From 06fa258b725921ab2f27d562f8594671fa4ab4cd Mon Sep 17 00:00:00 2001 From: mhjensen Date: Sun, 10 Nov 2019 11:32:41 +0100 Subject: [PATCH] more boosting stuff --- .../html/._DecisionTrees-bs000.html | 58 ++++---- .../html/._DecisionTrees-bs001.html | 58 ++++---- .../html/._DecisionTrees-bs002.html | 58 ++++---- .../html/._DecisionTrees-bs003.html | 58 ++++---- .../html/._DecisionTrees-bs004.html | 58 ++++---- .../html/._DecisionTrees-bs005.html | 58 ++++---- .../html/._DecisionTrees-bs006.html | 58 ++++---- .../html/._DecisionTrees-bs007.html | 58 ++++---- .../html/._DecisionTrees-bs008.html | 58 ++++---- .../html/._DecisionTrees-bs009.html | 58 ++++---- .../html/._DecisionTrees-bs010.html | 58 ++++---- .../html/._DecisionTrees-bs011.html | 58 ++++---- .../html/._DecisionTrees-bs012.html | 58 ++++---- .../html/._DecisionTrees-bs013.html | 58 ++++---- .../html/._DecisionTrees-bs014.html | 58 ++++---- .../html/._DecisionTrees-bs015.html | 58 ++++---- .../html/._DecisionTrees-bs016.html | 58 ++++---- .../html/._DecisionTrees-bs017.html | 58 ++++---- .../html/._DecisionTrees-bs018.html | 58 ++++---- .../html/._DecisionTrees-bs019.html | 58 ++++---- .../html/._DecisionTrees-bs020.html | 58 ++++---- .../html/._DecisionTrees-bs021.html | 58 ++++---- .../html/._DecisionTrees-bs022.html | 58 ++++---- .../html/._DecisionTrees-bs023.html | 58 ++++---- .../html/._DecisionTrees-bs024.html | 58 ++++---- .../html/._DecisionTrees-bs025.html | 58 ++++---- .../html/._DecisionTrees-bs026.html | 58 ++++---- .../html/._DecisionTrees-bs027.html | 58 ++++---- .../html/._DecisionTrees-bs028.html | 58 ++++---- .../html/._DecisionTrees-bs029.html | 58 ++++---- .../html/._DecisionTrees-bs030.html | 58 ++++---- .../html/._DecisionTrees-bs031.html | 58 ++++---- .../html/._DecisionTrees-bs032.html | 58 ++++---- .../html/._DecisionTrees-bs033.html | 58 ++++---- .../html/._DecisionTrees-bs034.html | 58 ++++---- .../html/._DecisionTrees-bs035.html | 58 ++++---- .../html/._DecisionTrees-bs036.html | 58 ++++---- .../html/._DecisionTrees-bs037.html | 58 ++++---- .../html/._DecisionTrees-bs038.html | 58 ++++---- .../html/._DecisionTrees-bs039.html | 58 ++++---- .../html/._DecisionTrees-bs040.html | 58 ++++---- .../html/._DecisionTrees-bs041.html | 58 ++++---- .../html/._DecisionTrees-bs042.html | 58 ++++---- .../html/._DecisionTrees-bs043.html | 58 ++++---- .../html/._DecisionTrees-bs044.html | 58 ++++---- .../html/._DecisionTrees-bs045.html | 58 ++++---- .../html/._DecisionTrees-bs046.html | 58 ++++---- .../html/._DecisionTrees-bs047.html | 58 ++++---- .../html/._DecisionTrees-bs048.html | 64 ++++----- .../html/._DecisionTrees-bs049.html | 88 +++++------- .../html/._DecisionTrees-bs050.html | 91 +++++++------ .../html/._DecisionTrees-bs051.html | 99 ++++++-------- .../html/._DecisionTrees-bs052.html | 105 +++++++++------ .../html/._DecisionTrees-bs053.html | 99 ++++++-------- .../html/._DecisionTrees-bs054.html | 110 ++++++++------- .../html/._DecisionTrees-bs055.html | 90 ++++++++----- .../html/._DecisionTrees-bs056.html | 85 ++++++------ .../html/._DecisionTrees-bs057.html | 127 +++++++----------- .../html/._DecisionTrees-bs058.html | 125 +++++++++-------- .../html/._DecisionTrees-bs059.html | 112 +++++++++------ .../html/._DecisionTrees-bs060.html | 117 ++++++---------- .../DecisionTrees/html/DecisionTrees-bs.html | 58 ++++---- .../html/DecisionTrees-reveal.html | 64 +++++---- .../html/DecisionTrees-solarized.html | 93 +++++++------ doc/pub/DecisionTrees/html/DecisionTrees.html | 93 +++++++------ .../DecisionTrees/ipynb/DecisionTrees.ipynb | 39 +++--- .../ipynb/ipynb-DecisionTrees-src.tar.gz | Bin 294061 -> 294061 bytes .../pdf/DecisionTrees-minted.pdf | Bin 540814 -> 541553 bytes doc/src/DecisionTrees/DecisionTrees.do.txt | 37 +++-- 69 files changed, 2312 insertions(+), 2168 deletions(-) diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html index 4e101a0bf..7b1ab4223 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -309,7 +311,7 @@ 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 2350d4bc8..eafffa067 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs001.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs001.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -314,7 +316,7 @@ 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 0654d72ab..4ee550be1 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs002.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs002.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -292,7 +294,7 @@ 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 919292c8d..1ad13205c 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs003.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs003.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -300,7 +302,7 @@ node.
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html index 1f7236227..c1ac1b1e5 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -301,7 +303,7 @@ 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 1befed5e0..e83300f6b 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -380,7 +382,7 @@ 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 a9c2a39d5..516738052 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -313,7 +315,7 @@ 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 0e901552c..38e49d9b5 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -305,7 +307,7 @@ 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 7b474afa2..eb2b695f5 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -338,7 +340,7 @@ 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 2410de3a5..f36e75ae0 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -307,7 +309,7 @@ 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 7a908fc23..c739a708d 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -320,7 +322,7 @@ 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 f04a514d6..304e80744 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -316,7 +318,7 @@ 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 ff80579eb..9797836d6 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -308,7 +310,7 @@ fall into that region.
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -313,7 +315,7 @@ than is the classification error rate.
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -339,7 +341,7 @@ $$
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html index 3274f962a..0e396da70 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -330,7 +332,7 @@ 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 113241694..9b7bfa0bd 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -321,7 +323,7 @@ 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 333924db2..c036e8e25 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -304,7 +306,7 @@ We discuss both algorithms with applications here. The popular library Scikit
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -294,7 +296,7 @@ MathJax.Hub.Config({
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -294,7 +296,7 @@ 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 56ec2bd6a..28a4ca907 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -334,7 +336,7 @@ The table here summarizes the various attributes and
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -365,7 +367,7 @@ 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 26e41d9c8..379cb05a9 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -367,7 +369,7 @@ split = get_split(dataset)
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -325,7 +327,7 @@ 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 21f476459..aac18ce99 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -485,7 +487,7 @@ 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 d04d0aa81..f908376e9 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -338,7 +340,7 @@ 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 5bb1aec14..4329762e6 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -361,7 +363,7 @@ 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 a7a02ac83..cfbb5765b 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -317,7 +319,7 @@ 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 642455066..35edf1d2d 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -311,7 +313,7 @@ tree_reg.fit(X, y)
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -367,7 +369,7 @@ 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 1cd52395f..dc6422ca8 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -303,7 +305,7 @@ 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 eae3bd37b..8d2c52dbb 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -308,7 +310,7 @@ trees can be substantially improved.
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -316,7 +318,7 @@ 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 5cc5e94f9..9d85bacaa 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -297,7 +299,7 @@ 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 7ad392ede..7ac72b06b 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -308,7 +310,7 @@ 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 91ed12dee..eb7537487 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -318,7 +320,7 @@ 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 7b3710689..67e4be8eb 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -310,7 +312,7 @@ 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 88d820227..7414b5019 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -340,7 +342,7 @@ voting_clf.fit(X_train, y_train)
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs038.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs038.html index 236afbadf..d07b2de26 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs038.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs038.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -348,7 +350,7 @@ voting_clf.fit(X_train, y_train)
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs039.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs039.html index ad37381f9..4a72f3034 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs039.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs039.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -351,7 +353,7 @@ plt.show()
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs040.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs040.html index 5f57d30db..515190eb1 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs040.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs040.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -352,7 +354,7 @@ plt.show()
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs041.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs041.html index b005c5e51..e5f1f6fb0 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs041.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs041.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -333,7 +335,7 @@ this setting.
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -315,7 +317,7 @@ We will grow of forest of say \( M \) trees.
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -362,7 +364,7 @@ plt.show()
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs044.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs044.html index a22dd778b..e1c3aaa31 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs044.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs044.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -311,7 +313,7 @@ np.sum(y_pred =
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -306,7 +308,7 @@ them with a factor.
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -341,7 +343,7 @@ In iterative fitting or additive modeling, we minimize the cost function with re
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -314,7 +316,7 @@ at the internal nodes, and the predictions at the terminal nodes.
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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -278,7 +280,7 @@ For simplicity we assume also that our functions \( b(x;\gamma)=\gamma_0+\gamma_ This means that for every iteration, we need to optmize $$ -(\beta_m,\gamma_m) \mathrm{armmin}_{\beta,\gambda}\hspace{0.2cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(\gamma_0+\gamma_1 x_i))^2. +(\beta_m,\gamma_m) \mathrm{argmin}_{\beta,\gambda}\hspace{0.2cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(\gamma_0+\gamma_1 x_i))^2. \[ $$ @@ -291,12 +293,12 @@ $$ and $$ -\frac{\partial {\cal C}}{\partial \gamma_0} = +\frac{\partial {\cal C}}{\partial \gamma_0} =-2\sum_{i}\beta(y_i-\beta(\gamma_0+\gamma_1 x_i))=0, $$ and $$ -\frac{\partial {\cal C}}{\partial \gamma_1} = +\frac{\partial {\cal C}}{\partial \gamma_1} = =-2\sum_{i}\beta x_i(y_i-\beta(\gamma_0+\gamma_1 x_i))=0. $$

    @@ -325,7 +327,7 @@ $$

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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,36 +268,10 @@ MathJax.Hub.Config({ -

    Iterative Fitting, Classification, AdaBoost

    +

    Finding the Optimal Parameters

    -Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of -observations. We define a classification function \( G(x) \) which produces a prediction taking any of the two values -\( \{-1,1\} \). - -

    -The error rate of the training sample is then - -$$ -\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i). -$$ - -

    -The iterative procedure starts with defining a weak classifier whose -error rate is barely better than random guessing. Teh iterative -procedure in boosting is to sequentially apply a the weak -classification algorithm to repeatedly modified versions of the data producing a sequence of weak classifiers \( G_m(x) \). - -

    -Here we will express our function \( f(x) \) in terms of \( G(x) \). That is -$$ -f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m), -$$ - -will be a function of -$$ -G_M(x) = \mathrm{sign} \sum_{i=1}^M \alpha_m G_m(x). -$$ +With these equations we can then in turn find the parameters \( \beta_1 \) and \( \gamma_0^{1} \) and \( \gamma_1^1 \) as

    @@ -323,7 +299,7 @@ $$

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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,30 +268,37 @@ MathJax.Hub.Config({ -

    Adaptive Boosting, AdaBoost

    +

    Iterative Fitting, Classification, AdaBoost

    -In our iterative procedure we define thus +Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of +observations. We define a classification function \( G(x) \) which produces a prediction taking any of the two values +\( \{-1,1\} \). + +

    +The error rate of the training sample is then + $$ -f_m(x) = f_{m-1}(x)+\beta_mG_m(x). +\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i)). $$

    -The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the -exponential cost/loss function defined as -$$ -C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1}(x_i)+\beta G(x_i))}. -$$ +The iterative procedure starts with defining a weak classifier whose +error rate is barely better than random guessing. The iterative +procedure in boosting is to sequentially apply a the weak +classification algorithm to repeatedly modified versions of the data +producing a sequence of weak classifiers \( G_m(x) \).

    -We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in the regression case. -This is normally done in two steps. Let us however first rewrite the cost function as - +Here we will express our function \( f(x) \) in terms of \( G(x) \). That is $$ -C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{-(y_i\beta G(x_i))}, +f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m), $$ -where we have defined \( w_i^m= \exp{-(y_if_{m-1}(x_i))} \). +will be a function of +$$ +G_M(x) = \mathrm{sign} \sum_{i=1}^M \alpha_m G_m(x). +$$

    @@ -317,7 +326,7 @@ where we have defined \( w_i^m= \exp{-(y_if_{m-1}(x_i))} \).

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  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,47 +268,32 @@ MathJax.Hub.Config({ -

    Building up AdaBoost

    +

    Adaptive Boosting, AdaBoost

    -First, for any \( \beta > 0 \), we optimize \( G \) by setting +In our iterative procedure we define thus $$ -G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)), +f_m(x) = f_{m-1}(x)+\beta_mG_m(x). $$ -which is the classifier that minimizes the weighted error rate in predicting \( y \). -

    -We can do this by rewriting +The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the +exponential cost/loss function defined as $$ -\exp{-(\beta)}\sum_{y_i=G(x_i)}w_i^m+\exp{(\beta)}\sum_{y_i\ne G(x_i)}w_i^m, +C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{(-y_i(f_{m-1}(x_i)+\beta G(x_i))}. $$ -which can be rewritten as +

    +We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in the regression case. +This is normally done in two steps. Let us however first rewrite the cost function as + $$ -(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{-(\beta)}\sum_{i=0}^{n-1}w_i^m=0, +C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{(-y_i\beta G(x_i))}, $$ -which leads to -$$ -\beta_m = \frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}}, -$$ - -where we have redefined the error as -$$ -\mathrm{\overline{err}}_m=\frac{1}{n}\frac{\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i)}{\sum_{i=0}^{n-1}w_i^m}, -$$ - -which leads to an update of -$$ -f_m(x) = f_{m-1}(x) +\beta_m G_m(x). -$$ - -This leads to the new weights -$$ -w_i^{m+1} = w_i^m \exp{-(y_i\beta_m G_m(x_i))} -$$ +where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \). +

    diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs052.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs052.html index 69e2a0f44..9cfb5899f 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs052.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs052.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,26 +268,47 @@ MathJax.Hub.Config({ -

    Adaptive boosting: AdaBoost, Basic Algorithm

    +

    Building up AdaBoost

    -The algorithm here is rather straightforward. Assume that our weak -classifier is a decision tree and we consider a binary set of outputs -with \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of -observations. Our design matrix is given in terms of the -feature/predictor vectors -\( \boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1}] \). Finally, we define also a -classifier determined by our data via a function \( G(x) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \). - -

    -We can then define the misclassification error \( \mathrm{err} \) as +First, for any \( \beta > 0 \), we optimize \( G \) by setting $$ -\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i), +G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)), $$ -where the function \( I() \) is one if we misclassify and zero if we classify correctly. +which is the classifier that minimizes the weighted error rate in predicting \( y \).

    +We can do this by rewriting +$$ +\exp{-(\beta)}\sum_{y_i=G(x_i)}w_i^m+\exp{(\beta)}\sum_{y_i\ne G(x_i)}w_i^m, +$$ + +which can be rewritten as +$$ +(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{(-\beta)}\sum_{i=0}^{n-1}w_i^m=0, +$$ + +which leads to +$$ +\beta_m = \frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}}, +$$ + +where we have redefined the error as +$$ +\mathrm{\overline{err}}_m=\frac{1}{n}\frac{\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i)}{\sum_{i=0}^{n-1}w_i^m}, +$$ + +which leads to an update of +$$ +f_m(x) = f_{m-1}(x) +\beta_m G_m(x). +$$ + +This leads to the new weights +$$ +w_i^{m+1} = w_i^m \exp{(-y_i\beta_m G_m(x_i))} +$$ +

      @@ -310,6 +333,8 @@ where the function \( I() \) is one if we misclassify and zero if we classify co
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    diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs053.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs053.html index c2495d95c..040d28dd3 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs053.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs053.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,42 +268,24 @@ MathJax.Hub.Config({ -

    Basic Steps of AdaBoost

    +

    Adaptive boosting: AdaBoost, Basic Algorithm

    -With the above definitions we are now ready to set up the algorithm for AdaBoost. -The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases. - -

      -
    1. We start by initializing all weights to \( w_i = 1/n \), with \( i=0,1,2,\dots n-1 \). It is to see then that \( \sum_{i=0}^{n-1}w_i = 1 \).
      2. -
    2. We rewrite the misclassification error as
      3. -
    +The algorithm here is rather straightforward. Assume that our weak +classifier is a decision tree and we consider a binary set of outputs +with \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of +observations. Our design matrix is given in terms of the +feature/predictor vectors +\( \boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1}] \). Finally, we define also a +classifier determined by our data via a function \( G(x) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \). +

    +We have already defined the misclassification error \( \mathrm{err} \) as $$ -\mathrm{\overline{err}}_m=\frac{\sum_{i=0}^{n-1}w_i^m I(y_i\ne G(x_i))}{\sum_{i=0}^{n-1}w_i}, +\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i)), $$ - -

      -
    1. Then we start looping over all attempts at classifying, namely we start an iterative process for \( m=1:M \), where \( M \) is the final number of classifications. Our given classifier could for example be a plain decision tree. - -
        -
      1. Fit then a given classifier to the training using the weights \( w_i \).
        2. -
      2. Compute then \( \mathrm{err} \) and figure out which events are classified properly and which are classified wrongly.
        3. -
      3. Define a quantity \( \alpha_{m} = \log{(1-\mathrm{\overline{err}}_m)/\mathrm{\overline{err}}_m} \)
        4. -
      4. Set the new weights to \( w_i = w_i\times \exp{(\alpha_m I(y_i\ne G(x_i)} \).
        5. -
      - -
    2. Compute the new classifier \( G(x)= \sum_{i=0}^{n-1}\alpha_m I(y_i\ne G(x_i) \).
      3. -
    - -For the iterations with \( m \le 2 \) the weights are modified -individually at each steps. The obersvations which were misclassified -at iteration \( m-1 \) have a weight which is larger than those which were -classified properly. As this proceeds, the observations which were -difficult to classifiy correctly are given a larger influence. Each -new classification step \( m \) is then forced to concentrate on those -observations that are missed in the previous iterations. +where the function \( I() \) is one if we misclassify and zero if we classify correctly.

    @@ -327,6 +311,7 @@ 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 1b5634857..11e78a670 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs054.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs054.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,36 +268,43 @@ MathJax.Hub.Config({ -

    AdaBoost Examples

    +

    Basic Steps of AdaBoost

    -Using Scikit-Learn it is easy to appply the adaptive boosting algorithm, as done here. +With the above definitions we are now ready to set up the algorithm for AdaBoost. +The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases. -

    +

      +
    1. We start by initializing all weights to \( w_i = 1/n \), with \( i=0,1,2,\dots n-1 \). It is to see then that \( \sum_{i=0}^{n-1}w_i = 1 \).
      2. +
    2. We rewrite the misclassification error as
      3. +
    - -
    from sklearn.ensemble import AdaBoostClassifier
+$$
+\mathrm{\overline{err}}_m=\frac{\sum_{i=0}^{n-1}w_i^m I(y_i\ne G(x_i))}{\sum_{i=0}^{n-1}w_i},
+$$
 
-ada_clf = AdaBoostClassifier(
-    DecisionTreeClassifier(max_depth=1), n_estimators=200,
-    algorithm="SAMME.R", learning_rate=0.5, random_state=42)
-ada_clf.fit(X_train, y_train)
 
-from sklearn.ensemble import AdaBoostClassifier
+
      
+
    1.  Then we start looping over all attempts at classifying, namely we start an iterative process for \( m=1:M \), where \( M \) is the final number of classifications. Our given classifier could for example be a plain decision tree.
+
+
        
+ 
      1.  Fit then a given classifier to the training using the weights \( w_i \).
        2. 
+ 
      2.  Compute then \( \mathrm{err} \) and figure out which events are classified properly and which are classified wrongly.
        3. 
+ 
      3.  Define a quantity \( \alpha_{m} = \log{(1-\mathrm{\overline{err}}_m)/\mathrm{\overline{err}}_m} \)
        4. 
+ 
      4.  Set the new weights to \( w_i = w_i\times \exp{(\alpha_m I(y_i\ne G(x_i)} \).
        5. 
+
      
+
+
    2.  Compute the new classifier \( G(x)= \sum_{i=0}^{n-1}\alpha_m I(y_i\ne G(x_i) \).
      3. 
+
    
+
+For the iterations with \( m \le 2 \) the weights are modified
+individually at each steps. The obersvations which were misclassified
+at iteration \( m-1 \) have a weight which is larger than those which were
+classified properly. As this proceeds, the observations which were
+difficult to classifiy correctly are given a larger influence. Each
+new classification step \( m \) is then forced to concentrate on those
+observations that are missed in the previous iterations.
 
-ada_clf = AdaBoostClassifier(
-    DecisionTreeClassifier(max_depth=1), n_estimators=200,
-    algorithm="SAMME.R", learning_rate=0.5, random_state=42)
-ada_clf.fit(X_train_scaled, y_train)
-y_pred = ada_clf.predict(X_test_scaled)
-skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
-plt.show()
-y_probas = ada_clf.predict_proba(X_test_scaled)
-skplt.metrics.plot_roc(y_test, y_probas)
-plt.show()
-skplt.metrics.plot_cumulative_gain(y_test, y_probas)
-plt.show()
-

    @@ -319,6 +328,7 @@ 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 efe62ae90..93e36c0a6 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs055.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs055.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,21 +268,36 @@ MathJax.Hub.Config({ -

    Gradient boosting: Basics

    +

    AdaBoost Examples

    -Gradient boosting is again a similar technique to Adapative boosting, -it combines so-called weak classifiers or regressors into a strong -method via a series of iterations. +Using Scikit-Learn it is easy to appply the adaptive boosting algorithm, as done here.

    -In order to understand the method, let us illustrate its basics by -bringing back the essential steps in linear regression, where our cost -function was the least squares function. -

    -See discussion during lecture November 8. + +

    from sklearn.ensemble import AdaBoostClassifier
 
+ada_clf = AdaBoostClassifier(
+    DecisionTreeClassifier(max_depth=1), n_estimators=200,
+    algorithm="SAMME.R", learning_rate=0.5, random_state=42)
+ada_clf.fit(X_train, y_train)
+
+from sklearn.ensemble import AdaBoostClassifier
+
+ada_clf = AdaBoostClassifier(
+    DecisionTreeClassifier(max_depth=1), n_estimators=200,
+    algorithm="SAMME.R", learning_rate=0.5, random_state=42)
+ada_clf.fit(X_train_scaled, y_train)
+y_pred = ada_clf.predict(X_test_scaled)
+skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
+plt.show()
+y_probas = ada_clf.predict_proba(X_test_scaled)
+skplt.metrics.plot_roc(y_test, y_probas)
+plt.show()
+skplt.metrics.plot_cumulative_gain(y_test, y_probas)
+plt.show()
+

    @@ -303,6 +320,7 @@ See discussion during lecture November 8.

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs056.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs056.html index 8e6bcc7cd..eb94bb397 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs056.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs056.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,30 +268,22 @@ MathJax.Hub.Config({ -

    Gradient Boosting, algorithm

    +

    Gradient boosting: Basics

    -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 square-error function -$$ -C(\boldsymbol{y},\boldsymbol{f})=\sum_{i=0}^{n-1}(y_i-f(x_i))^2. -$$ +Gradient boosting is again a similar technique to Adapative boosting, +it combines so-called weak classifiers or regressors into a strong +method via a series of iterations.

    -The way we proceed in an iterative fashion is to +In order to understand the method, let us illustrate its basics by +bringing back the essential steps in linear regression, where our cost +function was the least squares function. -

      -
    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. -
    +

    +See discussion during lecture November 8. +

      @@ -310,6 +304,7 @@ The way we proceed in an iterative fashion is to
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    diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs057.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs057.html index 37c8e5a53..8975c7810 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs057.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs057.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,58 +268,30 @@ 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 square-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-bs058.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs058.html index c52637bec..ddda5b9cf 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs058.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs058.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,49 +268,55 @@ MathJax.Hub.Config({ -

    Gradient Boosting, Examples of Classification

    +

    Gradient Boosting, Examples of Regression 

    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.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)
 
-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)))
+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]))
 
-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.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()

    @@ -330,6 +338,7 @@ plt.show()

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs059.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs059.html index 71e74eda9..f99146173 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs059.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs059.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,24 +268,51 @@ MathJax.Hub.Config({ -

    XGBoost: Extreme Gradient Boosting

    - +

    Gradient Boosting, Classification Example

    -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.datasets import load_breast_cancer
+import scikitplot as skplt
+from sklearn.ensemble import GradientBoostingClassifier
+from sklearn.model_selection import cross_validate
 
-
    
-It is now the algorithm which wins essentially all ML competitions!!!
+# 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()
+

    @@ -302,6 +331,7 @@ It is now the algorithm which wins essentially all ML competitions!!!

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs060.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs060.html index f09a36a74..864e4c3c6 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs060.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs060.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -266,58 +268,24 @@ MathJax.Hub.Config({ -

    Regression Case

    +

    XGBoost: Extreme Gradient Boosting

    +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. - -

    import matplotlib.pyplot as plt
-import numpy as np
-from sklearn.model_selection import train_test_split
-import xgboost as xgb
-from sklearn.preprocessing import StandardScaler
-import scikitplot as skplt
-from sklearn.metrics import mean_squared_error
+
    
+The authors design and build a highly scalable end-to-end tree
+boosting system. It has  a theoretically justified weighted quantile
+sketch for efficient proposal calculation. It introduces a novel sparsity-aware algorithm for parallel tree learning and an effective cache-aware block structure for out-of-core tree learning.
 
-n = 100
-maxdegree = 6
+
    
+It is now the algorithm which wins essentially all ML competitions!!!
 
-# 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(maxdegree):
-    model =  xgb.XGBRegressor(objective ='reg:squarederror', colsaobjective ='reg:squarederror', colsample_bytree = 0.3, learning_rate = 0.1,max_depth = degree, alpha = 10, n_estimators = 200)
-
-    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()
-plt.show()
-

    @@ -335,6 +303,7 @@ plt.show()

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    • diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html index 4e101a0bf..7b1ab4223 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html @@ -128,31 +128,32 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -238,19 +239,20 @@ MathJax.Hub.Config({
  • What is boosting? Additive Modelling/Iterative Fitting
  • Iterative Fitting, Regression and Squared-error Cost Function
  • Squared Error Exampe and Iterative Fitting
    • -
  • Iterative Fitting, Classification, AdaBoost
    • -
  • Adaptive Boosting, AdaBoost
    • -
  • Building up AdaBoost
    • -
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • -
  • Basic Steps of AdaBoost
    • -
  • AdaBoost Examples
    • -
  • Gradient boosting: Basics
    • -
  • Gradient Boosting, algorithm
    • -
  • Gradient Boosting, Examples of Regression
    • -
  • Gradient Boosting, Examples of Classification
    • -
  • XGBoost: Extreme Gradient Boosting
    • -
  • Regression Case
    • -
  • Xgboost on the Cancer Data
    • +
  • Finding the Optimal Parameters
    • +
  • Iterative Fitting, Classification, AdaBoost
    • +
  • Adaptive Boosting, AdaBoost
    • +
  • Building up AdaBoost
    • +
  • Adaptive boosting: AdaBoost, Basic Algorithm
    • +
  • Basic Steps of AdaBoost
    • +
  • AdaBoost Examples
    • +
  • Gradient boosting: Basics
    • +
  • Gradient Boosting, algorithm
    • +
  • Gradient Boosting, Examples of Regression
    • +
  • Gradient Boosting, Classification Example
    • +
  • XGBoost: Extreme Gradient Boosting
    • +
  • Regression Case
    • +
  • Xgboost on the Cancer Data
    • @@ -309,7 +311,7 @@ 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 3af01e830..31cd8c807 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html @@ -2078,7 +2078,7 @@ This means that for every iteration, we need to optmize

     
    $$ -(\beta_m,\gamma_m) \mathrm{armmin}_{\beta,\gambda}\hspace{0.2cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(\gamma_0+\gamma_1 x_i))^2. +(\beta_m,\gamma_m) \mathrm{argmin}_{\beta,\gambda}\hspace{0.2cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(\gamma_0+\gamma_1 x_i))^2. \[ $$

     
    @@ -2095,21 +2095,29 @@ $$ and

     
    $$ -\frac{\partial {\cal C}}{\partial \gamma_0} = +\frac{\partial {\cal C}}{\partial \gamma_0} =-2\sum_{i}\beta(y_i-\beta(\gamma_0+\gamma_1 x_i))=0, $$

     
    and

     
    $$ -\frac{\partial {\cal C}}{\partial \gamma_1} = +\frac{\partial {\cal C}}{\partial \gamma_1} = =-2\sum_{i}\beta x_i(y_i-\beta(\gamma_0+\gamma_1 x_i))=0. $$

     

    -

    Iterative Fitting, Classification, AdaBoost

    +

    Finding the Optimal Parameters

    + +

    +With these equations we can then in turn find the parameters \( \beta_1 \) and \( \gamma_0^{1} \) and \( \gamma_1^1 \) as +

    + + +
    +

    Iterative Fitting, Classification, AdaBoost

    Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of @@ -2121,15 +2129,16 @@ The error rate of the training sample is then

     
    $$ -\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i). +\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i)). $$

     

    The iterative procedure starts with defining a weak classifier whose -error rate is barely better than random guessing. Teh iterative +error rate is barely better than random guessing. The iterative procedure in boosting is to sequentially apply a the weak -classification algorithm to repeatedly modified versions of the data producing a sequence of weak classifiers \( G_m(x) \). +classification algorithm to repeatedly modified versions of the data +producing a sequence of weak classifiers \( G_m(x) \).

    Here we will express our function \( f(x) \) in terms of \( G(x) \). That is @@ -2149,7 +2158,7 @@ $$

    -

    Adaptive Boosting, AdaBoost

    +

    Adaptive Boosting, AdaBoost

    In our iterative procedure we define thus @@ -2164,7 +2173,7 @@ The simplest possible cost function which leads (also simple from a computationa exponential cost/loss function defined as

     
    $$ -C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1}(x_i)+\beta G(x_i))}. +C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{(-y_i(f_{m-1}(x_i)+\beta G(x_i))}. $$

     
    @@ -2174,16 +2183,16 @@ This is normally done in two steps. Let us however first rewrite the cost functi

     
    $$ -C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{-(y_i\beta G(x_i))}, +C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{(-y_i\beta G(x_i))}, $$

     
    -where we have defined \( w_i^m= \exp{-(y_if_{m-1}(x_i))} \). +where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \).

    -

    Building up AdaBoost

    +

    Building up AdaBoost

    First, for any \( \beta > 0 \), we optimize \( G \) by setting @@ -2206,7 +2215,7 @@ $$ which can be rewritten as

     
    $$ -(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{-(\beta)}\sum_{i=0}^{n-1}w_i^m=0, +(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{(-\beta)}\sum_{i=0}^{n-1}w_i^m=0, $$

     
    @@ -2234,14 +2243,14 @@ $$ This leads to the new weights

     
    $$ -w_i^{m+1} = w_i^m \exp{-(y_i\beta_m G_m(x_i))} +w_i^{m+1} = w_i^m \exp{(-y_i\beta_m G_m(x_i))} $$

     

    -

    Adaptive boosting: AdaBoost, Basic Algorithm

    +

    Adaptive boosting: AdaBoost, Basic Algorithm

    The algorithm here is rather straightforward. Assume that our weak @@ -2253,10 +2262,10 @@ feature/predictor vectors classifier determined by our data via a function \( G(x) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \).

    -We can then define the misclassification error \( \mathrm{err} \) as +We have already defined the misclassification error \( \mathrm{err} \) as

     
    $$ -\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i), +\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i)), $$

     
    @@ -2265,7 +2274,7 @@ where the function \( I() \) is one if we misclassify and zero if we classify co

    -

    Basic Steps of AdaBoost

    +

    Basic Steps of AdaBoost

    With the above definitions we are now ready to set up the algorithm for AdaBoost. @@ -2306,7 +2315,7 @@ observations that are missed in the previous iterations.

    -

    AdaBoost Examples

    +

    AdaBoost Examples

    Using Scikit-Learn it is easy to appply the adaptive boosting algorithm, as done here. @@ -2340,7 +2349,7 @@ plt.show()

    -

    Gradient boosting: Basics

    +

    Gradient boosting: Basics

    Gradient boosting is again a similar technique to Adapative boosting, @@ -2358,7 +2367,7 @@ See discussion during lecture November 8.

    -

    Gradient Boosting, algorithm

    +

    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 square-error function @@ -2386,7 +2395,7 @@ The way we proceed in an iterative fashion is to

    -

    Gradient Boosting, Examples of Regression

    +

    Gradient Boosting, Examples of Regression

    @@ -2441,7 +2450,7 @@ plt.show()

    -

    Gradient Boosting, Examples of Classification

    +

    Gradient Boosting, Classification Example

    @@ -2490,7 +2499,7 @@ plt.show()

    -

    XGBoost: Extreme Gradient Boosting

    +

    XGBoost: Extreme Gradient Boosting

    XGBoost or Extreme Gradient @@ -2511,7 +2520,7 @@ It is now the algorithm which wins essentially all ML competitions!!!

    -

    Regression Case

    +

    Regression Case

    @@ -2567,7 +2576,10 @@ 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 9d9bf9af6..e0c9995ac 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html @@ -148,31 +148,32 @@ div { text-align: justify; text-justify: inter-word; } 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -2079,7 +2080,7 @@ For simplicity we assume also that our functions \( b(x;\gamma)=\gamma_0+\gamma_ This means that for every iteration, we need to optmize $$ -(\beta_m,\gamma_m) \mathrm{armmin}_{\beta,\gambda}\hspace{0.2cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(\gamma_0+\gamma_1 x_i))^2. +(\beta_m,\gamma_m) \mathrm{argmin}_{\beta,\gambda}\hspace{0.2cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(\gamma_0+\gamma_1 x_i))^2. \[ $$ @@ -2092,18 +2093,26 @@ $$ and $$ -\frac{\partial {\cal C}}{\partial \gamma_0} = +\frac{\partial {\cal C}}{\partial \gamma_0} =-2\sum_{i}\beta(y_i-\beta(\gamma_0+\gamma_1 x_i))=0, $$ and $$ -\frac{\partial {\cal C}}{\partial \gamma_1} = +\frac{\partial {\cal C}}{\partial \gamma_1} = =-2\sum_{i}\beta x_i(y_i-\beta(\gamma_0+\gamma_1 x_i))=0. $$











    -

    Iterative Fitting, Classification, AdaBoost

    +

    Finding the Optimal Parameters

    + +

    +With these equations we can then in turn find the parameters \( \beta_1 \) and \( \gamma_0^{1} \) and \( \gamma_1^1 \) as + +

    +









    + +

    Iterative Fitting, Classification, AdaBoost

    Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of @@ -2114,14 +2123,15 @@ observations. We define a classification function \( G(x) \) which produces a pr The error rate of the training sample is then $$ -\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i). +\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i)). $$

    The iterative procedure starts with defining a weak classifier whose -error rate is barely better than random guessing. Teh iterative +error rate is barely better than random guessing. The iterative procedure in boosting is to sequentially apply a the weak -classification algorithm to repeatedly modified versions of the data producing a sequence of weak classifiers \( G_m(x) \). +classification algorithm to repeatedly modified versions of the data +producing a sequence of weak classifiers \( G_m(x) \).

    Here we will express our function \( f(x) \) in terms of \( G(x) \). That is @@ -2137,7 +2147,7 @@ $$











    -

    Adaptive Boosting, AdaBoost

    +

    Adaptive Boosting, AdaBoost

    In our iterative procedure we define thus @@ -2149,7 +2159,7 @@ $$ The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the exponential cost/loss function defined as $$ -C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1}(x_i)+\beta G(x_i))}. +C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{(-y_i(f_{m-1}(x_i)+\beta G(x_i))}. $$

    @@ -2157,15 +2167,15 @@ We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in t This is normally done in two steps. Let us however first rewrite the cost function as $$ -C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{-(y_i\beta G(x_i))}, +C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{(-y_i\beta G(x_i))}, $$ -where we have defined \( w_i^m= \exp{-(y_if_{m-1}(x_i))} \). +where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \).











    -

    Building up AdaBoost

    +

    Building up AdaBoost

    First, for any \( \beta > 0 \), we optimize \( G \) by setting @@ -2183,7 +2193,7 @@ $$ which can be rewritten as $$ -(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{-(\beta)}\sum_{i=0}^{n-1}w_i^m=0, +(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{(-\beta)}\sum_{i=0}^{n-1}w_i^m=0, $$ which leads to @@ -2203,12 +2213,12 @@ $$ This leads to the new weights $$ -w_i^{m+1} = w_i^m \exp{-(y_i\beta_m G_m(x_i))} +w_i^{m+1} = w_i^m \exp{(-y_i\beta_m G_m(x_i))} $$









    -

    Adaptive boosting: AdaBoost, Basic Algorithm

    +

    Adaptive boosting: AdaBoost, Basic Algorithm

    The algorithm here is rather straightforward. Assume that our weak @@ -2220,9 +2230,9 @@ feature/predictor vectors classifier determined by our data via a function \( G(x) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \).

    -We can then define the misclassification error \( \mathrm{err} \) as +We have already defined the misclassification error \( \mathrm{err} \) as $$ -\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i), +\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i)), $$ where the function \( I() \) is one if we misclassify and zero if we classify correctly. @@ -2230,7 +2240,7 @@ where the function \( I() \) is one if we misclassify and zero if we classify co











    -

    Basic Steps of AdaBoost

    +

    Basic Steps of AdaBoost

    With the above definitions we are now ready to set up the algorithm for AdaBoost. @@ -2270,7 +2280,7 @@ observations that are missed in the previous iterations.











    -

    AdaBoost Examples

    +

    AdaBoost Examples

    Using Scikit-Learn it is easy to appply the adaptive boosting algorithm, as done here. @@ -2303,7 +2313,7 @@ plt.show()











    -

    Gradient boosting: Basics

    +

    Gradient boosting: Basics

    Gradient boosting is again a similar technique to Adapative boosting, @@ -2321,7 +2331,7 @@ See discussion during lecture November 8.











    -

    Gradient Boosting, algorithm

    +

    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 square-error function @@ -2347,7 +2357,7 @@ The way we proceed in an iterative fashion is to









    -

    Gradient Boosting, Examples of Regression

    +

    Gradient Boosting, Examples of Regression

    @@ -2401,7 +2411,7 @@ plt.show()











    -

    Gradient Boosting, Examples of Classification

    +

    Gradient Boosting, Classification Example

    @@ -2449,7 +2459,7 @@ plt.show()











    -

    XGBoost: Extreme Gradient Boosting

    +

    XGBoost: Extreme Gradient Boosting

    XGBoost or Extreme Gradient @@ -2470,7 +2480,7 @@ It is now the algorithm which wins essentially all ML competitions!!!











    -

    Regression Case

    +

    Regression Case

    @@ -2525,7 +2535,10 @@ 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 054a1ea4b..d038bafd1 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees.html @@ -153,31 +153,32 @@ div { text-align: justify; text-justify: inter-word; } 2, None, '___sec47'), + ('Finding the Optimal Parameters', 2, None, '___sec48'), ('Iterative Fitting, Classification, AdaBoost', 2, None, - '___sec48'), - ('Adaptive Boosting, AdaBoost', 2, None, '___sec49'), - ('Building up AdaBoost', 2, None, '___sec50'), + '___sec49'), + ('Adaptive Boosting, AdaBoost', 2, None, '___sec50'), + ('Building up AdaBoost', 2, None, '___sec51'), ('Adaptive boosting: AdaBoost, Basic Algorithm', 2, None, - '___sec51'), - ('Basic Steps of AdaBoost', 2, None, '___sec52'), - ('AdaBoost Examples', 2, None, '___sec53'), - ('Gradient boosting: Basics', 2, None, '___sec54'), - ('Gradient Boosting, algorithm', 2, None, '___sec55'), + '___sec52'), + ('Basic Steps of AdaBoost', 2, None, '___sec53'), + ('AdaBoost Examples', 2, None, '___sec54'), + ('Gradient boosting: Basics', 2, None, '___sec55'), + ('Gradient Boosting, algorithm', 2, None, '___sec56'), ('Gradient Boosting, Examples of Regression', 2, None, - '___sec56'), - ('Gradient Boosting, Examples of Classification', + '___sec57'), + ('Gradient Boosting, Classification Example', 2, None, - '___sec57'), - ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec58'), - ('Regression Case', 2, None, '___sec59'), - ('Xgboost on the Cancer Data', 2, None, '___sec60')]} + '___sec58'), + ('XGBoost: Extreme Gradient Boosting', 2, None, '___sec59'), + ('Regression Case', 2, None, '___sec60'), + ('Xgboost on the Cancer Data', 2, None, '___sec61')]} end of tocinfo --> @@ -2084,7 +2085,7 @@ For simplicity we assume also that our functions \( b(x;\gamma)=\gamma_0+\gamma_ This means that for every iteration, we need to optmize $$ -(\beta_m,\gamma_m) \mathrm{armmin}_{\beta,\gambda}\hspace{0.2cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(\gamma_0+\gamma_1 x_i))^2. +(\beta_m,\gamma_m) \mathrm{argmin}_{\beta,\gambda}\hspace{0.2cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(\gamma_0+\gamma_1 x_i))^2. \[ $$ @@ -2097,18 +2098,26 @@ $$ and $$ -\frac{\partial {\cal C}}{\partial \gamma_0} = +\frac{\partial {\cal C}}{\partial \gamma_0} =-2\sum_{i}\beta(y_i-\beta(\gamma_0+\gamma_1 x_i))=0, $$ and $$ -\frac{\partial {\cal C}}{\partial \gamma_1} = +\frac{\partial {\cal C}}{\partial \gamma_1} = =-2\sum_{i}\beta x_i(y_i-\beta(\gamma_0+\gamma_1 x_i))=0. $$











    -

    Iterative Fitting, Classification, AdaBoost

    +

    Finding the Optimal Parameters

    + +

    +With these equations we can then in turn find the parameters \( \beta_1 \) and \( \gamma_0^{1} \) and \( \gamma_1^1 \) as + +

    +









    + +

    Iterative Fitting, Classification, AdaBoost

    Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of @@ -2119,14 +2128,15 @@ observations. We define a classification function \( G(x) \) which produces a pr The error rate of the training sample is then $$ -\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i). +\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i)). $$

    The iterative procedure starts with defining a weak classifier whose -error rate is barely better than random guessing. Teh iterative +error rate is barely better than random guessing. The iterative procedure in boosting is to sequentially apply a the weak -classification algorithm to repeatedly modified versions of the data producing a sequence of weak classifiers \( G_m(x) \). +classification algorithm to repeatedly modified versions of the data +producing a sequence of weak classifiers \( G_m(x) \).

    Here we will express our function \( f(x) \) in terms of \( G(x) \). That is @@ -2142,7 +2152,7 @@ $$











    -

    Adaptive Boosting, AdaBoost

    +

    Adaptive Boosting, AdaBoost

    In our iterative procedure we define thus @@ -2154,7 +2164,7 @@ $$ The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the exponential cost/loss function defined as $$ -C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{-(y_i(f_{m-1}(x_i)+\beta G(x_i))}. +C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{(-y_i(f_{m-1}(x_i)+\beta G(x_i))}. $$

    @@ -2162,15 +2172,15 @@ We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in t This is normally done in two steps. Let us however first rewrite the cost function as $$ -C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{-(y_i\beta G(x_i))}, +C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{(-y_i\beta G(x_i))}, $$ -where we have defined \( w_i^m= \exp{-(y_if_{m-1}(x_i))} \). +where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \).











    -

    Building up AdaBoost

    +

    Building up AdaBoost

    First, for any \( \beta > 0 \), we optimize \( G \) by setting @@ -2188,7 +2198,7 @@ $$ which can be rewritten as $$ -(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{-(\beta)}\sum_{i=0}^{n-1}w_i^m=0, +(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{(-\beta)}\sum_{i=0}^{n-1}w_i^m=0, $$ which leads to @@ -2208,12 +2218,12 @@ $$ This leads to the new weights $$ -w_i^{m+1} = w_i^m \exp{-(y_i\beta_m G_m(x_i))} +w_i^{m+1} = w_i^m \exp{(-y_i\beta_m G_m(x_i))} $$









    -

    Adaptive boosting: AdaBoost, Basic Algorithm

    +

    Adaptive boosting: AdaBoost, Basic Algorithm

    The algorithm here is rather straightforward. Assume that our weak @@ -2225,9 +2235,9 @@ feature/predictor vectors classifier determined by our data via a function \( G(x) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \).

    -We can then define the misclassification error \( \mathrm{err} \) as +We have already defined the misclassification error \( \mathrm{err} \) as $$ -\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i), +\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i)), $$ where the function \( I() \) is one if we misclassify and zero if we classify correctly. @@ -2235,7 +2245,7 @@ where the function \( I() \) is one if we misclassify and zero if we classify co











    -

    Basic Steps of AdaBoost

    +

    Basic Steps of AdaBoost

    With the above definitions we are now ready to set up the algorithm for AdaBoost. @@ -2275,7 +2285,7 @@ observations that are missed in the previous iterations.











    -

    AdaBoost Examples

    +

    AdaBoost Examples

    Using Scikit-Learn it is easy to appply the adaptive boosting algorithm, as done here. @@ -2308,7 +2318,7 @@ plt.show()











    -

    Gradient boosting: Basics

    +

    Gradient boosting: Basics

    Gradient boosting is again a similar technique to Adapative boosting, @@ -2326,7 +2336,7 @@ See discussion during lecture November 8.











    -

    Gradient Boosting, algorithm

    +

    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 square-error function @@ -2352,7 +2362,7 @@ The way we proceed in an iterative fashion is to









    -

    Gradient Boosting, Examples of Regression

    +

    Gradient Boosting, Examples of Regression

    @@ -2406,7 +2416,7 @@ plt.show()











    -

    Gradient Boosting, Examples of Classification

    +

    Gradient Boosting, Classification Example

    @@ -2454,7 +2464,7 @@ plt.show()











    -

    XGBoost: Extreme Gradient Boosting

    +

    XGBoost: Extreme Gradient Boosting

    XGBoost or Extreme Gradient @@ -2475,7 +2485,7 @@ It is now the algorithm which wins essentially all ML competitions!!!











    -

    Regression Case

    +

    Regression Case

    @@ -2530,7 +2540,10 @@ 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 1c70f99be..752b3f244 100644 --- a/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb +++ b/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb @@ -2131,7 +2131,7 @@ "metadata": {}, "source": [ "$$\n", - "(\\beta_m,\\gamma_m) \\mathrm{armmin}_{\\beta,\\gambda}\\hspace{0.2cm} \\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta(\\gamma_0+\\gamma_1 x_i))^2.\n", + "(\\beta_m,\\gamma_m) \\mathrm{argmin}_{\\beta,\\gambda}\\hspace{0.2cm} \\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta(\\gamma_0+\\gamma_1 x_i))^2.\n", "$$" ] }, @@ -2164,7 +2164,7 @@ "metadata": {}, "source": [ "$$\n", - "\\frac{\\partial {\\cal C}}{\\partial \\gamma_0} =\n", + "\\frac{\\partial {\\cal C}}{\\partial \\gamma_0} =-2\\sum_{i}\\beta(y_i-\\beta(\\gamma_0+\\gamma_1 x_i))=0,\n", "$$" ] }, @@ -2180,7 +2180,7 @@ "metadata": {}, "source": [ "$$\n", - "\\frac{\\partial {\\cal C}}{\\partial \\gamma_1} =\n", + "\\frac{\\partial {\\cal C}}{\\partial \\gamma_1} = =-2\\sum_{i}\\beta x_i(y_i-\\beta(\\gamma_0+\\gamma_1 x_i))=0.\n", "$$" ] }, @@ -2188,6 +2188,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "## Finding the Optimal Parameters\n", + "\n", + "With these equations we can then in turn find the parameters $\\beta_1$ and $\\gamma_0^{1}$ and $\\gamma_1^1$ as\n", + "\n", + "\n", + "\n", "## Iterative Fitting, Classification, AdaBoost\n", "\n", "Let us consider a binary classification problem with two outcomes $y_i \\in \\{-1,1\\}$ and $i=0,1,2,\\dots,n-1$ as our set of\n", @@ -2202,7 +2208,7 @@ "metadata": {}, "source": [ "$$\n", - "\\mathrm{\\overline{err}}=\\frac{1}{n} \\sum_{i=0}^{n-1} I(y_i\\ne G(x_i).\n", + "\\mathrm{\\overline{err}}=\\frac{1}{n} \\sum_{i=0}^{n-1} I(y_i\\ne G(x_i)).\n", "$$" ] }, @@ -2211,9 +2217,10 @@ "metadata": {}, "source": [ "The iterative procedure starts with defining a weak classifier whose\n", - "error rate is barely better than random guessing. Teh iterative\n", + "error rate is barely better than random guessing. The iterative\n", "procedure in boosting is to sequentially apply a the weak\n", - "classification algorithm to repeatedly modified versions of the data producing a sequence of weak classifiers $G_m(x)$.\n", + "classification algorithm to repeatedly modified versions of the data\n", + "producing a sequence of weak classifiers $G_m(x)$.\n", "\n", "Here we will express our function $f(x)$ in terms of $G(x)$. That is" ] @@ -2274,7 +2281,7 @@ "metadata": {}, "source": [ "$$\n", - "C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}\\exp{-(y_i(f_{m-1}(x_i)+\\beta G(x_i))}.\n", + "C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}\\exp{(-y_i(f_{m-1}(x_i)+\\beta G(x_i))}.\n", "$$" ] }, @@ -2291,7 +2298,7 @@ "metadata": {}, "source": [ "$$\n", - "C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}w_i^{m}\\exp{-(y_i\\beta G(x_i))},\n", + "C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}w_i^{m}\\exp{(-y_i\\beta G(x_i))},\n", "$$" ] }, @@ -2299,7 +2306,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "where we have defined $w_i^m= \\exp{-(y_if_{m-1}(x_i))}$.\n", + "where we have defined $w_i^m= \\exp{(-y_if_{m-1}(x_i))}$.\n", "\n", "## Building up AdaBoost\n", "\n", @@ -2345,7 +2352,7 @@ "metadata": {}, "source": [ "$$\n", - "(\\exp{(\\beta)}-\\exp{-(\\beta)})\\sum_{i=0}^{n-1}w_i^mI(y_i\\ne G(x_i))+\\exp{-(\\beta)}\\sum_{i=0}^{n-1}w_i^m=0,\n", + "(\\exp{(\\beta)}-\\exp{-(\\beta)})\\sum_{i=0}^{n-1}w_i^mI(y_i\\ne G(x_i))+\\exp{(-\\beta)}\\sum_{i=0}^{n-1}w_i^m=0,\n", "$$" ] }, @@ -2409,7 +2416,7 @@ "metadata": {}, "source": [ "$$\n", - "w_i^{m+1} = w_i^m \\exp{-(y_i\\beta_m G_m(x_i))}\n", + "w_i^{m+1} = w_i^m \\exp{(-y_i\\beta_m G_m(x_i))}\n", "$$" ] }, @@ -2427,7 +2434,7 @@ "$\\boldsymbol{X}=[\\boldsymbol{x}_0\\boldsymbol{x}_1\\dots\\boldsymbol{x}_{p-1}]$. Finally, we define also a\n", "classifier determined by our data via a function $G(x)$. This function tells us how well we are able to classify our outputs/targets $\\boldsymbol{y}$. \n", "\n", - "We can then define the misclassification error $\\mathrm{err}$ as" + "We have already defined the misclassification error $\\mathrm{err}$ as" ] }, { @@ -2435,7 +2442,7 @@ "metadata": {}, "source": [ "$$\n", - "\\mathrm{err}=\\frac{1}{n}\\sum_{i=0}^{n-1}I(y_i\\ne G(x_i),\n", + "\\mathrm{err}=\\frac{1}{n}\\sum_{i=0}^{n-1}I(y_i\\ne G(x_i)),\n", "$$" ] }, @@ -2637,7 +2644,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Gradient Boosting, Examples of Classification" + "## Gradient Boosting, Classification Example" ] }, { @@ -2773,7 +2780,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Xgboost on the Cancer Data" + "## Xgboost on the Cancer Data\n", + "\n", + "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 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