added steepest descent boosting

This commit is contained in:
mhjensen
2019-11-11 23:49:53 +01:00
parent fb0906d974
commit 18239e1a21
69 changed files with 1665 additions and 1128 deletions
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
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('Gradient Boosting, algorithm', 2, None, '___sec55'),
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('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'),
('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -309,7 +317,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs001.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
('Gradient boosting: Basics', 2, None, '___sec54'),
('Gradient Boosting, algorithm', 2, None, '___sec55'),
('Gradient boosting: Basics with Steepest Descent',
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None,
'___sec54'),
('The Squared-Error again! Steepest Descent',
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None,
'___sec55'),
('Gradient Boosting, algorithm', 2, None, '___sec56'),
('Gradient Boosting, Examples of Regression',
2,
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'___sec56'),
'___sec57'),
('Gradient Boosting, Classification Example',
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None,
'___sec57'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'),
('Regression Case', 2, None, '___sec59'),
('Xgboost on the Cancer Data', 2, None, '___sec60')]}
'___sec58'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'),
('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -314,7 +322,7 @@ given some assumptions, make predictions about the target feature value
<li><a href="._DecisionTrees-bs009.html">10</a></li>
<li><a href="._DecisionTrees-bs010.html">11</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs002.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
('Gradient boosting: Basics', 2, None, '___sec54'),
('Gradient Boosting, algorithm', 2, None, '___sec55'),
('Gradient boosting: Basics with Steepest Descent',
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None,
'___sec54'),
('The Squared-Error again! Steepest Descent',
2,
None,
'___sec55'),
('Gradient Boosting, algorithm', 2, None, '___sec56'),
('Gradient Boosting, Examples of Regression',
2,
None,
'___sec56'),
'___sec57'),
('Gradient Boosting, Classification Example',
2,
None,
'___sec57'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'),
('Regression Case', 2, None, '___sec59'),
('Xgboost on the Cancer Data', 2, None, '___sec60')]}
'___sec58'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'),
('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -292,7 +300,7 @@ This tree was produced using the Wisconsin cancer data (discussed here as well,
<li><a href="._DecisionTrees-bs010.html">11</a></li>
<li><a href="._DecisionTrees-bs011.html">12</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs003.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
('Gradient boosting: Basics', 2, None, '___sec54'),
('Gradient Boosting, algorithm', 2, None, '___sec55'),
('Gradient boosting: Basics with Steepest Descent',
2,
None,
'___sec54'),
('The Squared-Error again! Steepest Descent',
2,
None,
'___sec55'),
('Gradient Boosting, algorithm', 2, None, '___sec56'),
('Gradient Boosting, Examples of Regression',
2,
None,
'___sec56'),
'___sec57'),
('Gradient Boosting, Classification Example',
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'___sec57'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'),
('Regression Case', 2, None, '___sec59'),
('Xgboost on the Cancer Data', 2, None, '___sec60')]}
'___sec58'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'),
('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -300,7 +308,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs004.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
('Gradient boosting: Basics', 2, None, '___sec54'),
('Gradient Boosting, algorithm', 2, None, '___sec55'),
('Gradient boosting: Basics with Steepest Descent',
2,
None,
'___sec54'),
('The Squared-Error again! Steepest Descent',
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None,
'___sec55'),
('Gradient Boosting, algorithm', 2, None, '___sec56'),
('Gradient Boosting, Examples of Regression',
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'___sec56'),
'___sec57'),
('Gradient Boosting, Classification Example',
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None,
'___sec57'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'),
('Regression Case', 2, None, '___sec59'),
('Xgboost on the Cancer Data', 2, None, '___sec60')]}
'___sec58'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'),
('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -301,7 +309,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs005.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
('Gradient boosting: Basics', 2, None, '___sec54'),
('Gradient Boosting, algorithm', 2, None, '___sec55'),
('Gradient boosting: Basics with Steepest Descent',
2,
None,
'___sec54'),
('The Squared-Error again! Steepest Descent',
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None,
'___sec55'),
('Gradient Boosting, algorithm', 2, None, '___sec56'),
('Gradient Boosting, Examples of Regression',
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('Gradient Boosting, Classification Example',
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'___sec57'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'),
('Regression Case', 2, None, '___sec59'),
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'___sec58'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'),
('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -380,7 +388,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs006.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -313,7 +321,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs007.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -305,7 +313,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs008.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -338,7 +346,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs009.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -307,7 +315,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs010.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -320,7 +328,7 @@ subtree corresponding to \( \alpha \).
<li><a href="._DecisionTrees-bs018.html">19</a></li>
<li><a href="._DecisionTrees-bs019.html">20</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs011.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -316,7 +324,7 @@ 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>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs012.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -308,7 +316,7 @@ fall into that region.
<li><a href="._DecisionTrees-bs020.html">21</a></li>
<li><a href="._DecisionTrees-bs021.html">22</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs013.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -313,7 +321,7 @@ than is the classification error rate.
<li><a href="._DecisionTrees-bs021.html">22</a></li>
<li><a href="._DecisionTrees-bs022.html">23</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs014.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -339,7 +347,7 @@ $$
<li><a href="._DecisionTrees-bs022.html">23</a></li>
<li><a href="._DecisionTrees-bs023.html">24</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs015.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -330,7 +338,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs016.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -321,7 +329,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs017.html">&raquo;</a></li>
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@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -304,7 +312,7 @@ We discuss both algorithms with applications here. The popular library <b>Scikit
<li><a href="._DecisionTrees-bs025.html">26</a></li>
<li><a href="._DecisionTrees-bs026.html">27</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs018.html">&raquo;</a></li>
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<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -294,7 +302,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs019.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -294,7 +302,7 @@ MathJax.Hub.Config({
<li><a href="._DecisionTrees-bs027.html">28</a></li>
<li><a href="._DecisionTrees-bs028.html">29</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs020.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -334,7 +342,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs021.html">&raquo;</a></li>
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@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -365,7 +373,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs022.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -367,7 +375,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs023.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -325,7 +333,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs024.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -485,7 +493,7 @@ MathJax.Hub.Config({
<li><a href="._DecisionTrees-bs032.html">33</a></li>
<li><a href="._DecisionTrees-bs033.html">34</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs025.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -338,7 +346,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs026.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -361,7 +369,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs027.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -317,7 +325,7 @@ 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>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs028.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -311,7 +319,7 @@ 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>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs029.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -367,7 +375,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs030.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -303,7 +311,7 @@ MathJax.Hub.Config({
<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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs031.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -308,7 +316,7 @@ trees can be substantially improved.
<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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs032.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -316,7 +324,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs033.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -297,7 +305,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs034.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -308,7 +316,7 @@ learning method.
<li><a href="._DecisionTrees-bs042.html">43</a></li>
<li><a href="._DecisionTrees-bs043.html">44</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs035.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -318,7 +326,7 @@ predictor, averaged over all \( B \) trees.
<li><a href="._DecisionTrees-bs043.html">44</a></li>
<li><a href="._DecisionTrees-bs044.html">45</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs036.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -310,7 +318,7 @@ 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>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs037.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -340,7 +348,7 @@ 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>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs038.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -348,7 +356,7 @@ voting_clf<span style="color: #666666">.</span>fit(X_train, y_train)
<li><a href="._DecisionTrees-bs046.html">47</a></li>
<li><a href="._DecisionTrees-bs047.html">48</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs039.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -351,7 +359,7 @@ 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-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs040.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -352,7 +360,7 @@ 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>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs041.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -333,7 +341,7 @@ this setting.
<li><a href="._DecisionTrees-bs049.html">50</a></li>
<li><a href="._DecisionTrees-bs050.html">51</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs042.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -315,7 +323,7 @@ We will grow of forest of say \( M \) trees.
<li><a href="._DecisionTrees-bs050.html">51</a></li>
<li><a href="._DecisionTrees-bs051.html">52</a></li>
<li><a href="">...</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs043.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -362,7 +370,7 @@ plt<span style="color: #666666">.</span>show()
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -311,7 +319,7 @@ np<span style="color: #666666">.</span>sum(y_pred <span style="color: #666666">=
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -306,7 +314,7 @@ them with a factor.
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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</li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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</li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
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@@ -337,7 +345,7 @@ The solution to these two equations gives us in turn \( \beta_1 \) and \( \gamma
<li><a href="._DecisionTrees-bs056.html">57</a></li>
<li><a href="._DecisionTrees-bs057.html">58</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -324,7 +332,7 @@ $$
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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@@ -317,7 +325,7 @@ where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \).
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
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<li><a href="._DecisionTrees-bs060.html">61</a></li>
<li><a href="">...</a></li>
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<li><a href="._DecisionTrees-bs062.html">63</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -319,6 +327,7 @@ plt<span style="color: #666666">.</span>show()
<li><a href="._DecisionTrees-bs059.html">60</a></li>
<li><a href="._DecisionTrees-bs060.html">61</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs055.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -266,7 +274,7 @@ MathJax.Hub.Config({
<a name="part0055"></a>
<!-- !split -->
<h2 id="___sec54" class="anchor">Gradient boosting: Basics </h2>
<h2 id="___sec54" class="anchor">Gradient boosting: Basics with Steepest Descent </h2>
<p>
Gradient boosting is again a similar technique to Adaptive boosting,
@@ -278,9 +286,6 @@ 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>
See discussion during lecture November 8.
<p>
<p>
<!-- navigation buttons at the bottom of the page -->
@@ -303,6 +308,7 @@ See discussion during lecture November 8.
<li><a href="._DecisionTrees-bs059.html">60</a></li>
<li><a href="._DecisionTrees-bs060.html">61</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs056.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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('AdaBoost Examples', 2, None, '___sec53'),
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'___sec58'),
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('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
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<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -266,30 +274,17 @@ MathJax.Hub.Config({
<a name="part0056"></a>
<!-- !split -->
<h2 id="___sec55" class="anchor">Gradient Boosting, algorithm </h2>
<h2 id="___sec55" class="anchor">The Squared-Error again! Steepest Descent </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 squared-error function
We start again with our cost function \( {\cal C}(\boldsymbol{y}m\boldsymbol{f})=\sum_{i=0}^{n-1}{\cal L}(y_i, f(x_i)) \) where we want to minimize
This means that for every iteration, we need to optimize
$$
C(\boldsymbol{y},\boldsymbol{f})=\sum_{i=0}^{n-1}(y_i-f(x_i))^2.
(\hat{\boldsymbol{f}}) \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
$$
<p>
The way we proceed in an iterative fashion is to
<ol>
<li> Initialize our estimate \( f_0(x) \).</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">
@@ -310,6 +305,7 @@ The way we proceed in an iterative fashion is to
<li><a href="._DecisionTrees-bs059.html">60</a></li>
<li><a href="._DecisionTrees-bs060.html">61</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
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<li><a href="._DecisionTrees-bs057.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
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('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -266,58 +274,30 @@ MathJax.Hub.Config({
<a name="part0057"></a>
<!-- !split -->
<h2 id="___sec56" class="anchor">Gradient Boosting, Examples of Regression </h2>
<h2 id="___sec56" 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 squared-error function
$$
C(\boldsymbol{y},\boldsymbol{f})=\sum_{i=0}^{n-1}(y_i-f(x_i))^2.
$$
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> GradientBoostingRegressor
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> StandardScaler
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
<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
n <span style="color: #666666">=</span> <span style="color: #666666">100</span>
maxdegree <span style="color: #666666">=</span> <span style="color: #666666">6</span>
<span style="color: #408080; font-style: italic"># Make data set.</span>
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">-3</span>, <span style="color: #666666">3</span>, n)<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)
y <span style="color: #666666">=</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>x<span style="color: #666666">**2</span>) <span style="color: #666666">+</span> <span style="color: #666666">1.5</span> <span style="color: #666666">*</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>(x<span style="color: #666666">-2</span>)<span style="color: #666666">**2</span>)<span style="color: #666666">+</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>normal(<span style="color: #666666">0</span>, <span style="color: #666666">0.1</span>, x<span style="color: #666666">.</span>shape)
error <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
bias <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
variance <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
polydegree <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(x, y, test_size<span style="color: #666666">=0.2</span>)
scaler <span style="color: #666666">=</span> StandardScaler()
scaler<span style="color: #666666">.</span>fit(X_train)
X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_train)
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>,maxdegree):
model <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=</span>degree, n_estimators<span style="color: #666666">=100</span>, learning_rate<span style="color: #666666">=1.0</span>)
model<span style="color: #666666">.</span>fit(X_train_scaled,y_train)
y_pred <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(X_test_scaled)
polydegree[degree] <span style="color: #666666">=</span> degree
error[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( np<span style="color: #666666">.</span>mean((y_test <span style="color: #666666">-</span> y_pred)<span style="color: #666666">**2</span>) )
bias[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( (y_test <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(y_pred))<span style="color: #666666">**2</span> )
variance[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( np<span style="color: #666666">.</span>var(y_pred) )
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Max depth:&#39;</span>, degree)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Error:&#39;</span>, error[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Bias^2:&#39;</span>, bias[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Var:&#39;</span>, variance[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;{} &gt;= {} + {} = {}&#39;</span><span style="color: #666666">.</span>format(error[degree], bias[degree], variance[degree], bias[degree]<span style="color: #666666">+</span>variance[degree]))
plt<span style="color: #666666">.</span>xlim(<span style="color: #666666">1</span>,maxdegree<span style="color: #666666">-1</span>)
plt<span style="color: #666666">.</span>plot(polydegree, error, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Error&#39;</span>)
plt<span style="color: #666666">.</span>plot(polydegree, bias, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;bias&#39;</span>)
plt<span style="color: #666666">.</span>plot(polydegree, variance, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Variance&#39;</span>)
plt<span style="color: #666666">.</span>legend()
save_fig(<span style="color: #BA2121">&quot;gdregression&quot;</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 \( f_0(x) \).</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>
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@@ -337,6 +317,7 @@ plt<span style="color: #666666">.</span>show()
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<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
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('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
('Gradient boosting: Basics', 2, None, '___sec54'),
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'___sec58'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'),
('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -266,49 +274,55 @@ MathJax.Hub.Config({
<a name="part0058"></a>
<!-- !split -->
<h2 id="___sec57" class="anchor">Gradient Boosting, Classification Example </h2>
<h2 id="___sec57" class="anchor">Gradient Boosting, Examples of Regression </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">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_breast_cancer
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
<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> GradientBoostingClassifier
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> cross_validate
<span style="color: #408080; font-style: italic"># Load the data</span>
cancer <span style="color: #666666">=</span> load_breast_cancer()
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(cancer<span style="color: #666666">.</span>data,cancer<span style="color: #666666">.</span>target,random_state<span style="color: #666666">=0</span>)
<span style="color: #008000; font-weight: bold">print</span>(X_train<span style="color: #666666">.</span>shape)
<span style="color: #008000; font-weight: bold">print</span>(X_test<span style="color: #666666">.</span>shape)
<span style="color: #408080; font-style: italic">#now scale the data</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.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> GradientBoostingRegressor
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> StandardScaler
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
<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
n <span style="color: #666666">=</span> <span style="color: #666666">100</span>
maxdegree <span style="color: #666666">=</span> <span style="color: #666666">6</span>
<span style="color: #408080; font-style: italic"># Make data set.</span>
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">-3</span>, <span style="color: #666666">3</span>, n)<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)
y <span style="color: #666666">=</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>x<span style="color: #666666">**2</span>) <span style="color: #666666">+</span> <span style="color: #666666">1.5</span> <span style="color: #666666">*</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>(x<span style="color: #666666">-2</span>)<span style="color: #666666">**2</span>)<span style="color: #666666">+</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>normal(<span style="color: #666666">0</span>, <span style="color: #666666">0.1</span>, x<span style="color: #666666">.</span>shape)
error <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
bias <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
variance <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
polydegree <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(x, y, test_size<span style="color: #666666">=0.2</span>)
scaler <span style="color: #666666">=</span> StandardScaler()
scaler<span style="color: #666666">.</span>fit(X_train)
X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_train)
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
gd_clf <span style="color: #666666">=</span> GradientBoostingClassifier(max_depth<span style="color: #666666">=3</span>, n_estimators<span style="color: #666666">=100</span>, learning_rate<span style="color: #666666">=1.0</span>)
gd_clf<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
<span style="color: #408080; font-style: italic">#Cross validation</span>
accuracy <span style="color: #666666">=</span> cross_validate(gd_clf,X_test_scaled,y_test,cv<span style="color: #666666">=10</span>)[<span style="color: #BA2121">&#39;test_score&#39;</span>]
<span style="color: #008000; font-weight: bold">print</span>(accuracy)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy with Random Forests and scaled data: {:.2f}&quot;</span><span style="color: #666666">.</span>format(gd_clf<span style="color: #666666">.</span>score(X_test_scaled,y_test)))
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>,maxdegree):
model <span style="color: #666666">=</span> GradientBoostingRegressor(max_depth<span style="color: #666666">=</span>degree, n_estimators<span style="color: #666666">=100</span>, learning_rate<span style="color: #666666">=1.0</span>)
model<span style="color: #666666">.</span>fit(X_train_scaled,y_train)
y_pred <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(X_test_scaled)
polydegree[degree] <span style="color: #666666">=</span> degree
error[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( np<span style="color: #666666">.</span>mean((y_test <span style="color: #666666">-</span> y_pred)<span style="color: #666666">**2</span>) )
bias[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( (y_test <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(y_pred))<span style="color: #666666">**2</span> )
variance[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( np<span style="color: #666666">.</span>var(y_pred) )
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Max depth:&#39;</span>, degree)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Error:&#39;</span>, error[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Bias^2:&#39;</span>, bias[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Var:&#39;</span>, variance[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;{} &gt;= {} + {} = {}&#39;</span><span style="color: #666666">.</span>format(error[degree], bias[degree], variance[degree], bias[degree]<span style="color: #666666">+</span>variance[degree]))
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
y_pred <span style="color: #666666">=</span> gd_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>)
save_fig(<span style="color: #BA2121">&quot;gdclassiffierconfusion&quot;</span>)
plt<span style="color: #666666">.</span>show()
y_probas <span style="color: #666666">=</span> gd_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)
save_fig(<span style="color: #BA2121">&quot;gdclassiffierroc&quot;</span>)
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)
save_fig(<span style="color: #BA2121">&quot;gdclassiffiercgain&quot;</span>)
plt<span style="color: #666666">.</span>xlim(<span style="color: #666666">1</span>,maxdegree<span style="color: #666666">-1</span>)
plt<span style="color: #666666">.</span>plot(polydegree, error, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Error&#39;</span>)
plt<span style="color: #666666">.</span>plot(polydegree, bias, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;bias&#39;</span>)
plt<span style="color: #666666">.</span>plot(polydegree, variance, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Variance&#39;</span>)
plt<span style="color: #666666">.</span>legend()
save_fig(<span style="color: #BA2121">&quot;gdregression&quot;</span>)
plt<span style="color: #666666">.</span>show()
</pre></div>
<p>
@@ -330,6 +344,7 @@ plt<span style="color: #666666">.</span>show()
<li><a href="._DecisionTrees-bs059.html">60</a></li>
<li><a href="._DecisionTrees-bs060.html">61</a></li>
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<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs059.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
('Gradient boosting: Basics', 2, None, '___sec54'),
('Gradient Boosting, algorithm', 2, None, '___sec55'),
('Gradient boosting: Basics with Steepest Descent',
2,
None,
'___sec54'),
('The Squared-Error again! Steepest Descent',
2,
None,
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('Gradient Boosting, algorithm', 2, None, '___sec56'),
('Gradient Boosting, Examples of Regression',
2,
None,
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None,
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('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'),
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'___sec58'),
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('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -266,24 +274,51 @@ MathJax.Hub.Config({
<a name="part0059"></a>
<!-- !split -->
<h2 id="___sec58" class="anchor">XGBoost: Extreme Gradient Boosting </h2>
<h2 id="___sec58" class="anchor">Gradient Boosting, Classification Example </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">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_breast_cancer
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
<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> GradientBoostingClassifier
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> cross_validate
<p>
It is now the algorithm which wins essentially all ML competitions!!!
<span style="color: #408080; font-style: italic"># Load the data</span>
cancer <span style="color: #666666">=</span> load_breast_cancer()
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(cancer<span style="color: #666666">.</span>data,cancer<span style="color: #666666">.</span>target,random_state<span style="color: #666666">=0</span>)
<span style="color: #008000; font-weight: bold">print</span>(X_train<span style="color: #666666">.</span>shape)
<span style="color: #008000; font-weight: bold">print</span>(X_test<span style="color: #666666">.</span>shape)
<span style="color: #408080; font-style: italic">#now scale the data</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> StandardScaler
scaler <span style="color: #666666">=</span> StandardScaler()
scaler<span style="color: #666666">.</span>fit(X_train)
X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_train)
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
gd_clf <span style="color: #666666">=</span> GradientBoostingClassifier(max_depth<span style="color: #666666">=3</span>, n_estimators<span style="color: #666666">=100</span>, learning_rate<span style="color: #666666">=1.0</span>)
gd_clf<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
<span style="color: #408080; font-style: italic">#Cross validation</span>
accuracy <span style="color: #666666">=</span> cross_validate(gd_clf,X_test_scaled,y_test,cv<span style="color: #666666">=10</span>)[<span style="color: #BA2121">&#39;test_score&#39;</span>]
<span style="color: #008000; font-weight: bold">print</span>(accuracy)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy with Random Forests and scaled data: {:.2f}&quot;</span><span style="color: #666666">.</span>format(gd_clf<span style="color: #666666">.</span>score(X_test_scaled,y_test)))
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
y_pred <span style="color: #666666">=</span> gd_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>)
save_fig(<span style="color: #BA2121">&quot;gdclassiffierconfusion&quot;</span>)
plt<span style="color: #666666">.</span>show()
y_probas <span style="color: #666666">=</span> gd_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)
save_fig(<span style="color: #BA2121">&quot;gdclassiffierroc&quot;</span>)
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)
save_fig(<span style="color: #BA2121">&quot;gdclassiffiercgain&quot;</span>)
plt<span style="color: #666666">.</span>show()
</pre></div>
<p>
<p>
<!-- navigation buttons at the bottom of the page -->
@@ -302,6 +337,7 @@ It is now the algorithm which wins essentially all ML competitions!!!
<li class="active"><a href="._DecisionTrees-bs059.html">60</a></li>
<li><a href="._DecisionTrees-bs060.html">61</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs060.html">&raquo;</a></li>
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<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
('Gradient boosting: Basics', 2, None, '___sec54'),
('Gradient Boosting, algorithm', 2, None, '___sec55'),
('Gradient boosting: Basics with Steepest Descent',
2,
None,
'___sec54'),
('The Squared-Error again! Steepest Descent',
2,
None,
'___sec55'),
('Gradient Boosting, algorithm', 2, None, '___sec56'),
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2,
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'___sec56'),
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('Gradient Boosting, Classification Example',
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'___sec57'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'),
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('Xgboost on the Cancer Data', 2, None, '___sec60')]}
'___sec58'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'),
('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -266,58 +274,24 @@ MathJax.Hub.Config({
<a name="part0060"></a>
<!-- !split -->
<h2 id="___sec59" class="anchor">Regression Case </h2>
<h2 id="___sec59" class="anchor">XGBoost: Extreme Gradient Boosting </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>.
<!-- 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">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">xgboost</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">xgb</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> StandardScaler
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
<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>
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.
n <span style="color: #666666">=</span> <span style="color: #666666">100</span>
maxdegree <span style="color: #666666">=</span> <span style="color: #666666">6</span>
<p>
It is now the algorithm which wins essentially all ML competitions!!!
<span style="color: #408080; font-style: italic"># Make data set.</span>
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">-3</span>, <span style="color: #666666">3</span>, n)<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)
y <span style="color: #666666">=</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>x<span style="color: #666666">**2</span>) <span style="color: #666666">+</span> <span style="color: #666666">1.5</span> <span style="color: #666666">*</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>(x<span style="color: #666666">-2</span>)<span style="color: #666666">**2</span>)<span style="color: #666666">+</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>normal(<span style="color: #666666">0</span>, <span style="color: #666666">0.1</span>, x<span style="color: #666666">.</span>shape)
error <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
bias <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
variance <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
polydegree <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(x, y, test_size<span style="color: #666666">=0.2</span>)
scaler <span style="color: #666666">=</span> StandardScaler()
scaler<span style="color: #666666">.</span>fit(X_train)
X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_train)
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(maxdegree):
model <span style="color: #666666">=</span> xgb<span style="color: #666666">.</span>XGBRegressor(objective <span style="color: #666666">=</span><span style="color: #BA2121">&#39;reg:squarederror&#39;</span>, colsaobjective <span style="color: #666666">=</span><span style="color: #BA2121">&#39;reg:squarederror&#39;</span>, colsample_bytree <span style="color: #666666">=</span> <span style="color: #666666">0.3</span>, learning_rate <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>,max_depth <span style="color: #666666">=</span> degree, alpha <span style="color: #666666">=</span> <span style="color: #666666">10</span>, n_estimators <span style="color: #666666">=</span> <span style="color: #666666">200</span>)
model<span style="color: #666666">.</span>fit(X_train_scaled,y_train)
y_pred <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(X_test_scaled)
polydegree[degree] <span style="color: #666666">=</span> degree
error[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( np<span style="color: #666666">.</span>mean((y_test <span style="color: #666666">-</span> y_pred)<span style="color: #666666">**2</span>) )
bias[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( (y_test <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(y_pred))<span style="color: #666666">**2</span> )
variance[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( np<span style="color: #666666">.</span>var(y_pred) )
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Max depth:&#39;</span>, degree)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Error:&#39;</span>, error[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Bias^2:&#39;</span>, bias[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Var:&#39;</span>, variance[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;{} &gt;= {} + {} = {}&#39;</span><span style="color: #666666">.</span>format(error[degree], bias[degree], variance[degree], bias[degree]<span style="color: #666666">+</span>variance[degree]))
plt<span style="color: #666666">.</span>xlim(<span style="color: #666666">1</span>,maxdegree<span style="color: #666666">-1</span>)
plt<span style="color: #666666">.</span>plot(polydegree, error, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Error&#39;</span>)
plt<span style="color: #666666">.</span>plot(polydegree, bias, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;bias&#39;</span>)
plt<span style="color: #666666">.</span>plot(polydegree, variance, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Variance&#39;</span>)
plt<span style="color: #666666">.</span>legend()
plt<span style="color: #666666">.</span>show()
</pre></div>
<p>
<p>
<!-- navigation buttons at the bottom of the page -->
@@ -335,6 +309,7 @@ plt<span style="color: #666666">.</span>show()
<li><a href="._DecisionTrees-bs059.html">60</a></li>
<li class="active"><a href="._DecisionTrees-bs060.html">61</a></li>
<li><a href="._DecisionTrees-bs061.html">62</a></li>
<li><a href="._DecisionTrees-bs062.html">63</a></li>
<li><a href="._DecisionTrees-bs061.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
@@ -140,19 +140,26 @@ Automatically generated HTML file from DocOnce source
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
('Gradient boosting: Basics', 2, None, '___sec54'),
('Gradient Boosting, algorithm', 2, None, '___sec55'),
('Gradient boosting: Basics with Steepest Descent',
2,
None,
'___sec54'),
('The Squared-Error again! Steepest Descent',
2,
None,
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('Gradient Boosting, algorithm', 2, None, '___sec56'),
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('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'),
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('Xgboost on the Cancer Data', 2, None, '___sec60')]}
'___sec58'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'),
('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -244,13 +251,14 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Gradient Boosting, Classification Example</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs061.html#___sec60" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs062.html#___sec61" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
</ul>
</li>
@@ -309,7 +317,7 @@ MathJax.Hub.Config({
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@@ -2355,7 +2355,7 @@ plt.show()
<section>
<h2 id="___sec54">Gradient boosting: Basics </h2>
<h2 id="___sec54">Gradient boosting: Basics with Steepest Descent </h2>
<p>
Gradient boosting is again a similar technique to Adaptive boosting,
@@ -2366,14 +2366,26 @@ method via a series of iterations.
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>
See discussion during lecture November 8.
</section>
<section>
<h2 id="___sec55">Gradient Boosting, algorithm </h2>
<h2 id="___sec55">The Squared-Error again! Steepest Descent </h2>
<p>
We start again with our cost function \( {\cal C}(\boldsymbol{y}m\boldsymbol{f})=\sum_{i=0}^{n-1}{\cal L}(y_i, f(x_i)) \) where we want to minimize
This means that for every iteration, we need to optimize
<p>&nbsp;<br>
$$
(\hat{\boldsymbol{f}}) \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
$$
<p>&nbsp;<br>
</section>
<section>
<h2 id="___sec56">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 squared-error function
@@ -2401,7 +2413,7 @@ The way we proceed in an iterative fashion is to
<section>
<h2 id="___sec56">Gradient Boosting, Examples of Regression </h2>
<h2 id="___sec57">Gradient Boosting, Examples of Regression </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -2456,7 +2468,7 @@ plt.show()
<section>
<h2 id="___sec57">Gradient Boosting, Classification Example </h2>
<h2 id="___sec58">Gradient Boosting, Classification Example </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -2505,7 +2517,7 @@ plt.show()
<section>
<h2 id="___sec58">XGBoost: Extreme Gradient Boosting </h2>
<h2 id="___sec59">XGBoost: Extreme Gradient Boosting </h2>
<p>
<a href="https://github.com/dmlc/xgboost" target="_blank">XGBoost</a> or Extreme Gradient
@@ -2526,7 +2538,7 @@ It is now the algorithm which wins essentially all ML competitions!!!
<section>
<h2 id="___sec59">Regression Case </h2>
<h2 id="___sec60">Regression Case </h2>
<p>
@@ -2582,7 +2594,7 @@ plt.show()
<section>
<h2 id="___sec60">Xgboost on the Cancer Data </h2>
<h2 id="___sec61">Xgboost on the Cancer Data </h2>
<p>
As you will see from the confusion matrix below, XGBoots does an excellent job on the Wisconsin cancer data and outperforms essentially all agorithms we have discussed till now.
@@ -160,19 +160,26 @@ div { text-align: justify; text-justify: inter-word; }
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
('Gradient boosting: Basics', 2, None, '___sec54'),
('Gradient Boosting, algorithm', 2, None, '___sec55'),
('Gradient boosting: Basics with Steepest Descent',
2,
None,
'___sec54'),
('The Squared-Error again! Steepest Descent',
2,
None,
'___sec55'),
('Gradient Boosting, algorithm', 2, None, '___sec56'),
('Gradient Boosting, Examples of Regression',
2,
None,
'___sec56'),
'___sec57'),
('Gradient Boosting, Classification Example',
2,
None,
'___sec57'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'),
('Regression Case', 2, None, '___sec59'),
('Xgboost on the Cancer Data', 2, None, '___sec60')]}
'___sec58'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'),
('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -2316,7 +2323,7 @@ plt.show()
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec54">Gradient boosting: Basics </h2>
<h2 id="___sec54">Gradient boosting: Basics with Steepest Descent </h2>
<p>
Gradient boosting is again a similar technique to Adaptive boosting,
@@ -2329,12 +2336,22 @@ bringing back the essential steps in linear regression, where our cost
function was the least squares function.
<p>
See discussion during lecture November 8.
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec55">The Squared-Error again! Steepest Descent </h2>
<p>
We start again with our cost function \( {\cal C}(\boldsymbol{y}m\boldsymbol{f})=\sum_{i=0}^{n-1}{\cal L}(y_i, f(x_i)) \) where we want to minimize
This means that for every iteration, we need to optimize
$$
(\hat{\boldsymbol{f}}) \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
$$
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec55">Gradient Boosting, algorithm </h2>
<h2 id="___sec56">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 squared-error function
@@ -2360,7 +2377,7 @@ The way we proceed in an iterative fashion is to
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec56">Gradient Boosting, Examples of Regression </h2>
<h2 id="___sec57">Gradient Boosting, Examples of Regression </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -2414,7 +2431,7 @@ plt.show()
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec57">Gradient Boosting, Classification Example </h2>
<h2 id="___sec58">Gradient Boosting, Classification Example </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -2462,7 +2479,7 @@ plt.show()
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec58">XGBoost: Extreme Gradient Boosting </h2>
<h2 id="___sec59">XGBoost: Extreme Gradient Boosting </h2>
<p>
<a href="https://github.com/dmlc/xgboost" target="_blank">XGBoost</a> or Extreme Gradient
@@ -2483,7 +2500,7 @@ 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="___sec59">Regression Case </h2>
<h2 id="___sec60">Regression Case </h2>
<p>
@@ -2538,7 +2555,7 @@ plt.show()
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec60">Xgboost on the Cancer Data </h2>
<h2 id="___sec61">Xgboost on the Cancer Data </h2>
<p>
As you will see from the confusion matrix below, XGBoots does an excellent job on the Wisconsin cancer data and outperforms essentially all agorithms we have discussed till now.
+32 -15
View File
@@ -165,19 +165,26 @@ div { text-align: justify; text-justify: inter-word; }
'___sec51'),
('Basic Steps of AdaBoost', 2, None, '___sec52'),
('AdaBoost Examples', 2, None, '___sec53'),
('Gradient boosting: Basics', 2, None, '___sec54'),
('Gradient Boosting, algorithm', 2, None, '___sec55'),
('Gradient boosting: Basics with Steepest Descent',
2,
None,
'___sec54'),
('The Squared-Error again! Steepest Descent',
2,
None,
'___sec55'),
('Gradient Boosting, algorithm', 2, None, '___sec56'),
('Gradient Boosting, Examples of Regression',
2,
None,
'___sec56'),
'___sec57'),
('Gradient Boosting, Classification Example',
2,
None,
'___sec57'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'),
('Regression Case', 2, None, '___sec59'),
('Xgboost on the Cancer Data', 2, None, '___sec60')]}
'___sec58'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'),
('Regression Case', 2, None, '___sec60'),
('Xgboost on the Cancer Data', 2, None, '___sec61')]}
end of tocinfo -->
<body>
@@ -2321,7 +2328,7 @@ plt<span style="color: #666666">.</span>show()
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec54">Gradient boosting: Basics </h2>
<h2 id="___sec54">Gradient boosting: Basics with Steepest Descent </h2>
<p>
Gradient boosting is again a similar technique to Adaptive boosting,
@@ -2334,12 +2341,22 @@ bringing back the essential steps in linear regression, where our cost
function was the least squares function.
<p>
See discussion during lecture November 8.
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec55">The Squared-Error again! Steepest Descent </h2>
<p>
We start again with our cost function \( {\cal C}(\boldsymbol{y}m\boldsymbol{f})=\sum_{i=0}^{n-1}{\cal L}(y_i, f(x_i)) \) where we want to minimize
This means that for every iteration, we need to optimize
$$
(\hat{\boldsymbol{f}}) \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
$$
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec55">Gradient Boosting, algorithm </h2>
<h2 id="___sec56">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 squared-error function
@@ -2365,7 +2382,7 @@ The way we proceed in an iterative fashion is to
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec56">Gradient Boosting, Examples of Regression </h2>
<h2 id="___sec57">Gradient Boosting, Examples of Regression </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
@@ -2419,7 +2436,7 @@ plt<span style="color: #666666">.</span>show()
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec57">Gradient Boosting, Classification Example </h2>
<h2 id="___sec58">Gradient Boosting, Classification Example </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
@@ -2467,7 +2484,7 @@ plt<span style="color: #666666">.</span>show()
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec58">XGBoost: Extreme Gradient Boosting </h2>
<h2 id="___sec59">XGBoost: Extreme Gradient Boosting </h2>
<p>
<a href="https://github.com/dmlc/xgboost" target="_blank">XGBoost</a> or Extreme Gradient
@@ -2488,7 +2505,7 @@ 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="___sec59">Regression Case </h2>
<h2 id="___sec60">Regression Case </h2>
<p>
@@ -2543,7 +2560,7 @@ plt<span style="color: #666666">.</span>show()
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec60">Xgboost on the Cancer Data </h2>
<h2 id="___sec61">Xgboost on the Cancer Data </h2>
<p>
As you will see from the confusion matrix below, XGBoots does an excellent job on the Wisconsin cancer data and outperforms essentially all agorithms we have discussed till now.
@@ -2555,7 +2555,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"## Gradient boosting: Basics\n",
"## Gradient boosting: Basics with Steepest Descent\n",
"\n",
"Gradient boosting is again a similar technique to Adaptive boosting,\n",
"it combines so-called weak classifiers or regressors into a strong\n",
@@ -2565,8 +2565,25 @@
"bringing back the essential steps in linear regression, where our cost\n",
"function was the least squares function.\n",
"\n",
"See discussion during lecture November 8.\n",
"## The Squared-Error again! Steepest Descent\n",
"\n",
"We start again with our cost function ${\\cal C}(\\boldsymbol{y}m\\boldsymbol{f})=\\sum_{i=0}^{n-1}{\\cal L}(y_i, f(x_i))$ where we want to minimize\n",
"This means that for every iteration, we need to optimize"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"(\\hat{\\boldsymbol{f}}) \\mathrm{argmin}_{\\boldsymbol{f}}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i-f(x_i))^2.\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Gradient Boosting, algorithm\n",
"\n",
"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 squared-error function"
Binary file not shown.
+15 -2
View File
@@ -1938,7 +1938,7 @@ plt.show()
!split
===== Gradient boosting: Basics =====
===== Gradient boosting: Basics with Steepest Descent =====
Gradient boosting is again a similar technique to Adaptive boosting,
it combines so-called weak classifiers or regressors into a strong
@@ -1948,7 +1948,20 @@ 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.
See discussion during lecture November 8.
!split
===== The Squared-Error again! Steepest Descent =====
We start again with our cost function ${\cal C}(\bm{y}m\bm{f})=\sum_{i=0}^{n-1}{\cal L}(y_i, f(x_i))$ where we want to minimize
This means that for every iteration, we need to optimize
!bt
\[
(\hat{\bm{f}}) \mathrm{argmin}_{\bm{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
\]
!et
!split
===== Gradient Boosting, algorithm =====