold">import</span> mean_squared_error
|
||||
|
||||
<p>
|
||||
It is now the algorithm which wins essentially all ML competitions!!!
|
||||
X_train, X_val, y_train, y_val <span style="color: #666666">=</span> train_test_split(X, y, random_state<span style="color: #666666">=49</span>)
|
||||
|
||||
gbrt <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=2</span>, n_estimators<span style="color: #666666">=120</span>, random_state<span style="color: #666666">=42</span>)
|
||||
gbrt<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
|
||||
errors <span style="color: #666666">=</span> [mean_squared_error(y_val, y_pred)
|
||||
<span style="color: #008000; font-weight: bold">for</span> y_pred <span style="color: #AA22FF; font-weight: bold">in</span> gbrt<span style="color: #666666">.</span>staged_predict(X_val)]
|
||||
bst_n_estimators <span style="color: #666666">=</span> np<span style="color: #666666">.</span>argmin(errors) <span style="color: #666666">+</span> <span style="color: #666666">1</span>
|
||||
|
||||
gbrt_best <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=2</span>,n_estimators<span style="color: #666666">=</span>bst_n_estimators, random_state<span style="color: #666666">=42</span>)
|
||||
gbrt_best<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
|
||||
min_error <span style="color: #666666">=</span> np<span style="color: #666666">.</span>min(errors)
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>, <span style="color: #666666">4</span>))
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">121</span>)
|
||||
plt<span style="color: #666666">.</span>plot(errors, <span style="color: #BA2121">"b.-"</span>)
|
||||
plt<span style="color: #666666">.</span>plot([bst_n_estimators, bst_n_estimators], [<span style="color: #666666">0</span>, min_error], <span style="color: #BA2121">"k--"</span>)
|
||||
plt<span style="color: #666666">.</span>plot([<span style="color: #666666">0</span>, <span style="color: #666666">120</span>], [min_error, min_error], <span style="color: #BA2121">"k--"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(bst_n_estimators, min_error, <span style="color: #BA2121">"ko"</span>)
|
||||
plt<span style="color: #666666">.</span>text(bst_n_estimators, min_error<span style="color: #666666">*1.2</span>, <span style="color: #BA2121">"Minimum"</span>, ha<span style="color: #666666">=</span><span style="color: #BA2121">"center"</span>, fontsize<span style="color: #666666">=14</span>)
|
||||
plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0</span>, <span style="color: #666666">120</span>, <span style="color: #666666">0</span>, <span style="color: #666666">0.01</span>])
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">"Number of trees"</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Validation error"</span>, fontsize<span style="color: #666666">=14</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">122</span>)
|
||||
plot_predictions([gbrt_best], X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">0.8</span>])
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Best model (</span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121"> trees)"</span> <span style="color: #666666">%</span> bst_n_estimators, fontsize<span style="color: #666666">=14</span>)
|
||||
|
||||
save_fig(<span style="color: #BA2121">"early_stopping_gbrt_plot"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
|
||||
gbrt <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=2</span>, warm_start<span style="color: #666666">=</span><span style="color: #008000">True</span>, random_state<span style="color: #666666">=42</span>)
|
||||
|
||||
min_val_error <span style="color: #666666">=</span> <span style="color: #008000">float</span>(<span style="color: #BA2121">"inf"</span>)
|
||||
error_going_up <span style="color: #666666">=</span> <span style="color: #666666">0</span>
|
||||
<span style="color: #008000; font-weight: bold">for</span> n_estimators <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>, <span style="color: #666666">120</span>):
|
||||
gbrt<span style="color: #666666">.</span>n_estimators <span style="color: #666666">=</span> n_estimators
|
||||
gbrt<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
y_pred <span style="color: #666666">=</span> gbrt<span style="color: #666666">.</span>predict(X_val)
|
||||
val_error <span style="color: #666666">=</span> mean_squared_error(y_val, y_pred)
|
||||
<span style="color: #008000; font-weight: bold">if</span> val_error <span style="color: #666666"><</span> min_val_error:
|
||||
min_val_error <span style="color: #666666">=</span> val_error
|
||||
error_going_up <span style="color: #666666">=</span> <span style="color: #666666">0</span>
|
||||
<span style="color: #008000; font-weight: bold">else</span>:
|
||||
error_going_up <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
|
||||
<span style="color: #008000; font-weight: bold">if</span> error_going_up <span style="color: #666666">==</span> <span style="color: #666666">5</span>:
|
||||
<span style="color: #008000; font-weight: bold">break</span> <span style="color: #408080; font-style: italic"># early stopping</span>
|
||||
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span>(gbrt<span style="color: #666666">.</span>n_estimators)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Minimum validation MSE:"</span>, min_val_error)
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -289,6 +334,7 @@ It is now the algorithm which wins essentially all ML competitions!!!
|
||||
<li class="active"><a href="._DecisionTrees-bs057.html">58</a></li>
|
||||
<li><a href="._DecisionTrees-bs058.html">59</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs058.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -129,19 +129,20 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -228,16 +229,17 @@ MathJax.Hub.Config({
|
||||
<!-- 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%;">Iterative Fitting, Classification, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boots with Early Stopping</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -296,7 +298,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._DecisionTrees-bs008.html">9</a></li>
|
||||
<li><a href="._DecisionTrees-bs009.html">10</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DecisionTrees-bs059.html">60</a></li>
|
||||
<li><a href="._DecisionTrees-bs060.html">61</a></li>
|
||||
<li><a href="._DecisionTrees-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -2026,9 +2026,9 @@ The way we proceed is as follows (here we specialize to the squared-error cost f
|
||||
<p><li> For \( m=1:M \)
|
||||
|
||||
<ol type="a"></li>
|
||||
<p><li> minmize $\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 wrt \( \gamma \) and $\beta$$</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> Determine then the new values $f_m(x)=f_{m-1}(x) +\beta_m b(x;\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>
|
||||
</ol>
|
||||
@@ -2094,14 +2094,63 @@ The simplest possible cost function which leads (also simple from a computationa
|
||||
exponential cost/loss function defined as
|
||||
<p> <br>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1(x_i)+\beta G(x_i})}
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1}(x_i)+\beta G(x_i))}.
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>
|
||||
We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in the regression case.
|
||||
This is normally done in two steps. Let us however first rewrite the cost function as
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{-(y_i\beta G(x_i))},
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
where we have defined \( w_i^m= \exp{-(y_if_{m-1}(x_i))} \).
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec49">Building up AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
First, for any \( \beta > 0 \), we optimize \( G \) by setting
|
||||
<p> <br>
|
||||
$$
|
||||
G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)),
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
which is the classifier that minimizes the weighted error rate in predicting \( y \).
|
||||
|
||||
<p>
|
||||
We can do this by rewriting
|
||||
<p> <br>
|
||||
$$
|
||||
\exp{-\beta}\sum_{y_i=G(x_i)}w_i^m+\exp{\beta}\sum_{y_i\ne G(x_i)}w_i^m,
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
which can be rewritten as
|
||||
<p> <br>
|
||||
$$
|
||||
(\exp{\beta}-\exp{-\beta})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{-\beta}\sum_{i=0}^{n-1}w_i^m=0,
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
which leads to
|
||||
<p> <br>
|
||||
$$
|
||||
\beta_m = frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}},
|
||||
$$
|
||||
<p> <br>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec49">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
<h2 id="___sec50">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
|
||||
<p>
|
||||
The algorithm here is rather straightforward. Assume that our weak
|
||||
@@ -2125,7 +2174,7 @@ where the function \( I() \) is one if we misclassify and zero if we classify co
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec50">Basic Steps of AdaBoost </h2>
|
||||
<h2 id="___sec51">Basic Steps of AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
With the above definitions we are now ready to set up the algorithm for AdaBoost.
|
||||
@@ -2166,7 +2215,7 @@ observations that are missed in the previous iterations.
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec51">AdaBoost Examples </h2>
|
||||
<h2 id="___sec52">AdaBoost Examples </h2>
|
||||
|
||||
<p>
|
||||
Using <b>Scikit-Learn</b> it is easy to appply the adaptive boosting algorithm, as done here.
|
||||
@@ -2200,7 +2249,7 @@ plt.show()
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec52">Gradient boosting: Basics </h2>
|
||||
<h2 id="___sec53">Gradient boosting: Basics </h2>
|
||||
|
||||
<p>
|
||||
Gradient boosting is again a similar technique to Adapative boosting,
|
||||
@@ -2215,7 +2264,7 @@ function was the least squares function.
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec53">Gradient Boosting, algorithm </h2>
|
||||
<h2 id="___sec54">Gradient Boosting, algorithm </h2>
|
||||
|
||||
<p>
|
||||
Suppose we have a cost function \( C(f)=\sum_{i=0}^{n-1}L(y_i, f(x_i)) \) where \( y_i \) is our target and \( f(x_i) \) the function which is meant to model \( y_i \). The above cost function could be our standard least squares function
|
||||
@@ -2243,7 +2292,7 @@ The way we proceed in an iterative fashion is to
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec54">Gradient Boosting, Examples </h2>
|
||||
<h2 id="___sec55">Gradient Boosting, Examples </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
@@ -2334,7 +2383,7 @@ plt.show()
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec55">Gradient Boots with Early Stopping </h2>
|
||||
<h2 id="___sec56">Gradient Boots with Early Stopping </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
@@ -2399,7 +2448,7 @@ error_going_up = <span style="color: #B452CD">0</span>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec56">XGBoost: Extreme Gradient Boosting </h2>
|
||||
<h2 id="___sec57">XGBoost: Extreme Gradient Boosting </h2>
|
||||
|
||||
<p>
|
||||
<a href="https://github.com/dmlc/xgboost" target="_blank">XGBoost</a> or Extreme Gradient
|
||||
@@ -2420,7 +2469,7 @@ It is now the algorithm which wins essentially all ML competitions!!!
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec57">Regression Case </h2>
|
||||
<h2 id="___sec58">Regression Case </h2>
|
||||
|
||||
<p>
|
||||
|
||||
@@ -2476,7 +2525,7 @@ plt.show()
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec58">Xgboost on the Cancer Data </h2>
|
||||
<h2 id="___sec59">Xgboost on the Cancer Data </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
|
||||
@@ -149,19 +149,20 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
None,
|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -2018,9 +2019,9 @@ The way we proceed is as follows (here we specialize to the squared-error cost f
|
||||
<li> For \( m=1:M \)
|
||||
|
||||
<ol type="a"></li>
|
||||
<li> minmize $\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 wrt \( \gamma \) and $\beta$$</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> Determine then the new values $f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m)</li>
|
||||
<li> Determine then the new values \( f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m) \)</li>
|
||||
</ol>
|
||||
|
||||
</ol>
|
||||
@@ -2076,13 +2077,51 @@ $$
|
||||
The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the
|
||||
exponential cost/loss function defined as
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1(x_i)+\beta G(x_i})}
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1}(x_i)+\beta G(x_i))}.
|
||||
$$
|
||||
|
||||
<p>
|
||||
We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in the regression case.
|
||||
This is normally done in two steps. Let us however first rewrite the cost function as
|
||||
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{-(y_i\beta G(x_i))},
|
||||
$$
|
||||
|
||||
where we have defined \( w_i^m= \exp{-(y_if_{m-1}(x_i))} \).
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec49">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
<h2 id="___sec49">Building up AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
First, for any \( \beta > 0 \), we optimize \( G \) by setting
|
||||
$$
|
||||
G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)),
|
||||
$$
|
||||
|
||||
which is the classifier that minimizes the weighted error rate in predicting \( y \).
|
||||
|
||||
<p>
|
||||
We can do this by rewriting
|
||||
$$
|
||||
\exp{-\beta}\sum_{y_i=G(x_i)}w_i^m+\exp{\beta}\sum_{y_i\ne G(x_i)}w_i^m,
|
||||
$$
|
||||
|
||||
which can be rewritten as
|
||||
$$
|
||||
(\exp{\beta}-\exp{-\beta})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{-\beta}\sum_{i=0}^{n-1}w_i^m=0,
|
||||
$$
|
||||
|
||||
which leads to
|
||||
$$
|
||||
\beta_m = frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}},
|
||||
$$
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec50">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
|
||||
<p>
|
||||
The algorithm here is rather straightforward. Assume that our weak
|
||||
@@ -2104,7 +2143,7 @@ where the function \( I() \) is one if we misclassify and zero if we classify co
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec50">Basic Steps of AdaBoost </h2>
|
||||
<h2 id="___sec51">Basic Steps of AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
With the above definitions we are now ready to set up the algorithm for AdaBoost.
|
||||
@@ -2144,7 +2183,7 @@ observations that are missed in the previous iterations.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec51">AdaBoost Examples </h2>
|
||||
<h2 id="___sec52">AdaBoost Examples </h2>
|
||||
|
||||
<p>
|
||||
Using <b>Scikit-Learn</b> it is easy to appply the adaptive boosting algorithm, as done here.
|
||||
@@ -2177,7 +2216,7 @@ plt.show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec52">Gradient boosting: Basics </h2>
|
||||
<h2 id="___sec53">Gradient boosting: Basics </h2>
|
||||
|
||||
<p>
|
||||
Gradient boosting is again a similar technique to Adapative boosting,
|
||||
@@ -2192,7 +2231,7 @@ function was the least squares function.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec53">Gradient Boosting, algorithm </h2>
|
||||
<h2 id="___sec54">Gradient Boosting, algorithm </h2>
|
||||
|
||||
<p>
|
||||
Suppose we have a cost function \( C(f)=\sum_{i=0}^{n-1}L(y_i, f(x_i)) \) where \( y_i \) is our target and \( f(x_i) \) the function which is meant to model \( y_i \). The above cost function could be our standard least squares function
|
||||
@@ -2218,7 +2257,7 @@ The way we proceed in an iterative fashion is to
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec54">Gradient Boosting, Examples </h2>
|
||||
<h2 id="___sec55">Gradient Boosting, Examples </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
@@ -2308,7 +2347,7 @@ plt.show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec55">Gradient Boots with Early Stopping </h2>
|
||||
<h2 id="___sec56">Gradient Boots with Early Stopping </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
@@ -2372,7 +2411,7 @@ error_going_up = <span style="color: #B452CD">0</span>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec56">XGBoost: Extreme Gradient Boosting </h2>
|
||||
<h2 id="___sec57">XGBoost: Extreme Gradient Boosting </h2>
|
||||
|
||||
<p>
|
||||
<a href="https://github.com/dmlc/xgboost" target="_blank">XGBoost</a> or Extreme Gradient
|
||||
@@ -2393,7 +2432,7 @@ It is now the algorithm which wins essentially all ML competitions!!!
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec57">Regression Case </h2>
|
||||
<h2 id="___sec58">Regression Case </h2>
|
||||
|
||||
<p>
|
||||
|
||||
@@ -2448,7 +2487,7 @@ plt.show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec58">Xgboost on the Cancer Data </h2>
|
||||
<h2 id="___sec59">Xgboost on the Cancer Data </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
|
||||
@@ -154,19 +154,20 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
None,
|
||||
'___sec47'),
|
||||
('Adaptive Boosting, AdaBoost', 2, None, '___sec48'),
|
||||
('Building up AdaBoost', 2, None, '___sec49'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec50'),
|
||||
('AdaBoost Examples', 2, None, '___sec51'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec52'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec53'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec54'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec55'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec56'),
|
||||
('Regression Case', 2, None, '___sec57'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec58')]}
|
||||
'___sec50'),
|
||||
('Basic Steps of AdaBoost', 2, None, '___sec51'),
|
||||
('AdaBoost Examples', 2, None, '___sec52'),
|
||||
('Gradient boosting: Basics', 2, None, '___sec53'),
|
||||
('Gradient Boosting, algorithm', 2, None, '___sec54'),
|
||||
('Gradient Boosting, Examples', 2, None, '___sec55'),
|
||||
('Gradient Boots with Early Stopping', 2, None, '___sec56'),
|
||||
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
|
||||
('Regression Case', 2, None, '___sec58'),
|
||||
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -2023,9 +2024,9 @@ The way we proceed is as follows (here we specialize to the squared-error cost f
|
||||
<li> For \( m=1:M \)
|
||||
|
||||
<ol type="a"></li>
|
||||
<li> minmize $\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 wrt \( \gamma \) and $\beta$$</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> Determine then the new values $f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m)</li>
|
||||
<li> Determine then the new values \( f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m) \)</li>
|
||||
</ol>
|
||||
|
||||
</ol>
|
||||
@@ -2081,13 +2082,51 @@ $$
|
||||
The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the
|
||||
exponential cost/loss function defined as
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1(x_i)+\beta G(x_i})}
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1}(x_i)+\beta G(x_i))}.
|
||||
$$
|
||||
|
||||
<p>
|
||||
We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in the regression case.
|
||||
This is normally done in two steps. Let us however first rewrite the cost function as
|
||||
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{-(y_i\beta G(x_i))},
|
||||
$$
|
||||
|
||||
where we have defined \( w_i^m= \exp{-(y_if_{m-1}(x_i))} \).
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec49">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
<h2 id="___sec49">Building up AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
First, for any \( \beta > 0 \), we optimize \( G \) by setting
|
||||
$$
|
||||
G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)),
|
||||
$$
|
||||
|
||||
which is the classifier that minimizes the weighted error rate in predicting \( y \).
|
||||
|
||||
<p>
|
||||
We can do this by rewriting
|
||||
$$
|
||||
\exp{-\beta}\sum_{y_i=G(x_i)}w_i^m+\exp{\beta}\sum_{y_i\ne G(x_i)}w_i^m,
|
||||
$$
|
||||
|
||||
which can be rewritten as
|
||||
$$
|
||||
(\exp{\beta}-\exp{-\beta})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{-\beta}\sum_{i=0}^{n-1}w_i^m=0,
|
||||
$$
|
||||
|
||||
which leads to
|
||||
$$
|
||||
\beta_m = frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}},
|
||||
$$
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec50">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
|
||||
<p>
|
||||
The algorithm here is rather straightforward. Assume that our weak
|
||||
@@ -2109,7 +2148,7 @@ where the function \( I() \) is one if we misclassify and zero if we classify co
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec50">Basic Steps of AdaBoost </h2>
|
||||
<h2 id="___sec51">Basic Steps of AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
With the above definitions we are now ready to set up the algorithm for AdaBoost.
|
||||
@@ -2149,7 +2188,7 @@ observations that are missed in the previous iterations.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec51">AdaBoost Examples </h2>
|
||||
<h2 id="___sec52">AdaBoost Examples </h2>
|
||||
|
||||
<p>
|
||||
Using <b>Scikit-Learn</b> it is easy to appply the adaptive boosting algorithm, as done here.
|
||||
@@ -2182,7 +2221,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec52">Gradient boosting: Basics </h2>
|
||||
<h2 id="___sec53">Gradient boosting: Basics </h2>
|
||||
|
||||
<p>
|
||||
Gradient boosting is again a similar technique to Adapative boosting,
|
||||
@@ -2197,7 +2236,7 @@ function was the least squares function.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec53">Gradient Boosting, algorithm </h2>
|
||||
<h2 id="___sec54">Gradient Boosting, algorithm </h2>
|
||||
|
||||
<p>
|
||||
Suppose we have a cost function \( C(f)=\sum_{i=0}^{n-1}L(y_i, f(x_i)) \) where \( y_i \) is our target and \( f(x_i) \) the function which is meant to model \( y_i \). The above cost function could be our standard least squares function
|
||||
@@ -2223,7 +2262,7 @@ The way we proceed in an iterative fashion is to
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec54">Gradient Boosting, Examples </h2>
|
||||
<h2 id="___sec55">Gradient Boosting, Examples </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
@@ -2313,7 +2352,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec55">Gradient Boots with Early Stopping </h2>
|
||||
<h2 id="___sec56">Gradient Boots with Early Stopping </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
@@ -2377,7 +2416,7 @@ error_going_up <span style="color: #666666">=</span> <span style="color: #666666
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec56">XGBoost: Extreme Gradient Boosting </h2>
|
||||
<h2 id="___sec57">XGBoost: Extreme Gradient Boosting </h2>
|
||||
|
||||
<p>
|
||||
<a href="https://github.com/dmlc/xgboost" target="_blank">XGBoost</a> or Extreme Gradient
|
||||
@@ -2398,7 +2437,7 @@ It is now the algorithm which wins essentially all ML competitions!!!
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec57">Regression Case </h2>
|
||||
<h2 id="___sec58">Regression Case </h2>
|
||||
|
||||
<p>
|
||||
|
||||
@@ -2453,7 +2492,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec58">Xgboost on the Cancer Data </h2>
|
||||
<h2 id="___sec59">Xgboost on the Cancer Data </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
|
||||
@@ -2084,11 +2084,11 @@
|
||||
"\n",
|
||||
"3. For $m=1:M$\n",
|
||||
"\n",
|
||||
"a. minmize $\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2 wrt $\\gamma$ and $\\beta$$\n",
|
||||
"a. minimize $\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2$ wrt $\\gamma$ and $\\beta$\n",
|
||||
"\n",
|
||||
"b. This gives the optimial values $\\beta_m$ and $\\gamma_m$\n",
|
||||
"\n",
|
||||
"c. Determine then the new values $f_m(x)=f_{m-1}(x) +\\beta_m b(x;\\gamma_m)\n",
|
||||
"c. Determine then the new values $f_m(x)=f_{m-1}(x) +\\beta_m b(x;\\gamma_m)$\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"We could use any of the algorithms we have discussed till now. If we use trees, $\\gamma$ parameterizes the split variables and split points at the internal nodes, and the predictions at the terminal nodes. \n",
|
||||
@@ -2180,7 +2180,94 @@
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}\\exp{-(y_i(f_{m-1(x_i)+\\beta G(x_i})}\n",
|
||||
"C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}\\exp{-(y_i(f_{m-1}(x_i)+\\beta G(x_i))}.\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We optimize $\\beta$ and $G$ for each value of $m=1:M$ as we did in the regression case.\n",
|
||||
"This is normally done in two steps. Let us however first rewrite the cost function as"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}w_i^{m}\\exp{-(y_i\\beta G(x_i))},\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"where we have defined $w_i^m= \\exp{-(y_if_{m-1}(x_i))}$.\n",
|
||||
"\n",
|
||||
"## Building up AdaBoost\n",
|
||||
"\n",
|
||||
"First, for any $\\beta > 0$, we optimize $G$ by setting"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"G_m(x) = \\mathrm{sign} \\sum_{i=0}^{n-1} w_i^m I(y_i \\ne G_(x_i)),\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"which is the classifier that minimizes the weighted error rate in predicting $y$.\n",
|
||||
"\n",
|
||||
"We can do this by rewriting"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\exp{-\\beta}\\sum_{y_i=G(x_i)}w_i^m+\\exp{\\beta}\\sum_{y_i\\ne G(x_i)}w_i^m,\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"which can be rewritten as"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"(\\exp{\\beta}-\\exp{-\\beta})\\sum_{i=0}^{n-1}w_i^mI(y_i\\ne G(x_i))+\\exp{-\\beta}\\sum_{i=0}^{n-1}w_i^m=0,\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"which leads to"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\beta_m = frac{1}{2}\\log{\\frac{1-\\mathrm{\\overline{err}}}{\\mathrm{\\overline{err}}}},\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
|
||||
Binary file not shown.
Binary file not shown.
@@ -1664,9 +1664,9 @@ The way we proceed is as follows (here we specialize to the squared-error cost f
|
||||
o Establish a cost function, here $C(\bm{y},\bm{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f_M(x_i))^2$ with $f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m)$.
|
||||
o Initialize with a guess $f_0(x)$. It could be one or even zero or some random numbers.
|
||||
o For $m=1:M$
|
||||
o minmize $\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 wrt $\gamma$ and $\beta$$
|
||||
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 Determine then the new values $f_m(x)=f_{m-1}(x) +\beta_m b(x;\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 use trees, $\gamma$ parameterizes the split variables and split points at the internal nodes, and the predictions at the terminal nodes.
|
||||
|
||||
@@ -1720,10 +1720,49 @@ The simplest possible cost function which leads (also simple from a computationa
|
||||
exponential cost/loss function defined as
|
||||
!bt
|
||||
\[
|
||||
C(\bm{y},\bm{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1(x_i)+\beta G(x_i})}
|
||||
C(\bm{y},\bm{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1}(x_i)+\beta G(x_i))}.
|
||||
\]
|
||||
!et
|
||||
|
||||
We optimize $\beta$ and $G$ for each value of $m=1:M$ as we did in the regression case.
|
||||
This is normally done in two steps. Let us however first rewrite the cost function as
|
||||
|
||||
!bt
|
||||
\[
|
||||
C(\bm{y},\bm{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{-(y_i\beta G(x_i))},
|
||||
\]
|
||||
!et
|
||||
where we have defined $w_i^m= \exp{-(y_if_{m-1}(x_i))}$.
|
||||
|
||||
!split
|
||||
===== Building up AdaBoost =====
|
||||
|
||||
First, for any $\beta > 0$, we optimize $G$ by setting
|
||||
!bt
|
||||
\[
|
||||
G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)),
|
||||
\]
|
||||
!et
|
||||
which is the classifier that minimizes the weighted error rate in predicting $y$.
|
||||
|
||||
We can do this by rewriting
|
||||
!bt
|
||||
\[
|
||||
\exp{-\beta}\sum_{y_i=G(x_i)}w_i^m+\exp{\beta}\sum_{y_i\ne G(x_i)}w_i^m,
|
||||
\]
|
||||
!et
|
||||
which can be rewritten as
|
||||
!bt
|
||||
\[
|
||||
(\exp{\beta}-\exp{-\beta})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{-\beta}\sum_{i=0}^{n-1}w_i^m=0,
|
||||
\]
|
||||
!et
|
||||
which leads to
|
||||
!bt
|
||||
\[
|
||||
\beta_m = frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}},
|
||||
\]
|
||||
!et
|
||||
!split
|
||||
===== Adaptive boosting: AdaBoost, Basic Algorithm =====
|
||||
|
||||
|
||||
Reference in New Issue
Block a user