From dcf2c56e72d9f058268d82c4ee1c41f5644afac4 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Wed, 13 Nov 2019 22:41:07 +0100 Subject: [PATCH] updating steepest decsent --- .../html/._DecisionTrees-bs000.html | 32 +++--- .../html/._DecisionTrees-bs001.html | 30 +++--- .../html/._DecisionTrees-bs002.html | 30 +++--- .../html/._DecisionTrees-bs003.html | 30 +++--- .../html/._DecisionTrees-bs004.html | 30 +++--- .../html/._DecisionTrees-bs005.html | 30 +++--- .../html/._DecisionTrees-bs006.html | 30 +++--- .../html/._DecisionTrees-bs007.html | 30 +++--- .../html/._DecisionTrees-bs008.html | 30 +++--- .../html/._DecisionTrees-bs009.html | 30 +++--- .../html/._DecisionTrees-bs010.html | 30 +++--- .../html/._DecisionTrees-bs011.html | 30 +++--- .../html/._DecisionTrees-bs012.html | 30 +++--- .../html/._DecisionTrees-bs013.html | 30 +++--- .../html/._DecisionTrees-bs014.html | 30 +++--- .../html/._DecisionTrees-bs015.html | 30 +++--- .../html/._DecisionTrees-bs016.html | 30 +++--- .../html/._DecisionTrees-bs017.html | 30 +++--- .../html/._DecisionTrees-bs018.html | 30 +++--- .../html/._DecisionTrees-bs019.html | 30 +++--- .../html/._DecisionTrees-bs020.html | 30 +++--- .../html/._DecisionTrees-bs021.html | 30 +++--- .../html/._DecisionTrees-bs022.html | 30 +++--- .../html/._DecisionTrees-bs023.html | 30 +++--- .../html/._DecisionTrees-bs024.html | 30 +++--- .../html/._DecisionTrees-bs025.html | 30 +++--- .../html/._DecisionTrees-bs026.html | 30 +++--- .../html/._DecisionTrees-bs027.html | 30 +++--- .../html/._DecisionTrees-bs028.html | 30 +++--- .../html/._DecisionTrees-bs029.html | 30 +++--- .../html/._DecisionTrees-bs030.html | 30 +++--- .../html/._DecisionTrees-bs031.html | 30 +++--- .../html/._DecisionTrees-bs032.html | 30 +++--- .../html/._DecisionTrees-bs033.html | 30 +++--- .../html/._DecisionTrees-bs034.html | 30 +++--- .../html/._DecisionTrees-bs035.html | 30 +++--- .../html/._DecisionTrees-bs036.html | 30 +++--- .../html/._DecisionTrees-bs037.html | 30 +++--- .../html/._DecisionTrees-bs038.html | 30 +++--- .../html/._DecisionTrees-bs039.html | 30 +++--- .../html/._DecisionTrees-bs040.html | 38 ++++--- .../html/._DecisionTrees-bs041.html | 30 +++--- .../html/._DecisionTrees-bs042.html | 30 +++--- .../html/._DecisionTrees-bs043.html | 30 +++--- .../html/._DecisionTrees-bs044.html | 30 +++--- .../html/._DecisionTrees-bs045.html | 30 +++--- .../html/._DecisionTrees-bs046.html | 30 +++--- .../html/._DecisionTrees-bs047.html | 30 +++--- .../html/._DecisionTrees-bs048.html | 30 +++--- .../html/._DecisionTrees-bs049.html | 30 +++--- .../html/._DecisionTrees-bs050.html | 30 +++--- .../html/._DecisionTrees-bs051.html | 30 +++--- .../html/._DecisionTrees-bs052.html | 30 +++--- .../html/._DecisionTrees-bs053.html | 30 +++--- .../html/._DecisionTrees-bs054.html | 31 +++--- .../html/._DecisionTrees-bs055.html | 30 +++--- .../html/._DecisionTrees-bs056.html | 34 +++--- .../html/._DecisionTrees-bs057.html | 58 +++++----- .../html/._DecisionTrees-bs058.html | 100 +++++++----------- .../html/._DecisionTrees-bs059.html | 76 ++++--------- .../html/._DecisionTrees-bs060.html | 91 +++++++++++----- .../DecisionTrees/html/DecisionTrees-bs.html | 32 +++--- .../html/DecisionTrees-reveal.html | 56 ++++++++-- .../html/DecisionTrees-solarized.html | 66 +++++++++--- doc/pub/DecisionTrees/html/DecisionTrees.html | 66 +++++++++--- .../DecisionTrees/ipynb/DecisionTrees.ipynb | 55 +++++++++- .../ipynb/ipynb-DecisionTrees-src.tar.gz | Bin 294061 -> 294061 bytes .../pdf/DecisionTrees-minted.pdf | Bin 555886 -> 556703 bytes doc/src/DecisionTrees/DecisionTrees.do.txt | 31 +++++- 69 files changed, 1380 insertions(+), 976 deletions(-) diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html index 63f72251e..054a16087 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -293,7 +297,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Nov 12, 2019

    +

    Nov 13, 2019


    @@ -317,7 +321,7 @@ MathJax.Hub.Config({

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs001.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs001.html index 14644dacf..e6439cac4 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs001.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs001.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -322,7 +326,7 @@ given some assumptions, make predictions about the target feature value
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs002.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs002.html index e63554739..0720ea171 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs002.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs002.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -300,7 +304,7 @@ This tree was produced using the Wisconsin cancer data (discussed here as well,
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs003.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs003.html index 4e600418d..90b1c8bc9 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs003.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs003.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -308,7 +312,7 @@ node.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html index 3be2300a8..bc3c7dfd3 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -309,7 +313,7 @@ Then we are essentially done!
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html index c4e151984..36c28cb07 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -388,7 +392,7 @@ plt.show()
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html index b1ed4994b..a5a36ada9 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -321,7 +325,7 @@ within box \( j \).
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html index 6ba0f87aa..7ba7a39f7 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -313,7 +317,7 @@ better tree in some future step.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html index e04a391ef..e1133af99 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -346,7 +350,7 @@ region contains more than five observations.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html index b7bbf5820..60a1f766a 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -315,7 +319,7 @@ parameter \( \alpha \).
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html index bc537bee7..c546e8569 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -328,7 +332,7 @@ subtree corresponding to \( \alpha \).
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html index db8ea7bec..8406a60f2 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -324,7 +328,7 @@ MathJax.Hub.Config({
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html index bc1e25cec..c05cf4ecf 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -316,7 +320,7 @@ fall into that region.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html index adb09abbd..a61ffc1ac 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -321,7 +325,7 @@ than is the classification error rate.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html index ea417c0e5..5e5929834 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -347,7 +351,7 @@ $$
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html index 153a21ff7..33cb56d02 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -338,7 +342,7 @@ os.system(cmd)
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html index ad84db902..52b5efd36 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -329,7 +333,7 @@ os.system(cmd)
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html index faf5731cf..97a71b5e7 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -312,7 +316,7 @@ We discuss both algorithms with applications here. The popular library Scikit
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html index b47df258f..f106735bf 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -302,7 +306,7 @@ MathJax.Hub.Config({
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html index c7172a2d5..424959151 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -302,7 +306,7 @@ MathJax.Hub.Config({
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html index 4ac60dc1a..a9ee25501 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -342,7 +346,7 @@ The table here summarizes the various attributes and
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html index 514ad9f17..5dc811a81 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -373,7 +377,7 @@ os.system(cmd)
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html index 91c083d28..232b8dd59 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -375,7 +379,7 @@ split = get_split(dataset)
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html index 31e57ed9d..1f90bc946 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -333,7 +337,7 @@ attributes at each step while growing the tree.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html index dff28202c..e803e455f 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -493,7 +497,7 @@ MathJax.Hub.Config({
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html index 59df7c247..e21a40e45 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -346,7 +350,7 @@ deep_tree_clf.fit(X_train_scaled, y_train)
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html index f449fde9d..245809d8b 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -369,7 +373,7 @@ plt.show()
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html index c3c56e1b5..d59f2a5d8 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -325,7 +329,7 @@ plt.show()
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html index 5d0433429..34e3aa473 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -319,7 +323,7 @@ tree_reg.fit(X, y)
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html index 7354d4364..e3cde3ad9 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -375,7 +379,7 @@ plt.show()
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html index 285468122..700b71947 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -311,7 +315,7 @@ MathJax.Hub.Config({
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html index eca648ad4..a53e204a9 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -316,7 +320,7 @@ trees can be substantially improved.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html index 76d2740a8..b6ea7d58c 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -324,7 +328,7 @@ We discuss these methods here.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html index f590a7fbd..dfe9ef1b9 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -305,7 +309,7 @@ MathJax.Hub.Config({
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html index c57379bce..6cc5d67ab 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -316,7 +320,7 @@ learning method.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html index 09b74d888..57aba38e3 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -326,7 +330,7 @@ predictor, averaged over all \( B \) trees.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html index afd55b199..b259e0b3a 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -318,7 +322,7 @@ plt.show()
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html index fce7988c6..af4149eb6 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -348,7 +352,7 @@ voting_clf.fit(X_train, y_train)
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -356,7 +360,7 @@ voting_clf.fit(X_train, y_train)
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -359,7 +363,7 @@ plt.show()
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -308,6 +312,10 @@ scaler.fit(X_train) X_train_scaled = scaler.transform(X_train) X_test_scaled = scaler.transform(X_test) +# we produce a simple tree first as benchmark +simpletree = DecisionTreeRegressor(max_depth=3) +simpletree.fit(X_train_scaled, y_train) +simpleprediction = simpletree.predict(X_test_scaled) for degree in range(1,maxdepth): model = DecisionTreeRegressor(max_depth=degree) y_pred = np.empty((y_test.shape[0], n_boostraps)) @@ -326,8 +334,10 @@ X_test_scaled = scalerprint('Var:', variance[degree]) print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree])) +mse_simpletree = np.mean( np.mean((y_test - simpleprediction)**2) plt.xlim(1,maxdepth) -plt.plot(polydegree, error, label='Error') +plt.plot(polydegree, error, label='MSE simple tree') +plt.plot(polydegree, mse_simpletree, label='MSE for Bootstrap') plt.plot(polydegree, bias, label='bias') plt.plot(polydegree, variance, label='Variance') plt.legend() @@ -360,7 +370,7 @@ plt.show()
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -341,7 +345,7 @@ this setting.
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -323,7 +327,7 @@ We will grow of forest of say \( M \) trees.
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -370,7 +374,7 @@ plt.show()
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -319,7 +323,7 @@ np.sum(y_pred =
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -314,7 +318,7 @@ them with a factor.
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -349,7 +353,7 @@ In iterative fitting or additive modeling, we minimize the cost function with re
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -322,7 +326,7 @@ at the internal nodes, and the predictions at the terminal nodes.
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -345,7 +349,7 @@ The solution to these two equations gives us in turn \( \beta_1 \) and \( \gamma
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -332,7 +336,7 @@ $$
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -325,7 +329,7 @@ where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \).
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -340,7 +344,7 @@ $$
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -319,7 +323,7 @@ where the function \( I() \) is one if we misclassify and zero if we classify co
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  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -336,6 +340,8 @@ observations that are missed in the previous iterations.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs054.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs054.html index f8510a9a0..d48cd9d10 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs054.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs054.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -328,6 +332,9 @@ plt.show()
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs055.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs055.html index a02966033..8c26c6b11 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs055.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs055.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -309,6 +313,8 @@ function was the least squares function.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs056.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs056.html index 42a5f4c77..735f280fb 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs056.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs056.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -281,7 +285,7 @@ We start again with our cost function \( {\cal C}(\boldsymbol{y}m\boldsymbol{f}) This means that for every iteration, we need to optimize $$ -(\hat{\boldsymbol{f}}) \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. +(\hat{\boldsymbol{f}}) = \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. $$

    @@ -303,7 +307,7 @@ the gradient is \( g_m(x_i) = -2(y_i-f(x_i)) \).

    Choosing \( f_0(x)=0 \) we obtain \( g_m(x) = -2y_i \) and inserting this into the minimization problem for the cost function we have $$ -(\rho_1) \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2. +(\rho_1) = \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2. $$

    @@ -328,6 +332,8 @@ $$

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs057.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs057.html index 59ffb9c1c..ff663b1a9 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs057.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs057.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -274,30 +278,22 @@ MathJax.Hub.Config({ -

    Gradient Boosting, algorithm

    +

    Steepest Descent Example

    -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 +Optimizing with respect to \( \rho \) we obtain (taking the derivative) that \( \rho_1 = -1/2 \). We have then that $$ -C(\boldsymbol{y},\boldsymbol{f})=\sum_{i=0}^{n-1}(y_i-f(x_i))^2. +f_1(x) = f_{0}(x) -\rho_1 g_1(x)=-y_i. $$ +We can then proceed and compute +$$ +g_2(x_i) = \left[ \frac{\partial {\cal L}(y_i, f(x_i))}{\partial f(x_i)}\right]_{f(x_i)=f_{1}(x_i)=y_i}=-4y_i, +$$ + +and find a new value for \( \rho_2=-1/2 \) and continue till we have reached \( m=M \). We can modify the steepest descent method, or steepest boosting, by introducing what is called gradient boosting. +

    -The way we proceed in an iterative fashion is to - -

      -
    1. Initialize our estimate \( f_0(x) \).
      2. -
    2. For \( m=1:M \), we - -
        -
      1. compute the negative gradient vector \( \boldsymbol{u}_m = -\partial C(\boldsymbol{y},\boldsymbol{f})/\partial \boldsymbol{f}(x) \) at \( f(x) = f_{m-1}(x) \);
        2. -
      2. fit the so-called base-learner to the negative gradient \( h_m(u_m,x) \);
        3. -
      3. update the estimate \( f_m(x) = f_{m-1}(x)+\nu h_m(u_m,x) \);
        4. -
      - -
    3. The final estimate is then \( f_M(x) = \sum_{m=1}^M\nu h_m(u_m,x) \).
      4. -
    -

      @@ -318,6 +314,8 @@ The way we proceed in an iterative fashion is to
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    diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs058.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs058.html index 53fb8cb7a..5758ef294 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs058.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs058.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -274,58 +278,30 @@ MathJax.Hub.Config({ -

    Gradient Boosting, Examples of Regression

    +

    Gradient Boosting, algorithm

    +

    +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 +$$ +C(\boldsymbol{y},\boldsymbol{f})=\sum_{i=0}^{n-1}(y_i-f(x_i))^2. +$$ - -

    import matplotlib.pyplot as plt
-import numpy as np
-from sklearn.model_selection import train_test_split
-from sklearn.ensemble import GradientBoostingRegressor
-from sklearn.preprocessing import StandardScaler
-import scikitplot as skplt
-from sklearn.metrics import mean_squared_error
-
-n = 100
-maxdegree = 6
-
-# Make data set.
-x = np.linspace(-3, 3, n).reshape(-1, 1)
-y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)
-
-error = np.zeros(maxdegree)
-bias = np.zeros(maxdegree)
-variance = np.zeros(maxdegree)
-polydegree = np.zeros(maxdegree)
-X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2)
-scaler = StandardScaler()
-scaler.fit(X_train)
-X_train_scaled = scaler.transform(X_train)
-X_test_scaled = scaler.transform(X_test)
-
-for degree in range(1,maxdegree):
-    model = GradientBoostingRegressor(max_depth=degree, n_estimators=100, learning_rate=1.0)  
-    model.fit(X_train_scaled,y_train)
-    y_pred = model.predict(X_test_scaled)
-    polydegree[degree] = degree
-    error[degree] = np.mean( np.mean((y_test - y_pred)**2) )
-    bias[degree] = np.mean( (y_test - np.mean(y_pred))**2 )
-    variance[degree] = np.mean( np.var(y_pred) )
-    print('Max depth:', degree)
-    print('Error:', error[degree])
-    print('Bias^2:', bias[degree])
-    print('Var:', variance[degree])
-    print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))
-
-plt.xlim(1,maxdegree-1)
-plt.plot(polydegree, error, label='Error')
-plt.plot(polydegree, bias, label='bias')
-plt.plot(polydegree, variance, label='Variance')
-plt.legend()
-save_fig("gdregression")
-plt.show()
-

    +The way we proceed in an iterative fashion is to + +

      +
    1. Initialize our estimate \( f_0(x) \).
      2. +
    2. For \( m=1:M \), we + +
        +
      1. compute the negative gradient vector \( \boldsymbol{u}_m = -\partial C(\boldsymbol{y},\boldsymbol{f})/\partial \boldsymbol{f}(x) \) at \( f(x) = f_{m-1}(x) \);
        2. +
      2. fit the so-called base-learner to the negative gradient \( h_m(u_m,x) \);
        3. +
      3. update the estimate \( f_m(x) = f_{m-1}(x)+\nu h_m(u_m,x) \);
        4. +
      + +
    3. The final estimate is then \( f_M(x) = \sum_{m=1}^M\nu h_m(u_m,x) \).
      4. +
    +

    diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs059.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs059.html index 95c63fc44..98e82e736 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs059.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs059.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -274,51 +278,11 @@ MathJax.Hub.Config({ -

    Gradient Boosting, Classification Example

    +

    Gradient Boosting Example, Regression

    +

    +We discuss here the difference between the steepest descent approach and gradient boosting by repeating our simple regression example above. - -

    import matplotlib.pyplot as plt
-import numpy as np
-from sklearn.model_selection import  train_test_split 
-from sklearn.datasets import load_breast_cancer
-import scikitplot as skplt
-from sklearn.ensemble import GradientBoostingClassifier
-from sklearn.model_selection import cross_validate
-
-# Load the data
-cancer = load_breast_cancer()
-
-X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
-print(X_train.shape)
-print(X_test.shape)
-#now scale the data
-from sklearn.preprocessing import StandardScaler
-scaler = StandardScaler()
-scaler.fit(X_train)
-X_train_scaled = scaler.transform(X_train)
-X_test_scaled = scaler.transform(X_test)
-
-gd_clf = GradientBoostingClassifier(max_depth=3, n_estimators=100, learning_rate=1.0)  
-gd_clf.fit(X_train_scaled, y_train)
-#Cross validation
-accuracy = cross_validate(gd_clf,X_test_scaled,y_test,cv=10)['test_score']
-print(accuracy)
-print("Test set accuracy with Random Forests and scaled data: {:.2f}".format(gd_clf.score(X_test_scaled,y_test)))
-
-import scikitplot as skplt
-y_pred = gd_clf.predict(X_test_scaled)
-skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
-save_fig("gdclassiffierconfusion")
-plt.show()
-y_probas = gd_clf.predict_proba(X_test_scaled)
-skplt.metrics.plot_roc(y_test, y_probas)
-save_fig("gdclassiffierroc")
-plt.show()
-skplt.metrics.plot_cumulative_gain(y_test, y_probas)
-save_fig("gdclassiffiercgain")
-plt.show()
-

    @@ -338,6 +302,8 @@ plt.show()

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs060.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs060.html index 7c3c24e51..48b99df5b 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs060.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs060.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -274,24 +278,57 @@ MathJax.Hub.Config({ -

    XGBoost: Extreme Gradient Boosting

    - +

    Gradient Boosting, Examples of Regression

    -XGBoost 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 article by Chen and Guestrin. -

    -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. + +

    import matplotlib.pyplot as plt
+import numpy as np
+from sklearn.model_selection import train_test_split
+from sklearn.ensemble import GradientBoostingRegressor
+from sklearn.preprocessing import StandardScaler
+import scikitplot as skplt
+from sklearn.metrics import mean_squared_error
 
-
    
-It is now the algorithm which wins essentially all ML competitions!!!
+n = 100
+maxdegree = 6
 
+# Make data set.
+x = np.linspace(-3, 3, n).reshape(-1, 1)
+y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)
+
+error = np.zeros(maxdegree)
+bias = np.zeros(maxdegree)
+variance = np.zeros(maxdegree)
+polydegree = np.zeros(maxdegree)
+X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2)
+scaler = StandardScaler()
+scaler.fit(X_train)
+X_train_scaled = scaler.transform(X_train)
+X_test_scaled = scaler.transform(X_test)
+
+for degree in range(1,maxdegree):
+    model = GradientBoostingRegressor(max_depth=degree, n_estimators=100, learning_rate=1.0)  
+    model.fit(X_train_scaled,y_train)
+    y_pred = model.predict(X_test_scaled)
+    polydegree[degree] = degree
+    error[degree] = np.mean( np.mean((y_test - y_pred)**2) )
+    bias[degree] = np.mean( (y_test - np.mean(y_pred))**2 )
+    variance[degree] = np.mean( np.var(y_pred) )
+    print('Max depth:', degree)
+    print('Error:', error[degree])
+    print('Bias^2:', bias[degree])
+    print('Var:', variance[degree])
+    print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))
+
+plt.xlim(1,maxdegree-1)
+plt.plot(polydegree, error, label='Error')
+plt.plot(polydegree, bias, label='bias')
+plt.plot(polydegree, variance, label='Variance')
+plt.legend()
+save_fig("gdregression")
+plt.show()
+

    @@ -310,6 +347,8 @@ It is now the algorithm which wins essentially all ML competitions!!!

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    • diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html index 63f72251e..054a16087 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html @@ -148,18 +148,20 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -253,12 +255,14 @@ MathJax.Hub.Config({
  • AdaBoost Examples
  • Gradient boosting: Basics with Steepest Descent
  • The Squared-Error again! Steepest Descent
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Classification Example
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Steepest Descent Example
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting Example, Regression
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -293,7 +297,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Nov 12, 2019

    +

    Nov 13, 2019


    @@ -317,7 +321,7 @@ MathJax.Hub.Config({

  • 9
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    • -
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    • diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html index fd93c2216..c2b91f094 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html @@ -148,7 +148,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

     
    -

    Nov 12, 2019

    +

    Nov 13, 2019


    @@ -1758,6 +1758,10 @@ scaler.fit(X_train) X_train_scaled = scaler.transform(X_train) X_test_scaled = scaler.transform(X_test) +# we produce a simple tree first as benchmark +simpletree = DecisionTreeRegressor(max_depth=3) +simpletree.fit(X_train_scaled, y_train) +simpleprediction = simpletree.predict(X_test_scaled) for degree in range(1,maxdepth): model = DecisionTreeRegressor(max_depth=degree) y_pred = np.empty((y_test.shape[0], n_boostraps)) @@ -1776,8 +1780,10 @@ X_test_scaled = scaler.transform(X_test) print('Var:', variance[degree]) print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree])) +mse_simpletree = np.mean( np.mean((y_test - simpleprediction)**2) plt.xlim(1,maxdepth) -plt.plot(polydegree, error, label='Error') +plt.plot(polydegree, error, label='MSE simple tree') +plt.plot(polydegree, mse_simpletree, label='MSE for Bootstrap') plt.plot(polydegree, bias, label='bias') plt.plot(polydegree, variance, label='Variance') plt.legend() @@ -2378,7 +2384,7 @@ This means that for every iteration, we need to optimize

     
    $$ -(\hat{\boldsymbol{f}}) \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. +(\hat{\boldsymbol{f}}) = \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. $$

     
    @@ -2406,14 +2412,36 @@ the gradient is \( g_m(x_i) = -2(y_i-f(x_i)) \). Choosing \( f_0(x)=0 \) we obtain \( g_m(x) = -2y_i \) and inserting this into the minimization problem for the cost function we have

     
    $$ -(\rho_1) \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2. +(\rho_1) = \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2. $$

     

    -

    Gradient Boosting, algorithm

    +

    Steepest Descent Example

    + +

    +Optimizing with respect to \( \rho \) we obtain (taking the derivative) that \( \rho_1 = -1/2 \). We have then that +

     
    +$$ +f_1(x) = f_{0}(x) -\rho_1 g_1(x)=-y_i. +$$ +

     
    + +We can then proceed and compute +

     
    +$$ +g_2(x_i) = \left[ \frac{\partial {\cal L}(y_i, f(x_i))}{\partial f(x_i)}\right]_{f(x_i)=f_{1}(x_i)=y_i}=-4y_i, +$$ +

     
    + +and find a new value for \( \rho_2=-1/2 \) and continue till we have reached \( m=M \). We can modify the steepest descent method, or steepest boosting, by introducing what is called gradient boosting. +

    + + +
    +

    Gradient Boosting, algorithm

    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 @@ -2441,7 +2469,15 @@ The way we proceed in an iterative fashion is to

    -

    Gradient Boosting, Examples of Regression

    +

    Gradient Boosting Example, Regression

    + +

    +We discuss here the difference between the steepest descent approach and gradient boosting by repeating our simple regression example above. +

    + + +
    +

    Gradient Boosting, Examples of Regression

    @@ -2496,7 +2532,7 @@ plt.show()

    -

    Gradient Boosting, Classification Example

    +

    Gradient Boosting, Classification Example

    @@ -2545,7 +2581,7 @@ plt.show()

    -

    XGBoost: Extreme Gradient Boosting

    +

    XGBoost: Extreme Gradient Boosting

    XGBoost or Extreme Gradient @@ -2566,7 +2602,7 @@ It is now the algorithm which wins essentially all ML competitions!!!

    -

    Regression Case

    +

    Regression Case

    @@ -2622,7 +2658,7 @@ plt.show()

    -

    Xgboost on the Cancer Data

    +

    Xgboost on the Cancer Data

    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. diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html index 3045d1183..3285766a2 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html @@ -168,18 +168,20 @@ div { text-align: justify; text-justify: inter-word; } 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -221,7 +223,7 @@ MathJax.Hub.Config({

    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Nov 12, 2019

    +

    Nov 13, 2019












    @@ -1786,6 +1788,10 @@ scaler.fit(X_train) X_train_scaled = scaler.transform(X_train) X_test_scaled = scaler.transform(X_test) +# we produce a simple tree first as benchmark +simpletree = DecisionTreeRegressor(max_depth=3) +simpletree.fit(X_train_scaled, y_train) +simpleprediction = simpletree.predict(X_test_scaled) for degree in range(1,maxdepth): model = DecisionTreeRegressor(max_depth=degree) y_pred = np.empty((y_test.shape[0], n_boostraps)) @@ -1804,8 +1810,10 @@ X_test_scaled = scaler.transform(X_test) print('Var:', variance[degree]) print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree])) +mse_simpletree = np.mean( np.mean((y_test - simpleprediction)**2) plt.xlim(1,maxdepth) -plt.plot(polydegree, error, label='Error') +plt.plot(polydegree, error, label='MSE simple tree') +plt.plot(polydegree, mse_simpletree, label='MSE for Bootstrap') plt.plot(polydegree, bias, label='bias') plt.plot(polydegree, variance, label='Variance') plt.legend() @@ -2345,7 +2353,7 @@ We start again with our cost function \( {\cal C}(\boldsymbol{y}m\boldsymbol{f}) This means that for every iteration, we need to optimize $$ -(\hat{\boldsymbol{f}}) \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. +(\hat{\boldsymbol{f}}) = \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. $$

    @@ -2367,13 +2375,31 @@ the gradient is \( g_m(x_i) = -2(y_i-f(x_i)) \).

    Choosing \( f_0(x)=0 \) we obtain \( g_m(x) = -2y_i \) and inserting this into the minimization problem for the cost function we have $$ -(\rho_1) \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2. +(\rho_1) = \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2. $$











    -

    Gradient Boosting, algorithm

    +

    Steepest Descent Example

    + +

    +Optimizing with respect to \( \rho \) we obtain (taking the derivative) that \( \rho_1 = -1/2 \). We have then that +$$ +f_1(x) = f_{0}(x) -\rho_1 g_1(x)=-y_i. +$$ + +We can then proceed and compute +$$ +g_2(x_i) = \left[ \frac{\partial {\cal L}(y_i, f(x_i))}{\partial f(x_i)}\right]_{f(x_i)=f_{1}(x_i)=y_i}=-4y_i, +$$ + +and find a new value for \( \rho_2=-1/2 \) and continue till we have reached \( m=M \). We can modify the steepest descent method, or steepest boosting, by introducing what is called gradient boosting. + +

    +









    + +

    Gradient Boosting, algorithm

    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 @@ -2399,7 +2425,15 @@ The way we proceed in an iterative fashion is to









    -

    Gradient Boosting, Examples of Regression

    +

    Gradient Boosting Example, Regression

    + +

    +We discuss here the difference between the steepest descent approach and gradient boosting by repeating our simple regression example above. + +

    +









    + +

    Gradient Boosting, Examples of Regression

    @@ -2453,7 +2487,7 @@ plt.show()











    -

    Gradient Boosting, Classification Example

    +

    Gradient Boosting, Classification Example

    @@ -2501,7 +2535,7 @@ plt.show()











    -

    XGBoost: Extreme Gradient Boosting

    +

    XGBoost: Extreme Gradient Boosting

    XGBoost or Extreme Gradient @@ -2522,7 +2556,7 @@ It is now the algorithm which wins essentially all ML competitions!!!











    -

    Regression Case

    +

    Regression Case

    @@ -2577,7 +2611,7 @@ plt.show()











    -

    Xgboost on the Cancer Data

    +

    Xgboost on the Cancer Data

    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. diff --git a/doc/pub/DecisionTrees/html/DecisionTrees.html b/doc/pub/DecisionTrees/html/DecisionTrees.html index ab637865b..61f9eb3dd 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees.html @@ -173,18 +173,20 @@ div { text-align: justify; text-justify: inter-word; } 2, None, '___sec55'), - ('Gradient Boosting, algorithm', 2, None, '___sec56'), + ('Steepest Descent Example', 2, None, '___sec56'), + ('Gradient Boosting, algorithm', 2, None, '___sec57'), + ('Gradient Boosting Example, Regression', 2, None, '___sec58'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec57'), + '___sec59'), ('Gradient Boosting, Classification Example', 2, None, - '___sec58'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), - ('Regression Case', 2, None, '___sec60'), - ('Xgboost on the Cancer Data', 2, None, '___sec61')]} + '___sec60'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec61'), + ('Regression Case', 2, None, '___sec62'), + ('Xgboost on the Cancer Data', 2, None, '___sec63')]} end of tocinfo --> @@ -226,7 +228,7 @@ MathJax.Hub.Config({

    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Nov 12, 2019

    +

    Nov 13, 2019












    @@ -1791,6 +1793,10 @@ scaler.fit(X_train) X_train_scaled = scaler.transform(X_train) X_test_scaled = scaler.transform(X_test) +# we produce a simple tree first as benchmark +simpletree = DecisionTreeRegressor(max_depth=3) +simpletree.fit(X_train_scaled, y_train) +simpleprediction = simpletree.predict(X_test_scaled) for degree in range(1,maxdepth): model = DecisionTreeRegressor(max_depth=degree) y_pred = np.empty((y_test.shape[0], n_boostraps)) @@ -1809,8 +1815,10 @@ X_test_scaled = scalerprint('Var:', variance[degree]) print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree])) +mse_simpletree = np.mean( np.mean((y_test - simpleprediction)**2) plt.xlim(1,maxdepth) -plt.plot(polydegree, error, label='Error') +plt.plot(polydegree, error, label='MSE simple tree') +plt.plot(polydegree, mse_simpletree, label='MSE for Bootstrap') plt.plot(polydegree, bias, label='bias') plt.plot(polydegree, variance, label='Variance') plt.legend() @@ -2350,7 +2358,7 @@ We start again with our cost function \( {\cal C}(\boldsymbol{y}m\boldsymbol{f}) This means that for every iteration, we need to optimize $$ -(\hat{\boldsymbol{f}}) \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. +(\hat{\boldsymbol{f}}) = \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. $$

    @@ -2372,13 +2380,31 @@ the gradient is \( g_m(x_i) = -2(y_i-f(x_i)) \).

    Choosing \( f_0(x)=0 \) we obtain \( g_m(x) = -2y_i \) and inserting this into the minimization problem for the cost function we have $$ -(\rho_1) \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2. +(\rho_1) = \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2. $$











    -

    Gradient Boosting, algorithm

    +

    Steepest Descent Example

    + +

    +Optimizing with respect to \( \rho \) we obtain (taking the derivative) that \( \rho_1 = -1/2 \). We have then that +$$ +f_1(x) = f_{0}(x) -\rho_1 g_1(x)=-y_i. +$$ + +We can then proceed and compute +$$ +g_2(x_i) = \left[ \frac{\partial {\cal L}(y_i, f(x_i))}{\partial f(x_i)}\right]_{f(x_i)=f_{1}(x_i)=y_i}=-4y_i, +$$ + +and find a new value for \( \rho_2=-1/2 \) and continue till we have reached \( m=M \). We can modify the steepest descent method, or steepest boosting, by introducing what is called gradient boosting. + +

    +









    + +

    Gradient Boosting, algorithm

    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 @@ -2404,7 +2430,15 @@ The way we proceed in an iterative fashion is to









    -

    Gradient Boosting, Examples of Regression

    +

    Gradient Boosting Example, Regression

    + +

    +We discuss here the difference between the steepest descent approach and gradient boosting by repeating our simple regression example above. + +

    +









    + +

    Gradient Boosting, Examples of Regression

    @@ -2458,7 +2492,7 @@ plt.show()











    -

    Gradient Boosting, Classification Example

    +

    Gradient Boosting, Classification Example

    @@ -2506,7 +2540,7 @@ plt.show()











    -

    XGBoost: Extreme Gradient Boosting

    +

    XGBoost: Extreme Gradient Boosting

    XGBoost or Extreme Gradient @@ -2527,7 +2561,7 @@ It is now the algorithm which wins essentially all ML competitions!!!











    -

    Regression Case

    +

    Regression Case

    @@ -2582,7 +2616,7 @@ plt.show()











    -

    Xgboost on the Cancer Data

    +

    Xgboost on the Cancer Data

    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. diff --git a/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb b/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb index 333396a8e..5f72bcd04 100644 --- a/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb +++ b/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb @@ -10,7 +10,7 @@ " \n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", "\n", - "Date: **Nov 12, 2019**\n", + "Date: **Nov 13, 2019**\n", "\n", "Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", @@ -1780,6 +1780,10 @@ "X_train_scaled = scaler.transform(X_train)\n", "X_test_scaled = scaler.transform(X_test)\n", "\n", + "# we produce a simple tree first as benchmark\n", + "simpletree = DecisionTreeRegressor(max_depth=3) \n", + "simpletree.fit(X_train_scaled, y_train)\n", + "simpleprediction = simpletree.predict(X_test_scaled)\n", "for degree in range(1,maxdepth):\n", " model = DecisionTreeRegressor(max_depth=degree) \n", " y_pred = np.empty((y_test.shape[0], n_boostraps))\n", @@ -1798,8 +1802,10 @@ " print('Var:', variance[degree])\n", " print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n", "\n", + "mse_simpletree = np.mean( np.mean((y_test - simpleprediction)**2)\n", "plt.xlim(1,maxdepth)\n", - "plt.plot(polydegree, error, label='Error')\n", + "plt.plot(polydegree, error, label='MSE simple tree')\n", + "plt.plot(polydegree, mse_simpletree, label='MSE for Bootstrap')\n", "plt.plot(polydegree, bias, label='bias')\n", "plt.plot(polydegree, variance, label='Variance')\n", "plt.legend()\n", @@ -2576,7 +2582,7 @@ "metadata": {}, "source": [ "$$\n", - "(\\hat{\\boldsymbol{f}}) \\mathrm{argmin}_{\\boldsymbol{f}}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i-f(x_i))^2.\n", + "(\\hat{\\boldsymbol{f}}) = \\mathrm{argmin}_{\\boldsymbol{f}}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i-f(x_i))^2.\n", "$$" ] }, @@ -2627,7 +2633,7 @@ "metadata": {}, "source": [ "$$\n", - "(\\rho_1) \\mathrm{argmin}_{\\rho}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i+2\\rho y_i)^2.\n", + "(\\rho_1) = \\mathrm{argmin}_{\\rho}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i+2\\rho y_i)^2.\n", "$$" ] }, @@ -2635,6 +2641,42 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "## Steepest Descent Example\n", + "\n", + "Optimizing with respect to $\\rho$ we obtain (taking the derivative) that $\\rho_1 = -1/2$. We have then that" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "f_1(x) = f_{0}(x) -\\rho_1 g_1(x)=-y_i.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can then proceed and compute" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "g_2(x_i) = \\left[ \\frac{\\partial {\\cal L}(y_i, f(x_i))}{\\partial f(x_i)}\\right]_{f(x_i)=f_{1}(x_i)=y_i}=-4y_i,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and find a new value for $\\rho_2=-1/2$ and continue till we have reached $m=M$. We can modify the steepest descent method, or steepest boosting, by introducing what is called **gradient boosting**. \n", + "\n", "## 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" @@ -2667,6 +2709,11 @@ "\n", "4. The final estimate is then $f_M(x) = \\sum_{m=1}^M\\nu h_m(u_m,x)$.\n", "\n", + "## Gradient Boosting Example, Regression\n", + "\n", + "We discuss here the difference between the steepest descent approach and gradient boosting by repeating our simple regression example above. \n", + "\n", + "\n", "## Gradient Boosting, Examples of Regression" ] }, diff --git a/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz b/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz index 65c88d19deba8b825bd09ea157a8a4d93b53cf96..43c2508b62c318899cf313e21e011c75135d9115 100644 GIT binary patch delta 30 mcmZ4cQ*iB1L3a6W4u-&rGmY%6?2N7KOs(w9TiIEb)c^pi$_dc` delta 30 mcmZ4cQ*iB1L3a6W4u-;)CmY#Y*%@2enOfPIx3aS=s{sJD=?Y%} diff --git a/doc/pub/DecisionTrees/pdf/DecisionTrees-minted.pdf b/doc/pub/DecisionTrees/pdf/DecisionTrees-minted.pdf index 42f87b2c230232bc5b3463f69c96720ed7050d90..519b8268ce8f048306b412ff9afd42ace4ae4640 100644 GIT binary patch delta 16510 zcmaj`Q*dK 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variance[degree], bias[degree]+variance[degree])) +mse_simpletree = np.mean( np.mean((y_test - simpleprediction)**2) plt.xlim(1,maxdepth) -plt.plot(polydegree, error, label='Error') +plt.plot(polydegree, error, label='MSE simple tree') +plt.plot(polydegree, mse_simpletree, label='MSE for Bootstrap') plt.plot(polydegree, bias, label='bias') plt.plot(polydegree, variance, label='Variance') plt.legend() @@ -1956,7 +1962,7 @@ This means that for every iteration, we need to optimize !bt \[ -(\hat{\bm{f}}) \mathrm{argmin}_{\bm{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. +(\hat{\bm{f}}) = \mathrm{argmin}_{\bm{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. \] !et @@ -1980,10 +1986,26 @@ the gradient is $g_m(x_i) = -2(y_i-f(x_i))$. Choosing $f_0(x)=0$ we obtain $g_m(x) = -2y_i$ and inserting this into the minimization problem for the cost function we have !bt \[ -(\rho_1) \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2. +(\rho_1) = \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2. \] !et +!split +===== Steepest Descent Example ===== + +Optimizing with respect to $\rho$ we obtain (taking the derivative) that $\rho_1 = -1/2$. We have then that +!bt +\[ +f_1(x) = f_{0}(x) -\rho_1 g_1(x)=-y_i. +\] +!et +We can then proceed and compute +!bt +\[ +g_2(x_i) = \left[ \frac{\partial {\cal L}(y_i, f(x_i))}{\partial f(x_i)}\right]_{f(x_i)=f_{1}(x_i)=y_i}=-4y_i, +\] +!et +and find a new value for $\rho_2=-1/2$ and continue till we have reached $m=M$. We can modify the steepest descent method, or steepest boosting, by introducing what is called _gradient boosting_. !split ===== Gradient Boosting, algorithm ===== @@ -2003,7 +2025,10 @@ o For $m=1:M$, we o update the estimate $f_m(x) = f_{m-1}(x)+\nu h_m(u_m,x)$; o The final estimate is then $f_M(x) = \sum_{m=1}^M\nu h_m(u_m,x)$. +!split +===== Gradient Boosting Example, Regression ===== +We discuss here the difference between the steepest descent approach and gradient boosting by repeating our simple regression example above. !split