From 12f894501f38a24314d312bfaaee83c26ef47a1f Mon Sep 17 00:00:00 2001 From: mhjensen Date: Fri, 1 Nov 2019 06:31:36 +0100 Subject: [PATCH] update on decision trees --- .../html/._DecisionTrees-bs000.html | 39 +- .../html/._DecisionTrees-bs001.html | 37 +- .../html/._DecisionTrees-bs002.html | 37 +- .../html/._DecisionTrees-bs003.html | 37 +- .../html/._DecisionTrees-bs004.html | 37 +- .../html/._DecisionTrees-bs005.html | 37 +- .../html/._DecisionTrees-bs006.html | 37 +- .../html/._DecisionTrees-bs007.html | 37 +- .../html/._DecisionTrees-bs008.html | 37 +- .../html/._DecisionTrees-bs009.html | 37 +- .../html/._DecisionTrees-bs010.html | 37 +- .../html/._DecisionTrees-bs011.html | 37 +- .../html/._DecisionTrees-bs012.html | 37 +- .../html/._DecisionTrees-bs013.html | 37 +- .../html/._DecisionTrees-bs014.html | 37 +- .../html/._DecisionTrees-bs015.html | 37 +- .../html/._DecisionTrees-bs016.html | 37 +- .../html/._DecisionTrees-bs017.html | 37 +- .../html/._DecisionTrees-bs018.html | 37 +- .../html/._DecisionTrees-bs019.html | 37 +- .../html/._DecisionTrees-bs020.html | 37 +- .../html/._DecisionTrees-bs021.html | 37 +- .../html/._DecisionTrees-bs022.html | 37 +- .../html/._DecisionTrees-bs023.html | 37 +- .../html/._DecisionTrees-bs024.html | 37 +- .../html/._DecisionTrees-bs025.html | 37 +- .../html/._DecisionTrees-bs026.html | 37 +- .../html/._DecisionTrees-bs027.html | 37 +- .../html/._DecisionTrees-bs028.html | 37 +- .../html/._DecisionTrees-bs029.html | 38 +- .../html/._DecisionTrees-bs030.html | 39 +- .../html/._DecisionTrees-bs031.html | 40 +- .../html/._DecisionTrees-bs032.html | 40 +- .../html/._DecisionTrees-bs033.html | 114 ++-- .../html/._DecisionTrees-bs034.html | 103 +++- .../html/._DecisionTrees-bs035.html | 114 ++-- .../html/._DecisionTrees-bs036.html | 103 ++-- .../html/._DecisionTrees-bs037.html | 40 +- .../html/._DecisionTrees-bs038.html | 203 ++++--- .../DecisionTrees/html/DecisionTrees-bs.html | 39 +- .../html/DecisionTrees-reveal.html | 306 +++++++--- .../html/DecisionTrees-solarized.html | 317 +++++++--- doc/pub/DecisionTrees/html/DecisionTrees.html | 317 +++++++--- .../DecisionTrees/ipynb/DataFiles/cancer.dot | 4 +- .../DecisionTrees/ipynb/DataFiles/cancer.png | Bin 222354 -> 222008 bytes .../DecisionTrees/ipynb/DecisionTrees.ipynb | 540 ++++++++++++------ .../ipynb/ipynb-DecisionTrees-src.tar.gz | Bin 194 -> 194 bytes .../pdf/DecisionTrees-minted.pdf | Bin 268004 -> 268564 bytes doc/src/DecisionTrees/DecisionTrees.do.txt | 376 ++++++++---- 49 files changed, 2529 insertions(+), 1279 deletions(-) diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html index 04d083734..d91a75045 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -199,7 +208,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Oct 31, 2019

    +

    Nov 1, 2019


    @@ -223,7 +232,7 @@ MathJax.Hub.Config({

  • 9
  • 10
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs001.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs001.html index 0817b2bce..191a50988 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs001.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs001.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -228,7 +237,7 @@ given some assumptions, make predictions about the target feature value
  • 10
  • 11
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs002.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs002.html index b1e29cb56..97174d4d1 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs002.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs002.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -200,7 +209,7 @@ MathJax.Hub.Config({
  • 11
  • 12
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs003.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs003.html index 15b696ea9..b9b4b76e3 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs003.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs003.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -214,7 +223,7 @@ node.
  • 12
  • 13
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html index a508831df..64b753ba9 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -215,7 +224,7 @@ Then we are essentially done!
  • 13
  • 14
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html index f37c5bfe5..c4d112f29 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -294,7 +303,7 @@ plt.show()
  • 14
  • 15
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html index 3de39230d..ce06faa38 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -227,7 +236,7 @@ within box \( j \).
  • 15
  • 16
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html index 0b5e6e89c..99a8f8331 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -219,7 +228,7 @@ better tree in some future step.
  • 16
  • 17
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html index f94af650e..4c0cae669 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -252,7 +261,7 @@ region contains more than five observations.
  • 17
  • 18
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html index 76b5cf380..d9b6f74d3 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -221,7 +230,7 @@ parameter \( \alpha \).
  • 18
  • 19
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html index 7ee3b981d..c0c530fac 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -234,7 +243,7 @@ subtree corresponding to \( \alpha \).
  • 19
  • 20
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html index cf246be93..2515e42e3 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -230,7 +239,7 @@ MathJax.Hub.Config({
  • 20
  • 21
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html index 430fe05bb..2170a648f 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -222,7 +231,7 @@ fall into that region.
  • 21
  • 22
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html index 8e94771c2..66fc61304 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -227,7 +236,7 @@ than is the classification error rate.
  • 22
  • 23
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html index 1087f7553..1f1a28de7 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -253,7 +262,7 @@ $$
  • 23
  • 24
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html index e6ffb86b7..c3b00fb0d 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -244,7 +253,7 @@ os.system(cmd)
  • 24
  • 25
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html index cb3574a05..041680ff8 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -235,7 +244,7 @@ os.system(cmd)
  • 25
  • 26
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html index a59b8b30c..a7ed5c3d1 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -248,7 +257,7 @@ The table here summarizes the various attributes and
  • 26
  • 27
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html index c040c67aa..60e1782eb 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -279,7 +288,7 @@ os.system(cmd)
  • 27
  • 28
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html index 762b618dd..de95d67cb 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -281,7 +290,7 @@ split = get_split(dataset)
  • 28
  • 29
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html index 8ecc4b44e..89ebbaa6c 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -239,7 +248,7 @@ attributes at each step while growing the tree.
  • 29
  • 30
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html index 8911a2848..6478add80 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -399,7 +408,7 @@ MathJax.Hub.Config({
  • 30
  • 31
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html index d8f20bebc..c552ac1a9 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -252,7 +261,7 @@ deep_tree_clf.fit(X_train_scaled, y_train)
  • 31
  • 32
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html index 515b4e62d..abade5a6e 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -275,7 +284,7 @@ plt.show()
  • 32
  • 33
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html index 02c32ec42..dd4d38b8b 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -231,7 +240,7 @@ plt.show()
  • 33
  • 34
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html index 68fe4a2f0..c840d800b 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -225,7 +234,7 @@ tree_reg.fit(X, y)
  • 34
  • 35
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html index 90b999a65..838943d62 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -281,7 +290,7 @@ plt.show()
  • 35
  • 36
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html index a0e34bab1..94ede3d40 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -217,7 +226,7 @@ MathJax.Hub.Config({
  • 36
  • 37
  • ...
    • -
  • 38
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html index e754e3e50..87af9749a 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -219,6 +228,8 @@ However, by aggregating many decision trees, using methods like bagging, random
  • 36
  • 37
  • 38
    • +
  • ...
    • +
  • 41
  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html index 7c6e28014..72a7e053c 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -220,6 +229,9 @@ learning method.
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    • +
  • ...
    • +
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  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html index 593692d68..38f464d9f 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -229,6 +238,10 @@ predictor, averaged over all \( B \) trees.
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  • 38
    • +
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    • +
  • 40
    • +
  • ...
    • +
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  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html index a4e1169b8..dd9581608 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -180,7 +189,7 @@ MathJax.Hub.Config({ -

    Simple example, head or tail

    +

    Simple Voting Example, head or tail

    @@ -219,6 +228,9 @@ plt.show()

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    • +
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    • +
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html index 716eaa920..3c67203d2 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -180,7 +189,7 @@ MathJax.Hub.Config({ -

    Bagging Example

    +

    Using the Voting Classifier

    @@ -249,6 +258,9 @@ voting_clf.fit(X_train, y_train)

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html index 24ca6faad..b8655cea5 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -180,47 +189,61 @@ MathJax.Hub.Config({ -

    Random forests

    - +

    Please, not the moons again! Voting and Bagging

    -Random forests provide an improvement over bagged trees by way of a -small tweak that decorrelates the trees. + +

    from sklearn.model_selection import train_test_split
+from sklearn.datasets import make_moons
+
+X, y = make_moons(n_samples=500, noise=0.30, random_state=42)
+X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
+from sklearn.ensemble import RandomForestClassifier
+from sklearn.ensemble import VotingClassifier
+from sklearn.linear_model import LogisticRegression
+from sklearn.svm import SVC
+
+log_clf = LogisticRegression(random_state=42)
+rnd_clf = RandomForestClassifier(random_state=42)
+svm_clf = SVC(random_state=42)
+
+voting_clf = VotingClassifier(
+    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
+    voting='hard')
+voting_clf.fit(X_train, y_train)
+

    -As in bagging, we build a -number of decision trees on bootstrapped training samples. But when -building these decision trees, each time a split in a tree is -considered, a random sample of \( m \) predictors is chosen as split -candidates from the full set of \( p \) predictors. The split is allowed to -use only one of those \( m \) predictors. + +

    from sklearn.metrics import accuracy_score
+
+for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
+    clf.fit(X_train, y_train)
+    y_pred = clf.predict(X_test)
+    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
+

    -A fresh sample of \( m \) predictors is -taken at each split, and typically we choose -$$ -m\approx \sqrt{p}. -$$ + +

    log_clf = LogisticRegression(random_state=42)
+rnd_clf = RandomForestClassifier(random_state=42)
+svm_clf = SVC(probability=True, random_state=42)
 
+voting_clf = VotingClassifier(
+    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
+    voting='soft')
+voting_clf.fit(X_train, y_train)
+

    -In building a random forest, at -each split in the tree, the algorithm is not even allowed to consider -a majority of the available predictors. -

    -The reason for this is rather clever. Suppose that there is one very -strong predictor in the data set, along with a number of other -moderately strong predictors. Then in the collection of bagged -variable importance random forest trees, most or all of the trees will -use this strong predictor in the top split. Consequently, all of the -bagged trees will look quite similar to each other. Hence the -predictions from the bagged trees will be highly correlated. -Unfortunately, averaging many highly correlated quantities does not -lead to as large of a reduction in variance as averaging many -uncorrelated quanti- ties. In particular, this means that bagging will -not lead to a substantial reduction in variance over a single tree in -this setting. + +

    from sklearn.metrics import accuracy_score
 
+for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
+    clf.fit(X_train, y_train)
+    y_pred = clf.predict(X_test)
+    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
+

    @@ -241,6 +264,9 @@ this setting.

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    • +
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  • »
    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html index 924df127a..c17ca4391 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html @@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -158,13 +164,16 @@ MathJax.Hub.Config({
  • Disadvantages
  • Bagging
  • More bagging
    • -
  • Simple example, head or tail
    • -
  • Bagging Example
    • -
  • Random forests
    • -
  • A simple scikit-learn example
    • -
  • Please, not the moons again!
    • -
  • Bagging examples
    • +
  • Simple Voting Example, head or tail
    • +
  • Using the Voting Classifier
    • +
  • Please, not the moons again! Voting and Bagging
    • +
  • Now Bagging
    • +
  • Random forests
    • +
  • A simple scikit-learn example
  • Then random forests
    • +
  • Feature Importance
    • +
  • Boosting: AdaBoost
    • +
  • Gradient Boosting
    • @@ -180,20 +189,63 @@ MathJax.Hub.Config({ -

    A simple scikit-learn example

    +

    Now Bagging

    +

    -

    from sklearn.ensemble import RandomForestClassifier
-from sklearn.preprocessing import LabelEncoder
-from sklearn.model_selection import cross_validate
-# Data set not specificied
-X = dataset.XXX
-Y = dataset.YYY
-#Instantiate the model with 100 trees and entropy as splitting criteria
-Random_Forest_model = RandomForestClassifier(n_estimators=100,criterion="entropy")
-#Cross validation
-accuracy = cross_validate(Random_Forest_model,X,Y,cv=10)['test_score']
+
    from sklearn.ensemble import BaggingClassifier
+from sklearn.tree import DecisionTreeClassifier
+
+bag_clf = BaggingClassifier(
+    DecisionTreeClassifier(random_state=42), n_estimators=500,
+    max_samples=100, bootstrap=True, n_jobs=-1, random_state=42)
+bag_clf.fit(X_train, y_train)
+y_pred = bag_clf.predict(X_test)
+
    
+
    
+
+
+
    from sklearn.metrics import accuracy_score
+print(accuracy_score(y_test, y_pred))
+
    
+
    
+
+
+
    tree_clf = DecisionTreeClassifier(random_state=42)
+tree_clf.fit(X_train, y_train)
+y_pred_tree = tree_clf.predict(X_test)
+print(accuracy_score(y_test, y_pred_tree))
+
    
+
    
+
+
+
    from matplotlib.colors import ListedColormap
+
+def plot_decision_boundary(clf, X, y, axes=[-1.5, 2.5, -1, 1.5], alpha=0.5, contour=True):
+    x1s = np.linspace(axes[0], axes[1], 100)
+    x2s = np.linspace(axes[2], axes[3], 100)
+    x1, x2 = np.meshgrid(x1s, x2s)
+    X_new = np.c_[x1.ravel(), x2.ravel()]
+    y_pred = clf.predict(X_new).reshape(x1.shape)
+    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])
+    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)
+    if contour:
+        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])
+        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)
+    plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo", alpha=alpha)
+    plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs", alpha=alpha)
+    plt.axis(axes)
+    plt.xlabel(r"$x_1$", fontsize=18)
+    plt.ylabel(r"$x_2$", fontsize=18, rotation=0)
+plt.figure(figsize=(11,4))
+plt.subplot(121)
+plot_decision_boundary(tree_clf, X, y)
+plt.title("Decision Tree", fontsize=14)
+plt.subplot(122)
+plot_decision_boundary(bag_clf, X, y)
+plt.title("Decision Trees with Bagging", fontsize=14)
+plt.show()
 
    
 
    
 
    
@@ -214,6 +266,9 @@ accuracy = cross_validate(Random_Forest_mode
   
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+  
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+  
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  • »
    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html
index df2122fd9..23a113357 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html
@@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source
               ('Disadvantages', 2, None, '___sec27'),
               ('Bagging', 2, None, '___sec28'),
               ('More bagging', 2, None, '___sec29'),
-              ('Simple example, head or tail', 2, None, '___sec30'),
-              ('Bagging Example', 2, None, '___sec31'),
-              ('Random forests', 2, None, '___sec32'),
-              ('A simple scikit-learn example', 2, None, '___sec33'),
-              ('Please, not the moons again!', 2, None, '___sec34'),
-              ('Bagging examples', 2, None, '___sec35'),
-              ('Then random forests', 2, None, '___sec36')]}
+              ('Simple Voting Example, head or tail', 2, None, '___sec30'),
+              ('Using the Voting Classifier', 2, None, '___sec31'),
+              ('Please, not the moons again! Voting and Bagging',
+               2,
+               None,
+               '___sec32'),
+              ('Now Bagging', 2, None, '___sec33'),
+              ('Random forests', 2, None, '___sec34'),
+              ('A simple scikit-learn example', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36'),
+              ('Feature Importance', 2, None, '___sec37'),
+              ('Boosting: AdaBoost', 2, None, '___sec38'),
+              ('Gradient Boosting', 2, None, '___sec39')]}
 end of tocinfo -->
 
 
@@ -158,13 +164,16 @@ MathJax.Hub.Config({
       
  • Disadvantages
    • 
       
  • Bagging
    • 
       
  • More bagging
    • 
-      
  • Simple example, head or tail
    • 
-      
  • Bagging Example
    • 
-      
  • Random forests
    • 
-      
  • A simple scikit-learn example
    • 
-      
  • Please, not the moons again!
    • 
-      
  • Bagging examples
    • 
+      
  • Simple Voting Example, head or tail
    • 
+      
  • Using the Voting Classifier
    • 
+      
  • Please, not the moons again! Voting and Bagging
    • 
+      
  • Now Bagging
    • 
+      
  • Random forests
    • 
+      
  • A simple scikit-learn example
    • 
       
  • Then random forests
    • 
+      
  • Feature Importance
    • 
+      
  • Boosting: AdaBoost
    • 
+      
  • Gradient Boosting
    • 
 
         
       
@@ -180,61 +189,47 @@ MathJax.Hub.Config({
 
 
 
-
    Please, not the moons again! 
    
+
    Random forests 
    
+
 
    
+Random forests provide an improvement over bagged trees by way of a
+small tweak that decorrelates the trees.
 
-
-
    from sklearn.model_selection import train_test_split
-from sklearn.datasets import make_moons
-
-X, y = make_moons(n_samples=500, noise=0.30, random_state=42)
-X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
-from sklearn.ensemble import RandomForestClassifier
-from sklearn.ensemble import VotingClassifier
-from sklearn.linear_model import LogisticRegression
-from sklearn.svm import SVC
-
-log_clf = LogisticRegression(random_state=42)
-rnd_clf = RandomForestClassifier(random_state=42)
-svm_clf = SVC(random_state=42)
-
-voting_clf = VotingClassifier(
-    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
-    voting='hard')
-voting_clf.fit(X_train, y_train)
-
    
 
    
+As in bagging, we build a
+number of decision trees on bootstrapped training samples. But when
+building these decision trees, each time a split in a tree is
+considered, a random sample of \( m \) predictors is chosen as split
+candidates from the full set of \( p \) predictors. The split is allowed to
+use only one of those \( m \) predictors.
 
-
-
    from sklearn.metrics import accuracy_score
-
-for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
-    clf.fit(X_train, y_train)
-    y_pred = clf.predict(X_test)
-    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
-
    
 
    
+A fresh sample of \( m \) predictors is
+taken at each split, and typically we choose 
 
-
-
    log_clf = LogisticRegression(random_state=42)
-rnd_clf = RandomForestClassifier(random_state=42)
-svm_clf = SVC(probability=True, random_state=42)
+$$
+m\approx \sqrt{p}.
+$$
 
-voting_clf = VotingClassifier(
-    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
-    voting='soft')
-voting_clf.fit(X_train, y_train)
-
    
 
    
+In building a random forest, at
+each split in the tree, the algorithm is not even allowed to consider
+a majority of the available predictors.
 
-
-
    from sklearn.metrics import accuracy_score
+
    
+The reason for this is rather clever. Suppose that there is one very
+strong predictor in the data set, along with a number of other
+moderately strong predictors. Then in the collection of bagged
+variable importance random forest trees, most or all of the trees will
+use this strong predictor in the top split. Consequently, all of the
+bagged trees will look quite similar to each other. Hence the
+predictions from the bagged trees will be highly correlated.
+Unfortunately, averaging many highly correlated quantities does not
+lead to as large of a reduction in variance as averaging many
+uncorrelated quanti- ties. In particular, this means that bagging will
+not lead to a substantial reduction in variance over a single tree in
+this setting.
 
-for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
-    clf.fit(X_train, y_train)
-    y_pred = clf.predict(X_test)
-    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
-
    
 
    
 
    
 
@@ -253,6 +248,9 @@ voting_clf.fit(X_train, y_train)
   
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    • 
   
  • 37
    • 
   
  • 38
    • 
+  
  • 39
    • 
+  
  • 40
    • 
+  
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    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html
index 4fe8b451a..3f2df2d42 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html
@@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source
               ('Disadvantages', 2, None, '___sec27'),
               ('Bagging', 2, None, '___sec28'),
               ('More bagging', 2, None, '___sec29'),
-              ('Simple example, head or tail', 2, None, '___sec30'),
-              ('Bagging Example', 2, None, '___sec31'),
-              ('Random forests', 2, None, '___sec32'),
-              ('A simple scikit-learn example', 2, None, '___sec33'),
-              ('Please, not the moons again!', 2, None, '___sec34'),
-              ('Bagging examples', 2, None, '___sec35'),
-              ('Then random forests', 2, None, '___sec36')]}
+              ('Simple Voting Example, head or tail', 2, None, '___sec30'),
+              ('Using the Voting Classifier', 2, None, '___sec31'),
+              ('Please, not the moons again! Voting and Bagging',
+               2,
+               None,
+               '___sec32'),
+              ('Now Bagging', 2, None, '___sec33'),
+              ('Random forests', 2, None, '___sec34'),
+              ('A simple scikit-learn example', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36'),
+              ('Feature Importance', 2, None, '___sec37'),
+              ('Boosting: AdaBoost', 2, None, '___sec38'),
+              ('Gradient Boosting', 2, None, '___sec39')]}
 end of tocinfo -->
 
 
@@ -158,13 +164,16 @@ MathJax.Hub.Config({
       
  • Disadvantages
    • 
       
  • Bagging
    • 
       
  • More bagging
    • 
-      
  • Simple example, head or tail
    • 
-      
  • Bagging Example
    • 
-      
  • Random forests
    • 
-      
  • A simple scikit-learn example
    • 
-      
  • Please, not the moons again!
    • 
-      
  • Bagging examples
    • 
+      
  • Simple Voting Example, head or tail
    • 
+      
  • Using the Voting Classifier
    • 
+      
  • Please, not the moons again! Voting and Bagging
    • 
+      
  • Now Bagging
    • 
+      
  • Random forests
    • 
+      
  • A simple scikit-learn example
    • 
       
  • Then random forests
    • 
+      
  • Feature Importance
    • 
+      
  • Boosting: AdaBoost
    • 
+      
  • Gradient Boosting
    • 
 
         
       
@@ -180,63 +189,20 @@ MathJax.Hub.Config({
 
 
 
-
    Bagging examples 
    
-
+
    A simple scikit-learn example 
    
 
    
 
 
-
    from sklearn.ensemble import BaggingClassifier
-from sklearn.tree import DecisionTreeClassifier
-
-bag_clf = BaggingClassifier(
-    DecisionTreeClassifier(random_state=42), n_estimators=500,
-    max_samples=100, bootstrap=True, n_jobs=-1, random_state=42)
-bag_clf.fit(X_train, y_train)
-y_pred = bag_clf.predict(X_test)
-
    
-
    
-
-
-
    from sklearn.metrics import accuracy_score
-print(accuracy_score(y_test, y_pred))
-
    
-
    
-
-
-
    tree_clf = DecisionTreeClassifier(random_state=42)
-tree_clf.fit(X_train, y_train)
-y_pred_tree = tree_clf.predict(X_test)
-print(accuracy_score(y_test, y_pred_tree))
-
    
-
    
-
-
-
    from matplotlib.colors import ListedColormap
-
-def plot_decision_boundary(clf, X, y, axes=[-1.5, 2.5, -1, 1.5], alpha=0.5, contour=True):
-    x1s = np.linspace(axes[0], axes[1], 100)
-    x2s = np.linspace(axes[2], axes[3], 100)
-    x1, x2 = np.meshgrid(x1s, x2s)
-    X_new = np.c_[x1.ravel(), x2.ravel()]
-    y_pred = clf.predict(X_new).reshape(x1.shape)
-    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])
-    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)
-    if contour:
-        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])
-        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)
-    plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo", alpha=alpha)
-    plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs", alpha=alpha)
-    plt.axis(axes)
-    plt.xlabel(r"$x_1$", fontsize=18)
-    plt.ylabel(r"$x_2$", fontsize=18, rotation=0)
-plt.figure(figsize=(11,4))
-plt.subplot(121)
-plot_decision_boundary(tree_clf, X, y)
-plt.title("Decision Tree", fontsize=14)
-plt.subplot(122)
-plot_decision_boundary(bag_clf, X, y)
-plt.title("Decision Trees with Bagging", fontsize=14)
-plt.show()
+
    from sklearn.ensemble import RandomForestClassifier
+from sklearn.preprocessing import LabelEncoder
+from sklearn.model_selection import cross_validate
+# Data set not specificied
+X = dataset.XXX
+Y = dataset.YYY
+#Instantiate the model with 100 trees and entropy as splitting criteria
+Random_Forest_model = RandomForestClassifier(n_estimators=100,criterion="entropy")
+#Cross validation
+accuracy = cross_validate(Random_Forest_model,X,Y,cv=10)['test_score']
 
    
 
    
 
    
@@ -255,6 +221,9 @@ plt.show()
   
  • 36
    • 
   
  • 37
    • 
   
  • 38
    • 
+  
  • 39
    • 
+  
  • 40
    • 
+  
  • 41
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html
index bc2bb73ed..dae9353a5 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html
@@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source
               ('Disadvantages', 2, None, '___sec27'),
               ('Bagging', 2, None, '___sec28'),
               ('More bagging', 2, None, '___sec29'),
-              ('Simple example, head or tail', 2, None, '___sec30'),
-              ('Bagging Example', 2, None, '___sec31'),
-              ('Random forests', 2, None, '___sec32'),
-              ('A simple scikit-learn example', 2, None, '___sec33'),
-              ('Please, not the moons again!', 2, None, '___sec34'),
-              ('Bagging examples', 2, None, '___sec35'),
-              ('Then random forests', 2, None, '___sec36')]}
+              ('Simple Voting Example, head or tail', 2, None, '___sec30'),
+              ('Using the Voting Classifier', 2, None, '___sec31'),
+              ('Please, not the moons again! Voting and Bagging',
+               2,
+               None,
+               '___sec32'),
+              ('Now Bagging', 2, None, '___sec33'),
+              ('Random forests', 2, None, '___sec34'),
+              ('A simple scikit-learn example', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36'),
+              ('Feature Importance', 2, None, '___sec37'),
+              ('Boosting: AdaBoost', 2, None, '___sec38'),
+              ('Gradient Boosting', 2, None, '___sec39')]}
 end of tocinfo -->
 
 
@@ -158,13 +164,16 @@ MathJax.Hub.Config({
       
  • Disadvantages
    • 
       
  • Bagging
    • 
       
  • More bagging
    • 
-      
  • Simple example, head or tail
    • 
-      
  • Bagging Example
    • 
-      
  • Random forests
    • 
-      
  • A simple scikit-learn example
    • 
-      
  • Please, not the moons again!
    • 
-      
  • Bagging examples
    • 
+      
  • Simple Voting Example, head or tail
    • 
+      
  • Using the Voting Classifier
    • 
+      
  • Please, not the moons again! Voting and Bagging
    • 
+      
  • Now Bagging
    • 
+      
  • Random forests
    • 
+      
  • A simple scikit-learn example
    • 
       
  • Then random forests
    • 
+      
  • Feature Importance
    • 
+      
  • Boosting: AdaBoost
    • 
+      
  • Gradient Boosting
    • 
 
         
       
@@ -200,7 +209,6 @@ y_pred_rf = rnd_clf.sum(y_pred == y_pred_rf) / len(y_pred) 
 
    
 
    
-
 
    
 
 
    
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs038.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs038.html
index 52e58f32b..c3f2f82cd 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs038.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs038.html
@@ -47,52 +47,56 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data and perform Classification',
+               2,
+               None,
+               '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple Voting Example, head or tail', 2, None, '___sec30'),
+              ('Using the Voting Classifier', 2, None, '___sec31'),
+              ('Please, not the moons again! Voting and Bagging',
+               2,
+               None,
+               '___sec32'),
+              ('Now Bagging', 2, None, '___sec33'),
+              ('Random forests', 2, None, '___sec34'),
+              ('A simple scikit-learn example', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36'),
+              ('Feature Importance', 2, None, '___sec37'),
+              ('Boosting: AdaBoost', 2, None, '___sec38'),
+              ('Gradient Boosting', 2, None, '___sec39')]}
 end of tocinfo -->
 
 
@@ -132,42 +136,44 @@ MathJax.Hub.Config({
         
       
@@ -183,27 +189,37 @@ MathJax.Hub.Config({
 
 
 
-
    Then random forests 
    
+
    Feature Importance 
    
+
 
    
 
 
-
    bag_clf = BaggingClassifier(
-    DecisionTreeClassifier(splitter="random", max_leaf_nodes=16, random_state=42),
-    n_estimators=500, max_samples=1.0, bootstrap=True, n_jobs=-1, random_state=42)
+
    try:
+    from sklearn.datasets import fetch_openml
+    mnist = fetch_openml('mnist_784', version=1)
+    mnist.target = mnist.target.astype(np.int64)
+except ImportError:
+    from sklearn.datasets import fetch_mldata
+    mnist = fetch_mldata('MNIST original')
+
+rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
+rnd_clf.fit(mnist["data"], mnist["target"])
+
+def plot_digit(data):
+    image = data.reshape(28, 28)
+    plt.imshow(image, cmap = mpl.cm.hot,
+               interpolation="nearest")
+    plt.axis("off")
+
+plot_digit(rnd_clf.feature_importances_)
+
+cbar = plt.colorbar(ticks=[rnd_clf.feature_importances_.min(), rnd_clf.feature_importances_.max()])
+cbar.ax.set_yticklabels(['Not important', 'Very important'])
+
+#save_fig("mnist_feature_importance_plot")
+plt.show()
 
    
 
    
-
-
-
    bag_clf.fit(X_train, y_train)
-y_pred = bag_clf.predict(X_test)
-from sklearn.ensemble import RandomForestClassifier
-rnd_clf = RandomForestClassifier(n_estimators=500, max_leaf_nodes=16, n_jobs=-1, random_state=42)
-rnd_clf.fit(X_train, y_train)
-y_pred_rf = rnd_clf.predict(X_test)
-np.sum(y_pred == y_pred_rf) / len(y_pred) 
-
    
-
    
-
 
    
 
 
      
@@ -219,6 +235,9 @@ np.sum(y_pred =
   
    • 37
      • 
   
    • 38
      • 
   
    • 39
      • 
+  
    • 40
      • 
+  
    • 41
      • 
+  
    • »
      • 
 
    
 
 
diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html
index 04d083734..d91a75045 100644
--- a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html
+++ b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html
@@ -84,13 +84,19 @@ Automatically generated HTML file from DocOnce source
               ('Disadvantages', 2, None, '___sec27'),
               ('Bagging', 2, None, '___sec28'),
               ('More bagging', 2, None, '___sec29'),
-              ('Simple example, head or tail', 2, None, '___sec30'),
-              ('Bagging Example', 2, None, '___sec31'),
-              ('Random forests', 2, None, '___sec32'),
-              ('A simple scikit-learn example', 2, None, '___sec33'),
-              ('Please, not the moons again!', 2, None, '___sec34'),
-              ('Bagging examples', 2, None, '___sec35'),
-              ('Then random forests', 2, None, '___sec36')]}
+              ('Simple Voting Example, head or tail', 2, None, '___sec30'),
+              ('Using the Voting Classifier', 2, None, '___sec31'),
+              ('Please, not the moons again! Voting and Bagging',
+               2,
+               None,
+               '___sec32'),
+              ('Now Bagging', 2, None, '___sec33'),
+              ('Random forests', 2, None, '___sec34'),
+              ('A simple scikit-learn example', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36'),
+              ('Feature Importance', 2, None, '___sec37'),
+              ('Boosting: AdaBoost', 2, None, '___sec38'),
+              ('Gradient Boosting', 2, None, '___sec39')]}
 end of tocinfo -->
 
 
@@ -158,13 +164,16 @@ MathJax.Hub.Config({
       
  • Disadvantages
    • 
       
  • Bagging
    • 
       
  • More bagging
    • 
-      
  • Simple example, head or tail
    • 
-      
  • Bagging Example
    • 
-      
  • Random forests
    • 
-      
  • A simple scikit-learn example
    • 
-      
  • Please, not the moons again!
    • 
-      
  • Bagging examples
    • 
+      
  • Simple Voting Example, head or tail
    • 
+      
  • Using the Voting Classifier
    • 
+      
  • Please, not the moons again! Voting and Bagging
    • 
+      
  • Now Bagging
    • 
+      
  • Random forests
    • 
+      
  • A simple scikit-learn example
    • 
       
  • Then random forests
    • 
+      
  • Feature Importance
    • 
+      
  • Boosting: AdaBoost
    • 
+      
  • Gradient Boosting
    • 
 
         
       
@@ -199,7 +208,7 @@ MathJax.Hub.Config({
 
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
    
 
    
 
    
-
    Oct 31, 2019
     
+
    Nov 1, 2019
     
 
    
 
    
 
@@ -223,7 +232,7 @@ MathJax.Hub.Config({
   
  • 9
    • 
   
  • 10
    • 
   
  • ...
    • 
-  
  • 38
    • 
+  
  • 41
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html
index 87be866d9..579723a54 100644
--- a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html
+++ b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html
@@ -148,7 +148,7 @@ MathJax.Hub.Config({
 
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
    
 
    
 
     
    
-
    Oct 31, 2019
     
+
    Nov 1, 2019
     
 
    
 
    
 
@@ -1457,7 +1457,7 @@ predictor, averaged over all \( B \) trees.
 
 
 
    
-
    Simple example, head or tail 
    
+
    Simple Voting Example, head or tail 
    
 
    
 
 
@@ -1478,7 +1478,7 @@ plt.show()
 
 
 
    
-
    Bagging Example 
    
+
    Using the Voting Classifier 
    
 
    
 
 
@@ -1530,72 +1530,7 @@ voting_clf.fit(X_train, y_train)
 
 
 
    
-
    Random forests 
    
-
-
    
-Random forests provide an improvement over bagged trees by way of a
-small tweak that decorrelates the trees.
-
-
    
-As in bagging, we build a
-number of decision trees on bootstrapped training samples. But when
-building these decision trees, each time a split in a tree is
-considered, a random sample of \( m \) predictors is chosen as split
-candidates from the full set of \( p \) predictors. The split is allowed to
-use only one of those \( m \) predictors.
-
-
    
-A fresh sample of \( m \) predictors is
-taken at each split, and typically we choose
-
-
     
    
-$$
-m\approx \sqrt{p}.
-$$
-
     
    
-
-
    
-In building a random forest, at
-each split in the tree, the algorithm is not even allowed to consider
-a majority of the available predictors.
-
-
    
-The reason for this is rather clever. Suppose that there is one very
-strong predictor in the data set, along with a number of other
-moderately strong predictors. Then in the collection of bagged
-variable importance random forest trees, most or all of the trees will
-use this strong predictor in the top split. Consequently, all of the
-bagged trees will look quite similar to each other. Hence the
-predictions from the bagged trees will be highly correlated.
-Unfortunately, averaging many highly correlated quantities does not
-lead to as large of a reduction in variance as averaging many
-uncorrelated quanti- ties. In particular, this means that bagging will
-not lead to a substantial reduction in variance over a single tree in
-this setting.
-
    
-
-
-
    
-
    A simple scikit-learn example 
    
-
    
-
-
-
    from sklearn.ensemble import RandomForestClassifier
-from sklearn.preprocessing import LabelEncoder
-from sklearn.model_selection import cross_validate
-# Data set not specificied
-X = dataset.XXX
-Y = dataset.YYY
-#Instantiate the model with 100 trees and entropy as splitting criteria
-Random_Forest_model = RandomForestClassifier(n_estimators=100,criterion="entropy")
-#Cross validation
-accuracy = cross_validate(Random_Forest_model,X,Y,cv=10)['test_score']
-
    
-
    
-
-
-
    
-
    Please, not the moons again! 
    
+
    Please, not the moons again! Voting and Bagging 
    
 
    
 
 
@@ -1654,7 +1589,7 @@ voting_clf.fit(X_train, y_train)
 
 
 
    
-
    Bagging examples 
    
+
    Now Bagging  
    
 
 
    
 
@@ -1715,6 +1650,71 @@ plt.show()
 
    
 
 
+
    
+
    Random forests 
    
+
+
    
+Random forests provide an improvement over bagged trees by way of a
+small tweak that decorrelates the trees.
+
+
    
+As in bagging, we build a
+number of decision trees on bootstrapped training samples. But when
+building these decision trees, each time a split in a tree is
+considered, a random sample of \( m \) predictors is chosen as split
+candidates from the full set of \( p \) predictors. The split is allowed to
+use only one of those \( m \) predictors.
+
+
    
+A fresh sample of \( m \) predictors is
+taken at each split, and typically we choose
+
+
     
    
+$$
+m\approx \sqrt{p}.
+$$
+
     
    
+
+
    
+In building a random forest, at
+each split in the tree, the algorithm is not even allowed to consider
+a majority of the available predictors.
+
+
    
+The reason for this is rather clever. Suppose that there is one very
+strong predictor in the data set, along with a number of other
+moderately strong predictors. Then in the collection of bagged
+variable importance random forest trees, most or all of the trees will
+use this strong predictor in the top split. Consequently, all of the
+bagged trees will look quite similar to each other. Hence the
+predictions from the bagged trees will be highly correlated.
+Unfortunately, averaging many highly correlated quantities does not
+lead to as large of a reduction in variance as averaging many
+uncorrelated quanti- ties. In particular, this means that bagging will
+not lead to a substantial reduction in variance over a single tree in
+this setting.
+
    
+
+
+
    
+
    A simple scikit-learn example 
    
+
    
+
+
+
    from sklearn.ensemble import RandomForestClassifier
+from sklearn.preprocessing import LabelEncoder
+from sklearn.model_selection import cross_validate
+# Data set not specificied
+X = dataset.XXX
+Y = dataset.YYY
+#Instantiate the model with 100 trees and entropy as splitting criteria
+Random_Forest_model = RandomForestClassifier(n_estimators=100,criterion="entropy")
+#Cross validation
+accuracy = cross_validate(Random_Forest_model,X,Y,cv=10)['test_score']
+
    
+
    
+
+
 
    
 
    Then random forests 
    
 
    
@@ -1738,6 +1738,172 @@ np.sum(y_pred == y_pred_rf) / len(y_pred)
 
    
 
 
+
    
+
    Feature Importance 
    
+
+
    
+
+
+
    try:
+    from sklearn.datasets import fetch_openml
+    mnist = fetch_openml('mnist_784', version=1)
+    mnist.target = mnist.target.astype(np.int64)
+except ImportError:
+    from sklearn.datasets import fetch_mldata
+    mnist = fetch_mldata('MNIST original')
+
+rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
+rnd_clf.fit(mnist["data"], mnist["target"])
+
+def plot_digit(data):
+    image = data.reshape(28, 28)
+    plt.imshow(image, cmap = mpl.cm.hot,
+               interpolation="nearest")
+    plt.axis("off")
+
+plot_digit(rnd_clf.feature_importances_)
+
+cbar = plt.colorbar(ticks=[rnd_clf.feature_importances_.min(), rnd_clf.feature_importances_.max()])
+cbar.ax.set_yticklabels(['Not important', 'Very important'])
+
+#save_fig("mnist_feature_importance_plot")
+plt.show()
+
    
+
    
+
+
+
    
+
    Boosting: AdaBoost 
    
+
+
    
+
+
+
    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)
+
+plot_decision_boundary(ada_clf, X, y)
+
+m = len(X_train)
+
+plt.figure(figsize=(11, 4))
+for subplot, learning_rate in ((121, 1), (122, 0.5)):
+    sample_weights = np.ones(m)
+    plt.subplot(subplot)
+    for i in range(5):
+        svm_clf = SVC(kernel="rbf", C=0.05, gamma="auto", random_state=42)
+        svm_clf.fit(X_train, y_train, sample_weight=sample_weights)
+        y_pred = svm_clf.predict(X_train)
+        sample_weights[y_pred != y_train] *= (1 + learning_rate)
+        plot_decision_boundary(svm_clf, X, y, alpha=0.2)
+        plt.title("learning_rate = {}".format(learning_rate), fontsize=16)
+    if subplot == 121:
+        plt.text(-0.7, -0.65, "1", fontsize=14)
+        plt.text(-0.6, -0.10, "2", fontsize=14)
+        plt.text(-0.5,  0.10, "3", fontsize=14)
+        plt.text(-0.4,  0.55, "4", fontsize=14)
+        plt.text(-0.3,  0.90, "5", fontsize=14)
+
+save_fig("boosting_plot")
+plt.show()
+
    
+
    
+
+
+
    
+
    Gradient Boosting 
    
+
    
+
+
+
    np.random.seed(42)
+X = np.random.rand(100, 1) - 0.5
+y = 3*X[:, 0]**2 + 0.05 * np.random.randn(100)
+
+from sklearn.tree import DecisionTreeRegressor
+
+tree_reg1 = DecisionTreeRegressor(max_depth=2, random_state=42)
+tree_reg1.fit(X, y)
+
+y2 = y - tree_reg1.predict(X)
+tree_reg2 = DecisionTreeRegressor(max_depth=2, random_state=42)
+tree_reg2.fit(X, y2)
+
+y3 = y2 - tree_reg2.predict(X)
+tree_reg3 = DecisionTreeRegressor(max_depth=2, random_state=42)
+tree_reg3.fit(X, y3)
+
+X_new = np.array([[0.8]])
+y_pred = sum(tree.predict(X_new) for tree in (tree_reg1, tree_reg2, tree_reg3))
+
+def plot_predictions(regressors, X, y, axes, label=None, style="r-", data_style="b.", data_label=None):
+    x1 = np.linspace(axes[0], axes[1], 500)
+    y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)
+    plt.plot(X[:, 0], y, data_style, label=data_label)
+    plt.plot(x1, y_pred, style, linewidth=2, label=label)
+    if label or data_label:
+        plt.legend(loc="upper center", fontsize=16)
+    plt.axis(axes)
+
+plt.figure(figsize=(11,11))
+
+plt.subplot(321)
+plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h_1(x_1)$", style="g-", data_label="Training set")
+plt.ylabel("$y$", fontsize=16, rotation=0)
+plt.title("Residuals and tree predictions", fontsize=16)
+
+plt.subplot(322)
+plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1)$", data_label="Training set")
+plt.ylabel("$y$", fontsize=16, rotation=0)
+plt.title("Ensemble predictions", fontsize=16)
+
+plt.subplot(323)
+plot_predictions([tree_reg2], X, y2, axes=[-0.5, 0.5, -0.5, 0.5], label="$h_2(x_1)$", style="g-", data_style="k+", data_label="Residuals")
+plt.ylabel("$y - h_1(x_1)$", fontsize=16)
+
+plt.subplot(324)
+plot_predictions([tree_reg1, tree_reg2], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1) + h_2(x_1)$")
+plt.ylabel("$y$", fontsize=16, rotation=0)
+
+plt.subplot(325)
+plot_predictions([tree_reg3], X, y3, axes=[-0.5, 0.5, -0.5, 0.5], label="$h_3(x_1)$", style="g-", data_style="k+")
+plt.ylabel("$y - h_1(x_1) - h_2(x_1)$", fontsize=16)
+plt.xlabel("$x_1$", fontsize=16)
+
+plt.subplot(326)
+plot_predictions([tree_reg1, tree_reg2, tree_reg3], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1) + h_2(x_1) + h_3(x_1)$")
+plt.xlabel("$x_1$", fontsize=16)
+plt.ylabel("$y$", fontsize=16, rotation=0)
+
+save_fig("gradient_boosting_plot")
+plt.show()
+
+from sklearn.ensemble import GradientBoostingRegressor
+
+gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=3, learning_rate=1.0, random_state=42)
+gbrt.fit(X, y)
+
+gbrt_slow = GradientBoostingRegressor(max_depth=2, n_estimators=200, learning_rate=0.1, random_state=42)
+gbrt_slow.fit(X, y)
+
+plt.figure(figsize=(11,4))
+
+plt.subplot(121)
+plot_predictions([gbrt], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="Ensemble predictions")
+plt.title("learning_rate={}, n_estimators={}".format(gbrt.learning_rate, gbrt.n_estimators), fontsize=14)
+
+plt.subplot(122)
+plot_predictions([gbrt_slow], X, y, axes=[-0.5, 0.5, -0.1, 0.8])
+plt.title("learning_rate={}, n_estimators={}".format(gbrt_slow.learning_rate, gbrt_slow.n_estimators), fontsize=14)
+
+save_fig("gbrt_learning_rate_plot")
+plt.show()
+
    
+
    
+
+
    diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html index 320de8458..9c117867f 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html @@ -104,13 +104,19 @@ div { text-align: justify; text-justify: inter-word; } ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -152,7 +158,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Oct 31, 2019

    +

    Nov 1, 2019












    @@ -1422,7 +1428,7 @@ predictor, averaged over all \( B \) trees.











    -

    Simple example, head or tail

    +

    Simple Voting Example, head or tail

    @@ -1442,7 +1448,7 @@ plt.show()











    -

    Bagging Example

    +

    Using the Voting Classifier

    @@ -1493,69 +1499,7 @@ voting_clf.fit(X_train, y_train)











    -

    Random forests

    - -

    -Random forests provide an improvement over bagged trees by way of a -small tweak that decorrelates the trees. - -

    -As in bagging, we build a -number of decision trees on bootstrapped training samples. But when -building these decision trees, each time a split in a tree is -considered, a random sample of \( m \) predictors is chosen as split -candidates from the full set of \( p \) predictors. The split is allowed to -use only one of those \( m \) predictors. - -

    -A fresh sample of \( m \) predictors is -taken at each split, and typically we choose - -$$ -m\approx \sqrt{p}. -$$ - -

    -In building a random forest, at -each split in the tree, the algorithm is not even allowed to consider -a majority of the available predictors. - -

    -The reason for this is rather clever. Suppose that there is one very -strong predictor in the data set, along with a number of other -moderately strong predictors. Then in the collection of bagged -variable importance random forest trees, most or all of the trees will -use this strong predictor in the top split. Consequently, all of the -bagged trees will look quite similar to each other. Hence the -predictions from the bagged trees will be highly correlated. -Unfortunately, averaging many highly correlated quantities does not -lead to as large of a reduction in variance as averaging many -uncorrelated quanti- ties. In particular, this means that bagging will -not lead to a substantial reduction in variance over a single tree in -this setting. - -

    -









    - -

    A simple scikit-learn example

    -

    - - -

    from sklearn.ensemble import RandomForestClassifier
-from sklearn.preprocessing import LabelEncoder
-from sklearn.model_selection import cross_validate
-# Data set not specificied
-X = dataset.XXX
-Y = dataset.YYY
-#Instantiate the model with 100 trees and entropy as splitting criteria
-Random_Forest_model = RandomForestClassifier(n_estimators=100,criterion="entropy")
-#Cross validation
-accuracy = cross_validate(Random_Forest_model,X,Y,cv=10)['test_score']
-
    -

    -









    - -

    Please, not the moons again!

    +

    Please, not the moons again! Voting and Bagging

    @@ -1613,7 +1557,7 @@ voting_clf.fit(X_train, y_train)











    -

    Bagging examples

    +

    Now Bagging

    @@ -1674,6 +1618,68 @@ plt.show()











    +

    Random forests

    + +

    +Random forests provide an improvement over bagged trees by way of a +small tweak that decorrelates the trees. + +

    +As in bagging, we build a +number of decision trees on bootstrapped training samples. But when +building these decision trees, each time a split in a tree is +considered, a random sample of \( m \) predictors is chosen as split +candidates from the full set of \( p \) predictors. The split is allowed to +use only one of those \( m \) predictors. + +

    +A fresh sample of \( m \) predictors is +taken at each split, and typically we choose + +$$ +m\approx \sqrt{p}. +$$ + +

    +In building a random forest, at +each split in the tree, the algorithm is not even allowed to consider +a majority of the available predictors. + +

    +The reason for this is rather clever. Suppose that there is one very +strong predictor in the data set, along with a number of other +moderately strong predictors. Then in the collection of bagged +variable importance random forest trees, most or all of the trees will +use this strong predictor in the top split. Consequently, all of the +bagged trees will look quite similar to each other. Hence the +predictions from the bagged trees will be highly correlated. +Unfortunately, averaging many highly correlated quantities does not +lead to as large of a reduction in variance as averaging many +uncorrelated quanti- ties. In particular, this means that bagging will +not lead to a substantial reduction in variance over a single tree in +this setting. + +

    +









    + +

    A simple scikit-learn example

    +

    + + +

    from sklearn.ensemble import RandomForestClassifier
+from sklearn.preprocessing import LabelEncoder
+from sklearn.model_selection import cross_validate
+# Data set not specificied
+X = dataset.XXX
+Y = dataset.YYY
+#Instantiate the model with 100 trees and entropy as splitting criteria
+Random_Forest_model = RandomForestClassifier(n_estimators=100,criterion="entropy")
+#Cross validation
+accuracy = cross_validate(Random_Forest_model,X,Y,cv=10)['test_score']
+
    +

    +









    +

    Then random forests

    @@ -1694,6 +1700,169 @@ y_pred_rf = rnd_clf.predict(X_test) np.sum(y_pred == y_pred_rf) / len(y_pred)

    +









    + +

    Feature Importance

    + +

    + + +

    try:
+    from sklearn.datasets import fetch_openml
+    mnist = fetch_openml('mnist_784', version=1)
+    mnist.target = mnist.target.astype(np.int64)
+except ImportError:
+    from sklearn.datasets import fetch_mldata
+    mnist = fetch_mldata('MNIST original')
+
+rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
+rnd_clf.fit(mnist["data"], mnist["target"])
+
+def plot_digit(data):
+    image = data.reshape(28, 28)
+    plt.imshow(image, cmap = mpl.cm.hot,
+               interpolation="nearest")
+    plt.axis("off")
+
+plot_digit(rnd_clf.feature_importances_)
+
+cbar = plt.colorbar(ticks=[rnd_clf.feature_importances_.min(), rnd_clf.feature_importances_.max()])
+cbar.ax.set_yticklabels(['Not important', 'Very important'])
+
+#save_fig("mnist_feature_importance_plot")
+plt.show()
+
    +

    +









    + +

    Boosting: AdaBoost

    + +

    + + +

    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)
+
+plot_decision_boundary(ada_clf, X, y)
+
+m = len(X_train)
+
+plt.figure(figsize=(11, 4))
+for subplot, learning_rate in ((121, 1), (122, 0.5)):
+    sample_weights = np.ones(m)
+    plt.subplot(subplot)
+    for i in range(5):
+        svm_clf = SVC(kernel="rbf", C=0.05, gamma="auto", random_state=42)
+        svm_clf.fit(X_train, y_train, sample_weight=sample_weights)
+        y_pred = svm_clf.predict(X_train)
+        sample_weights[y_pred != y_train] *= (1 + learning_rate)
+        plot_decision_boundary(svm_clf, X, y, alpha=0.2)
+        plt.title("learning_rate = {}".format(learning_rate), fontsize=16)
+    if subplot == 121:
+        plt.text(-0.7, -0.65, "1", fontsize=14)
+        plt.text(-0.6, -0.10, "2", fontsize=14)
+        plt.text(-0.5,  0.10, "3", fontsize=14)
+        plt.text(-0.4,  0.55, "4", fontsize=14)
+        plt.text(-0.3,  0.90, "5", fontsize=14)
+
+save_fig("boosting_plot")
+plt.show()
+
    +

    +









    + +

    Gradient Boosting

    +

    + + +

    np.random.seed(42)
+X = np.random.rand(100, 1) - 0.5
+y = 3*X[:, 0]**2 + 0.05 * np.random.randn(100)
+
+from sklearn.tree import DecisionTreeRegressor
+
+tree_reg1 = DecisionTreeRegressor(max_depth=2, random_state=42)
+tree_reg1.fit(X, y)
+
+y2 = y - tree_reg1.predict(X)
+tree_reg2 = DecisionTreeRegressor(max_depth=2, random_state=42)
+tree_reg2.fit(X, y2)
+
+y3 = y2 - tree_reg2.predict(X)
+tree_reg3 = DecisionTreeRegressor(max_depth=2, random_state=42)
+tree_reg3.fit(X, y3)
+
+X_new = np.array([[0.8]])
+y_pred = sum(tree.predict(X_new) for tree in (tree_reg1, tree_reg2, tree_reg3))
+
+def plot_predictions(regressors, X, y, axes, label=None, style="r-", data_style="b.", data_label=None):
+    x1 = np.linspace(axes[0], axes[1], 500)
+    y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)
+    plt.plot(X[:, 0], y, data_style, label=data_label)
+    plt.plot(x1, y_pred, style, linewidth=2, label=label)
+    if label or data_label:
+        plt.legend(loc="upper center", fontsize=16)
+    plt.axis(axes)
+
+plt.figure(figsize=(11,11))
+
+plt.subplot(321)
+plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h_1(x_1)$", style="g-", data_label="Training set")
+plt.ylabel("$y$", fontsize=16, rotation=0)
+plt.title("Residuals and tree predictions", fontsize=16)
+
+plt.subplot(322)
+plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1)$", data_label="Training set")
+plt.ylabel("$y$", fontsize=16, rotation=0)
+plt.title("Ensemble predictions", fontsize=16)
+
+plt.subplot(323)
+plot_predictions([tree_reg2], X, y2, axes=[-0.5, 0.5, -0.5, 0.5], label="$h_2(x_1)$", style="g-", data_style="k+", data_label="Residuals")
+plt.ylabel("$y - h_1(x_1)$", fontsize=16)
+
+plt.subplot(324)
+plot_predictions([tree_reg1, tree_reg2], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1) + h_2(x_1)$")
+plt.ylabel("$y$", fontsize=16, rotation=0)
+
+plt.subplot(325)
+plot_predictions([tree_reg3], X, y3, axes=[-0.5, 0.5, -0.5, 0.5], label="$h_3(x_1)$", style="g-", data_style="k+")
+plt.ylabel("$y - h_1(x_1) - h_2(x_1)$", fontsize=16)
+plt.xlabel("$x_1$", fontsize=16)
+
+plt.subplot(326)
+plot_predictions([tree_reg1, tree_reg2, tree_reg3], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1) + h_2(x_1) + h_3(x_1)$")
+plt.xlabel("$x_1$", fontsize=16)
+plt.ylabel("$y$", fontsize=16, rotation=0)
+
+save_fig("gradient_boosting_plot")
+plt.show()
+
+from sklearn.ensemble import GradientBoostingRegressor
+
+gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=3, learning_rate=1.0, random_state=42)
+gbrt.fit(X, y)
+
+gbrt_slow = GradientBoostingRegressor(max_depth=2, n_estimators=200, learning_rate=0.1, random_state=42)
+gbrt_slow.fit(X, y)
+
+plt.figure(figsize=(11,4))
+
+plt.subplot(121)
+plot_predictions([gbrt], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="Ensemble predictions")
+plt.title("learning_rate={}, n_estimators={}".format(gbrt.learning_rate, gbrt.n_estimators), fontsize=14)
+
+plt.subplot(122)
+plot_predictions([gbrt_slow], X, y, axes=[-0.5, 0.5, -0.1, 0.8])
+plt.title("learning_rate={}, n_estimators={}".format(gbrt_slow.learning_rate, gbrt_slow.n_estimators), fontsize=14)
+
+save_fig("gbrt_learning_rate_plot")
+plt.show()
+
    +

    diff --git a/doc/pub/DecisionTrees/html/DecisionTrees.html b/doc/pub/DecisionTrees/html/DecisionTrees.html index 5b6adb746..8a7179846 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees.html @@ -109,13 +109,19 @@ div { text-align: justify; text-justify: inter-word; } ('Disadvantages', 2, None, '___sec27'), ('Bagging', 2, None, '___sec28'), ('More bagging', 2, None, '___sec29'), - ('Simple example, head or tail', 2, None, '___sec30'), - ('Bagging Example', 2, None, '___sec31'), - ('Random forests', 2, None, '___sec32'), - ('A simple scikit-learn example', 2, None, '___sec33'), - ('Please, not the moons again!', 2, None, '___sec34'), - ('Bagging examples', 2, None, '___sec35'), - ('Then random forests', 2, None, '___sec36')]} + ('Simple Voting Example, head or tail', 2, None, '___sec30'), + ('Using the Voting Classifier', 2, None, '___sec31'), + ('Please, not the moons again! Voting and Bagging', + 2, + None, + '___sec32'), + ('Now Bagging', 2, None, '___sec33'), + ('Random forests', 2, None, '___sec34'), + ('A simple scikit-learn example', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36'), + ('Feature Importance', 2, None, '___sec37'), + ('Boosting: AdaBoost', 2, None, '___sec38'), + ('Gradient Boosting', 2, None, '___sec39')]} end of tocinfo --> @@ -157,7 +163,7 @@ MathJax.Hub.Config({

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

    -

    Oct 31, 2019

    +

    Nov 1, 2019












    @@ -1427,7 +1433,7 @@ predictor, averaged over all \( B \) trees.











    -

    Simple example, head or tail

    +

    Simple Voting Example, head or tail

    @@ -1447,7 +1453,7 @@ plt.show()











    -

    Bagging Example

    +

    Using the Voting Classifier

    @@ -1498,69 +1504,7 @@ voting_clf.fit(X_train, y_train)











    -

    Random forests

    - -

    -Random forests provide an improvement over bagged trees by way of a -small tweak that decorrelates the trees. - -

    -As in bagging, we build a -number of decision trees on bootstrapped training samples. But when -building these decision trees, each time a split in a tree is -considered, a random sample of \( m \) predictors is chosen as split -candidates from the full set of \( p \) predictors. The split is allowed to -use only one of those \( m \) predictors. - -

    -A fresh sample of \( m \) predictors is -taken at each split, and typically we choose - -$$ -m\approx \sqrt{p}. -$$ - -

    -In building a random forest, at -each split in the tree, the algorithm is not even allowed to consider -a majority of the available predictors. - -

    -The reason for this is rather clever. Suppose that there is one very -strong predictor in the data set, along with a number of other -moderately strong predictors. Then in the collection of bagged -variable importance random forest trees, most or all of the trees will -use this strong predictor in the top split. Consequently, all of the -bagged trees will look quite similar to each other. Hence the -predictions from the bagged trees will be highly correlated. -Unfortunately, averaging many highly correlated quantities does not -lead to as large of a reduction in variance as averaging many -uncorrelated quanti- ties. In particular, this means that bagging will -not lead to a substantial reduction in variance over a single tree in -this setting. - -

    -









    - -

    A simple scikit-learn example

    -

    - - -

    from sklearn.ensemble import RandomForestClassifier
-from sklearn.preprocessing import LabelEncoder
-from sklearn.model_selection import cross_validate
-# Data set not specificied
-X = dataset.XXX
-Y = dataset.YYY
-#Instantiate the model with 100 trees and entropy as splitting criteria
-Random_Forest_model = RandomForestClassifier(n_estimators=100,criterion="entropy")
-#Cross validation
-accuracy = cross_validate(Random_Forest_model,X,Y,cv=10)['test_score']
-
    -

    -









    - -

    Please, not the moons again!

    +

    Please, not the moons again! Voting and Bagging

    @@ -1618,7 +1562,7 @@ voting_clf.fit(X_train, y_train)











    -

    Bagging examples

    +

    Now Bagging

    @@ -1679,6 +1623,68 @@ plt.show()











    +

    Random forests

    + +

    +Random forests provide an improvement over bagged trees by way of a +small tweak that decorrelates the trees. + +

    +As in bagging, we build a +number of decision trees on bootstrapped training samples. But when +building these decision trees, each time a split in a tree is +considered, a random sample of \( m \) predictors is chosen as split +candidates from the full set of \( p \) predictors. The split is allowed to +use only one of those \( m \) predictors. + +

    +A fresh sample of \( m \) predictors is +taken at each split, and typically we choose + +$$ +m\approx \sqrt{p}. +$$ + +

    +In building a random forest, at +each split in the tree, the algorithm is not even allowed to consider +a majority of the available predictors. + +

    +The reason for this is rather clever. Suppose that there is one very +strong predictor in the data set, along with a number of other +moderately strong predictors. Then in the collection of bagged +variable importance random forest trees, most or all of the trees will +use this strong predictor in the top split. Consequently, all of the +bagged trees will look quite similar to each other. Hence the +predictions from the bagged trees will be highly correlated. +Unfortunately, averaging many highly correlated quantities does not +lead to as large of a reduction in variance as averaging many +uncorrelated quanti- ties. In particular, this means that bagging will +not lead to a substantial reduction in variance over a single tree in +this setting. + +

    +









    + +

    A simple scikit-learn example

    +

    + + +

    from sklearn.ensemble import RandomForestClassifier
+from sklearn.preprocessing import LabelEncoder
+from sklearn.model_selection import cross_validate
+# Data set not specificied
+X = dataset.XXX
+Y = dataset.YYY
+#Instantiate the model with 100 trees and entropy as splitting criteria
+Random_Forest_model = RandomForestClassifier(n_estimators=100,criterion="entropy")
+#Cross validation
+accuracy = cross_validate(Random_Forest_model,X,Y,cv=10)['test_score']
+
    +

    +









    +

    Then random forests

    @@ -1699,6 +1705,169 @@ y_pred_rf = rnd_clf.sum(y_pred == y_pred_rf) / len(y_pred)

    +









    + +

    Feature Importance

    + +

    + + +

    try:
+    from sklearn.datasets import fetch_openml
+    mnist = fetch_openml('mnist_784', version=1)
+    mnist.target = mnist.target.astype(np.int64)
+except ImportError:
+    from sklearn.datasets import fetch_mldata
+    mnist = fetch_mldata('MNIST original')
+
+rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
+rnd_clf.fit(mnist["data"], mnist["target"])
+
+def plot_digit(data):
+    image = data.reshape(28, 28)
+    plt.imshow(image, cmap = mpl.cm.hot,
+               interpolation="nearest")
+    plt.axis("off")
+
+plot_digit(rnd_clf.feature_importances_)
+
+cbar = plt.colorbar(ticks=[rnd_clf.feature_importances_.min(), rnd_clf.feature_importances_.max()])
+cbar.ax.set_yticklabels(['Not important', 'Very important'])
+
+#save_fig("mnist_feature_importance_plot")
+plt.show()
+
    +

    +









    + +

    Boosting: AdaBoost

    + +

    + + +

    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)
+
+plot_decision_boundary(ada_clf, X, y)
+
+m = len(X_train)
+
+plt.figure(figsize=(11, 4))
+for subplot, learning_rate in ((121, 1), (122, 0.5)):
+    sample_weights = np.ones(m)
+    plt.subplot(subplot)
+    for i in range(5):
+        svm_clf = SVC(kernel="rbf", C=0.05, gamma="auto", random_state=42)
+        svm_clf.fit(X_train, y_train, sample_weight=sample_weights)
+        y_pred = svm_clf.predict(X_train)
+        sample_weights[y_pred != y_train] *= (1 + learning_rate)
+        plot_decision_boundary(svm_clf, X, y, alpha=0.2)
+        plt.title("learning_rate = {}".format(learning_rate), fontsize=16)
+    if subplot == 121:
+        plt.text(-0.7, -0.65, "1", fontsize=14)
+        plt.text(-0.6, -0.10, "2", fontsize=14)
+        plt.text(-0.5,  0.10, "3", fontsize=14)
+        plt.text(-0.4,  0.55, "4", fontsize=14)
+        plt.text(-0.3,  0.90, "5", fontsize=14)
+
+save_fig("boosting_plot")
+plt.show()
+
    +

    +









    + +

    Gradient Boosting

    +

    + + +

    np.random.seed(42)
+X = np.random.rand(100, 1) - 0.5
+y = 3*X[:, 0]**2 + 0.05 * np.random.randn(100)
+
+from sklearn.tree import DecisionTreeRegressor
+
+tree_reg1 = DecisionTreeRegressor(max_depth=2, random_state=42)
+tree_reg1.fit(X, y)
+
+y2 = y - tree_reg1.predict(X)
+tree_reg2 = DecisionTreeRegressor(max_depth=2, random_state=42)
+tree_reg2.fit(X, y2)
+
+y3 = y2 - tree_reg2.predict(X)
+tree_reg3 = DecisionTreeRegressor(max_depth=2, random_state=42)
+tree_reg3.fit(X, y3)
+
+X_new = np.array([[0.8]])
+y_pred = sum(tree.predict(X_new) for tree in (tree_reg1, tree_reg2, tree_reg3))
+
+def plot_predictions(regressors, X, y, axes, label=None, style="r-", data_style="b.", data_label=None):
+    x1 = np.linspace(axes[0], axes[1], 500)
+    y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)
+    plt.plot(X[:, 0], y, data_style, label=data_label)
+    plt.plot(x1, y_pred, style, linewidth=2, label=label)
+    if label or data_label:
+        plt.legend(loc="upper center", fontsize=16)
+    plt.axis(axes)
+
+plt.figure(figsize=(11,11))
+
+plt.subplot(321)
+plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h_1(x_1)$", style="g-", data_label="Training set")
+plt.ylabel("$y$", fontsize=16, rotation=0)
+plt.title("Residuals and tree predictions", fontsize=16)
+
+plt.subplot(322)
+plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1)$", data_label="Training set")
+plt.ylabel("$y$", fontsize=16, rotation=0)
+plt.title("Ensemble predictions", fontsize=16)
+
+plt.subplot(323)
+plot_predictions([tree_reg2], X, y2, axes=[-0.5, 0.5, -0.5, 0.5], label="$h_2(x_1)$", style="g-", data_style="k+", data_label="Residuals")
+plt.ylabel("$y - h_1(x_1)$", fontsize=16)
+
+plt.subplot(324)
+plot_predictions([tree_reg1, tree_reg2], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1) + h_2(x_1)$")
+plt.ylabel("$y$", fontsize=16, rotation=0)
+
+plt.subplot(325)
+plot_predictions([tree_reg3], X, y3, axes=[-0.5, 0.5, -0.5, 0.5], label="$h_3(x_1)$", style="g-", data_style="k+")
+plt.ylabel("$y - h_1(x_1) - h_2(x_1)$", fontsize=16)
+plt.xlabel("$x_1$", fontsize=16)
+
+plt.subplot(326)
+plot_predictions([tree_reg1, tree_reg2, tree_reg3], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1) + h_2(x_1) + h_3(x_1)$")
+plt.xlabel("$x_1$", fontsize=16)
+plt.ylabel("$y$", fontsize=16, rotation=0)
+
+save_fig("gradient_boosting_plot")
+plt.show()
+
+from sklearn.ensemble import GradientBoostingRegressor
+
+gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=3, learning_rate=1.0, random_state=42)
+gbrt.fit(X, y)
+
+gbrt_slow = GradientBoostingRegressor(max_depth=2, n_estimators=200, learning_rate=0.1, random_state=42)
+gbrt_slow.fit(X, y)
+
+plt.figure(figsize=(11,4))
+
+plt.subplot(121)
+plot_predictions([gbrt], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="Ensemble predictions")
+plt.title("learning_rate={}, n_estimators={}".format(gbrt.learning_rate, gbrt.n_estimators), fontsize=14)
+
+plt.subplot(122)
+plot_predictions([gbrt_slow], X, y, axes=[-0.5, 0.5, -0.1, 0.8])
+plt.title("learning_rate={}, n_estimators={}".format(gbrt_slow.learning_rate, gbrt_slow.n_estimators), fontsize=14)
+
+save_fig("gbrt_learning_rate_plot")
+plt.show()
+
    +

    diff --git a/doc/pub/DecisionTrees/ipynb/DataFiles/cancer.dot b/doc/pub/DecisionTrees/ipynb/DataFiles/cancer.dot index 252087b50..0d1aedaf9 100644 --- a/doc/pub/DecisionTrees/ipynb/DataFiles/cancer.dot +++ b/doc/pub/DecisionTrees/ipynb/DataFiles/cancer.dot @@ -10,7 +10,7 @@ edge [fontname=helvetica] ; 2 -> 3 ; 4 [label="gini = 0.0\nsamples = 239\nvalue = [[239, 0]\n[0, 239]]", fillcolor="#e58139ff"] ; 3 -> 4 ; -5 [label="mean area <= 469.25\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#e5813913"] ; +5 [label="worst area <= 566.55\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#e5813913"] ; 3 -> 5 ; 6 [label="gini = 0.0\nsamples = 1\nvalue = [[0, 1]\n[1, 0]]", fillcolor="#e58139ff"] ; 5 -> 6 ; @@ -30,7 +30,7 @@ edge [fontname=helvetica] ; 11 -> 13 ; 14 [label="worst texture <= 20.645\ngini = 0.202\nsamples = 167\nvalue = [[19, 148]\n[148, 19]]", fillcolor="#e5813994"] ; 0 -> 14 [labeldistance=2.5, labelangle=-45, headlabel="False"] ; -15 [label="worst perimeter <= 116.8\ngini = 0.375\nsamples = 16\nvalue = [[12, 4]\n[4, 12]]", fillcolor="#e5813938"] ; +15 [label="worst radius <= 17.74\ngini = 0.375\nsamples = 16\nvalue = [[12, 4]\n[4, 12]]", fillcolor="#e5813938"] ; 14 -> 15 ; 16 [label="gini = 0.0\nsamples = 11\nvalue = [[11, 0]\n[0, 11]]", fillcolor="#e58139ff"] ; 15 -> 16 ; diff --git a/doc/pub/DecisionTrees/ipynb/DataFiles/cancer.png b/doc/pub/DecisionTrees/ipynb/DataFiles/cancer.png index 045c6e0a3de4270d04a650fb472b2809f461f978..4626c9fe14e9330463e01db4f9d54e20207da26c 100644 GIT binary patch literal 222008 zcmZ_01yq$^^erj~N+{h(DBXh6sdR^QBPCrT-3lrV(p}Oa9fy(zDd~{zLpO(dn|t2{ ze*br$V=%bI$dBQ;-vXib90);K75Zk`f|H4;~<{Ja_=_i}VP*Qr>}_ z2>ya|P!fOpps4TJI{1f(vAU#*tn34N@IBH4xB#;U2sdv5Uqs;R!GnjXa1S1Wzu|6P zONIYGKSf+gefWRAhxfgCqkN&$<%0)84-Fkm)c1}xr&(R76@KI1~kMc%0M+|Ceu{zrbJ>Df%7w|NDmj_1{tv2x3?9eg1zw0N9D*m*4Sv_oA< zJm^kxiqEw-RtZ_M8m=zG9nZEQo|i;j5mdt8ap=NW^aQxLxH_NX-M@ZXAEZC5{WkD- z>-4Tbc6Mf`bVTrmC9%6Kakcl6D7#v756#uw30LNDNQdMSXZ0IeKtE;Qu|6QWvnqTlW z8_LcQ3nnsvJ{s4$y9+-0Hy^0ZJwb5$d8tAlP=bg#(S|BgS4-Oh71Bla1~yTOW#P); z#Y0JjBUhM)JI}5z&l3t;lJ14lC`(flA>qRtwg>qj@TBm2euxkk(4OYA zVUt0IxE`U1O8~fXj-dm*tPV7qqcsv%}pfQ#d z3hU|Wv~g_Rcz8HeN|{&;8u@3!(+C{q_TvH`Fa&oji+drg9`)eif$9;L%d6X^l3yTi z&eRh}Qp>eY4AHb$DO?R^h&x|hAlk3|!MtjCU~m{>*bx%EDo^^{sR6z-nV&aLITuT8 z=kvdxcjx95)90(8Jyw6(-Ak$7R7mbu7lb-IPVK)D4;bk^dV3Q%2W^^!Ans>uBC#gD zae>_)Td&dfip7U|^ZmT^R6%LMP^G8lIBB~d#@ zGi!ygEz^^mBs!bdcyypeF18b&?97VSp^=1hc!)9OB$KuHhc;E&%sx?}S1tPPEBZa& zz0!Khgv%Q8-q6r5D-i$pFKK-Di_^hVj4`^q1W=&u?c>7W)dbW$V< zm9nJ1#aBQV=34@&w>te1`k}-5==f@CGD&=xIu+iq({GW(70aiB*B5^LZYSwVZQnl( zkl;yccvV<82oGX}!E2ZYBx;3i?u)-UG=krSwn#T*H2_Wy`1d7*=g>Kx&VO z=Q_hP{Gsa%Y_3{jX`CO1)swWU)$N`MdcGAbh<;_-D>eg<7*21+qp~wo?`Gau)3Euk ziY()rAU~u(q49xz%Fxe#p=0eD72+vuP%sHa~wPeDz$bPn&?t8L7ejY{7I^hIy%@9W0C7L%aIJFEaLvnalZ> z$4p!TnBpO%qCo_#?kb5KhL4PlV7@L6if^d3lGrpZYu}Glb!i(PvMG*{D4=J zRTdVfAnBfN#O#HT{!4mk+IMnAu(Qf@n;ufVk5FE|w5jipb`rZSOa+>A>qFVLjdl-> zdw%R42!I5V2H&7Ge|E5{8RkMUYBQdSsH2zTpjxcq$7T0E|H%4Zl1gerFrFm|ugU9e zbD!M^F|*}TM&U=3!e5(V z{h-s4s?bpBAx`FVVXLsdSltb$SlbvTnVAuqooQU$nyRAJ%Vh&UOwW@Y5HsNYy#^EY-59yN~V93dovMSb zCLk7wCtIPIrTKK(etX(QSf^2S35H$~Be){Ae(s2N^6m~ce71wz(sR|g4<;~H5I${= z&+9a}bMM%s2*S=Z%Jm!YVE!kO0Vnm>RmUtlYl9hX;@@$)w4^l_w$}HQ3X3&=X_LfU z)_d(3e}KkMQ8{ieeZz(v9o0H+ID4I~Wo;-IDR=Rz1Qpmk2x zYOA$+j<3p1r~9kz7F}2SQ~J-L+2|XmOeYpIm@hxEbbKcWSv28Ys~yri;w{tL2H`91^Q> z>v1HTt}iTlK8tF_rn*z0QI@l1)D_`kfn64#NHMnlwbUOh*-p)BC@JsHEFNxud*hykwjO-0kEclG`UUajW$rbl)y{iZ4W5_Zm8hf% zCVNtYKS$%xjuq*NFH7N$T(t)ik-u-<5#-t09>!%GG&Mgz%u%iQ&cRb3L1bq0f!sSP zf=WsVwLM?c>~H3q$#S!iuTZTj>v>QeosTaFjc^)u%kdxQv4{rZsMZCYr;iQBXzG*2 zy)soz_-2WnYn+9GJFFxY+Yv;FovbNv=v|ammCe$h$epixvOSfp)X~|V#OtI&PfW;K zbPa1NZs;n;tvy*olXf!8^Z@=exfzQ|q{uuC&#O`grjLcJ?Dv$q34Ct}go1D?KsAVN4dPl#&tZ zTh*wHOe|21r2ChdDb_{zkaV?ozV^4*ASJi-No zIg5z4eDdqf0}D~zzY=wfw-C)6eqPv{d!+?zm5$PF=E=tn)1Hm!=S_X#GpJMNw75Cp zKp*40u0%Bgi!Pi}9#HO+kK_q97o)})>3PcJRUd%YDxbof)X-zZZ9n{honDg~x87?t znuw{<>im-xyuvJ;P9*mAziQX5c!R1S?HI)+jWQ#jdJoNtM)kq;0j05={>`{o<I;mNKikGN4@)_bG-qA`(l9806y_1e3t(AWM zPe$NZot|Vz=PMxZVNJ$gN|2tWMn9VRCY&geFJS1< zvtS`x!be@$DwEJs>Pu=6{DNPO24Y z`y|hZirJcW|3H3a+V79Bq}Sm7tywrAx5+ER|LGrHaq48p?FrO?igGTtzh})Y0bj`k z8#pE`>|4K*3MV;io+3-o<2o3heUBP1cPW#~7#iu)$m$&2kFdz7j!gZStE67~k?=~h zOch#3tXW|eXy+9YkeP$rhZSq_ZK@?8)K*7&{au-uV-$RjeB)JEImiBsbhE(d@dm>H zj`sp`-a3&@WikW|jjyZiwosPT9yqM@`FT8g9EG$!2(-RXWtT5dI@nZW3TZSp4(F)pW~%uo#%64Pa!RcmQ zf3xL79lZ)wq3s?DyccJNHa4MxVxhlx(}YVrTg3h(^Wrn875iWCkaI}~Z;YhLenlm; z5;Rz#JbM2oVE{j(UE;g;^-8Z608u(tJxDOZp`Up%T&0HnGamjpZ}()yQ9!y$9u7aM$)G^WPKE_Bz6$#@uJbKD}uZf|>P(@hz z6X)k(+ONNIXx2PxjQmr##$F{jwl9Lp!8_M}NiR#M9J0<9Zds(wEem^YRquKvmF2QW zNE>PsiRAa_P<&O6#O`Q=eW^2Cr~cVXYoYzA9@?X^;#ncsduDNn-DQdf`kH3Mq^Ny& zk5RP}<*EDnU*lzpMvh$~1TN5=D!v2RoS5bbE4(LW7I}yai#p?<0UsHj)H^oZf>HPla z?bUm;qe{HwuI`BK{9uM0@wl=RY47b9l=wnsE6F^9>+eBJ{Yktr6ZBY{(T6;?RxBVqX*aPuDk11Oh?=1t5j{MF0 zv(Fu+u5I?Mp=2ygTJk9ZBq5|cNO7s`T-}|D8LY6-U$MKZT$yr7C@tb4Z+}H(&41d1 zOdzWqSrqA<2>yxV?WgqU?}=eitXH+Nve(x76U%{%PA1UW)GVyb8=}Lrc<}|b+G$6? 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National Superconducting Cyclotron Laboratory, Michigan State University\n", "\n", - "Date: **Oct 31, 2019**\n", + "Date: **Nov 1, 2019**\n", "\n", "Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", @@ -1411,7 +1411,7 @@ "amount that the Gini index is decreased by splits over a given\n", "predictor, averaged over all $B$ trees.\n", "\n", - "## Simple example, head or tail" + "## Simple Voting Example, head or tail" ] }, { @@ -1440,7 +1440,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Bagging Example" + "## Using the Voting Classifier" ] }, { @@ -1496,6 +1496,178 @@ " print(clf.__class__.__name__, accuracy_score(y_test, y_pred))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Please, not the moons again! Voting and Bagging" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from sklearn.model_selection import train_test_split\n", + "from sklearn.datasets import make_moons\n", + "\n", + "X, y = make_moons(n_samples=500, noise=0.30, random_state=42)\n", + "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n", + "from sklearn.ensemble import RandomForestClassifier\n", + "from sklearn.ensemble import VotingClassifier\n", + "from sklearn.linear_model import LogisticRegression\n", + "from sklearn.svm import SVC\n", + "\n", + "log_clf = LogisticRegression(random_state=42)\n", + "rnd_clf = RandomForestClassifier(random_state=42)\n", + "svm_clf = SVC(random_state=42)\n", + "\n", + "voting_clf = VotingClassifier(\n", + " estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n", + " voting='hard')\n", + "voting_clf.fit(X_train, y_train)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from sklearn.metrics import accuracy_score\n", + "\n", + "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n", + " clf.fit(X_train, y_train)\n", + " y_pred = clf.predict(X_test)\n", + " print(clf.__class__.__name__, accuracy_score(y_test, y_pred))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "log_clf = LogisticRegression(random_state=42)\n", + "rnd_clf = RandomForestClassifier(random_state=42)\n", + "svm_clf = SVC(probability=True, random_state=42)\n", + "\n", + "voting_clf = VotingClassifier(\n", + " estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n", + " voting='soft')\n", + "voting_clf.fit(X_train, y_train)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from sklearn.metrics import accuracy_score\n", + "\n", + "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n", + " clf.fit(X_train, y_train)\n", + " y_pred = clf.predict(X_test)\n", + " print(clf.__class__.__name__, accuracy_score(y_test, y_pred))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Now Bagging" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from sklearn.ensemble import BaggingClassifier\n", + "from sklearn.tree import DecisionTreeClassifier\n", + "\n", + "bag_clf = BaggingClassifier(\n", + " DecisionTreeClassifier(random_state=42), n_estimators=500,\n", + " max_samples=100, bootstrap=True, n_jobs=-1, random_state=42)\n", + "bag_clf.fit(X_train, y_train)\n", + "y_pred = bag_clf.predict(X_test)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from sklearn.metrics import accuracy_score\n", + "print(accuracy_score(y_test, y_pred))" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "tree_clf = DecisionTreeClassifier(random_state=42)\n", + "tree_clf.fit(X_train, y_train)\n", + "y_pred_tree = tree_clf.predict(X_test)\n", + "print(accuracy_score(y_test, y_pred_tree))" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from matplotlib.colors import ListedColormap\n", + "\n", + "def plot_decision_boundary(clf, X, y, axes=[-1.5, 2.5, -1, 1.5], alpha=0.5, contour=True):\n", + " x1s = np.linspace(axes[0], axes[1], 100)\n", + " x2s = np.linspace(axes[2], axes[3], 100)\n", + " x1, x2 = np.meshgrid(x1s, x2s)\n", + " X_new = np.c_[x1.ravel(), x2.ravel()]\n", + " y_pred = clf.predict(X_new).reshape(x1.shape)\n", + " custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n", + " plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n", + " if contour:\n", + " custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n", + " plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n", + " plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", alpha=alpha)\n", + " plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", alpha=alpha)\n", + " plt.axis(axes)\n", + " plt.xlabel(r\"$x_1$\", fontsize=18)\n", + " plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n", + "plt.figure(figsize=(11,4))\n", + "plt.subplot(121)\n", + "plot_decision_boundary(tree_clf, X, y)\n", + "plt.title(\"Decision Tree\", fontsize=14)\n", + "plt.subplot(122)\n", + "plot_decision_boundary(bag_clf, X, y)\n", + "plt.title(\"Decision Trees with Bagging\", fontsize=14)\n", + "plt.show()" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1551,7 +1723,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 24, "metadata": { "collapsed": false }, @@ -1569,178 +1741,6 @@ "accuracy = cross_validate(Random_Forest_model,X,Y,cv=10)['test_score']" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Please, not the moons again!" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from sklearn.model_selection import train_test_split\n", - "from sklearn.datasets import make_moons\n", - "\n", - "X, y = make_moons(n_samples=500, noise=0.30, random_state=42)\n", - "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n", - "from sklearn.ensemble import RandomForestClassifier\n", - "from sklearn.ensemble import VotingClassifier\n", - "from sklearn.linear_model import LogisticRegression\n", - "from sklearn.svm import SVC\n", - "\n", - "log_clf = LogisticRegression(random_state=42)\n", - "rnd_clf = RandomForestClassifier(random_state=42)\n", - "svm_clf = SVC(random_state=42)\n", - "\n", - "voting_clf = VotingClassifier(\n", - " estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n", - " voting='hard')\n", - "voting_clf.fit(X_train, y_train)" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from sklearn.metrics import accuracy_score\n", - "\n", - "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n", - " clf.fit(X_train, y_train)\n", - " y_pred = clf.predict(X_test)\n", - " print(clf.__class__.__name__, accuracy_score(y_test, y_pred))" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "log_clf = LogisticRegression(random_state=42)\n", - "rnd_clf = RandomForestClassifier(random_state=42)\n", - "svm_clf = SVC(probability=True, random_state=42)\n", - "\n", - "voting_clf = VotingClassifier(\n", - " estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n", - " voting='soft')\n", - "voting_clf.fit(X_train, y_train)" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from sklearn.metrics import accuracy_score\n", - "\n", - "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n", - " clf.fit(X_train, y_train)\n", - " y_pred = clf.predict(X_test)\n", - " print(clf.__class__.__name__, accuracy_score(y_test, y_pred))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Bagging examples" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from sklearn.ensemble import BaggingClassifier\n", - "from sklearn.tree import DecisionTreeClassifier\n", - "\n", - "bag_clf = BaggingClassifier(\n", - " DecisionTreeClassifier(random_state=42), n_estimators=500,\n", - " max_samples=100, bootstrap=True, n_jobs=-1, random_state=42)\n", - "bag_clf.fit(X_train, y_train)\n", - "y_pred = bag_clf.predict(X_test)" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from sklearn.metrics import accuracy_score\n", - "print(accuracy_score(y_test, y_pred))" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "tree_clf = DecisionTreeClassifier(random_state=42)\n", - "tree_clf.fit(X_train, y_train)\n", - "y_pred_tree = tree_clf.predict(X_test)\n", - "print(accuracy_score(y_test, y_pred_tree))" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from matplotlib.colors import ListedColormap\n", - "\n", - "def plot_decision_boundary(clf, X, y, axes=[-1.5, 2.5, -1, 1.5], alpha=0.5, contour=True):\n", - " x1s = np.linspace(axes[0], axes[1], 100)\n", - " x2s = np.linspace(axes[2], axes[3], 100)\n", - " x1, x2 = np.meshgrid(x1s, x2s)\n", - " X_new = np.c_[x1.ravel(), x2.ravel()]\n", - " y_pred = clf.predict(X_new).reshape(x1.shape)\n", - " custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n", - " plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n", - " if contour:\n", - " custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n", - " plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n", - " plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", alpha=alpha)\n", - " plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", alpha=alpha)\n", - " plt.axis(axes)\n", - " plt.xlabel(r\"$x_1$\", fontsize=18)\n", - " plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n", - "plt.figure(figsize=(11,4))\n", - "plt.subplot(121)\n", - "plot_decision_boundary(tree_clf, X, y)\n", - "plt.title(\"Decision Tree\", fontsize=14)\n", - "plt.subplot(122)\n", - "plot_decision_boundary(bag_clf, X, y)\n", - "plt.title(\"Decision Trees with Bagging\", fontsize=14)\n", - "plt.show()" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -1777,6 +1777,194 @@ "y_pred_rf = rnd_clf.predict(X_test)\n", "np.sum(y_pred == y_pred_rf) / len(y_pred)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Feature Importance" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "try:\n", + " from sklearn.datasets import fetch_openml\n", + " mnist = fetch_openml('mnist_784', version=1)\n", + " mnist.target = mnist.target.astype(np.int64)\n", + "except ImportError:\n", + " from sklearn.datasets import fetch_mldata\n", + " mnist = fetch_mldata('MNIST original')\n", + "\n", + "rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)\n", + "rnd_clf.fit(mnist[\"data\"], mnist[\"target\"])\n", + "\n", + "def plot_digit(data):\n", + " image = data.reshape(28, 28)\n", + " plt.imshow(image, cmap = mpl.cm.hot,\n", + " interpolation=\"nearest\")\n", + " plt.axis(\"off\")\n", + "\n", + "plot_digit(rnd_clf.feature_importances_)\n", + "\n", + "cbar = plt.colorbar(ticks=[rnd_clf.feature_importances_.min(), rnd_clf.feature_importances_.max()])\n", + "cbar.ax.set_yticklabels(['Not important', 'Very important'])\n", + "\n", + "#save_fig(\"mnist_feature_importance_plot\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Boosting: AdaBoost" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from sklearn.ensemble import AdaBoostClassifier\n", + "\n", + "ada_clf = AdaBoostClassifier(\n", + " DecisionTreeClassifier(max_depth=1), n_estimators=200,\n", + " algorithm=\"SAMME.R\", learning_rate=0.5, random_state=42)\n", + "ada_clf.fit(X_train, y_train)\n", + "\n", + "plot_decision_boundary(ada_clf, X, y)\n", + "\n", + "m = len(X_train)\n", + "\n", + "plt.figure(figsize=(11, 4))\n", + "for subplot, learning_rate in ((121, 1), (122, 0.5)):\n", + " sample_weights = np.ones(m)\n", + " plt.subplot(subplot)\n", + " for i in range(5):\n", + " svm_clf = SVC(kernel=\"rbf\", C=0.05, gamma=\"auto\", random_state=42)\n", + " svm_clf.fit(X_train, y_train, sample_weight=sample_weights)\n", + " y_pred = svm_clf.predict(X_train)\n", + " sample_weights[y_pred != y_train] *= (1 + learning_rate)\n", + " plot_decision_boundary(svm_clf, X, y, alpha=0.2)\n", + " plt.title(\"learning_rate = {}\".format(learning_rate), fontsize=16)\n", + " if subplot == 121:\n", + " plt.text(-0.7, -0.65, \"1\", fontsize=14)\n", + " plt.text(-0.6, -0.10, \"2\", fontsize=14)\n", + " plt.text(-0.5, 0.10, \"3\", fontsize=14)\n", + " plt.text(-0.4, 0.55, \"4\", fontsize=14)\n", + " plt.text(-0.3, 0.90, \"5\", fontsize=14)\n", + "\n", + "save_fig(\"boosting_plot\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Gradient Boosting" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "np.random.seed(42)\n", + "X = np.random.rand(100, 1) - 0.5\n", + "y = 3*X[:, 0]**2 + 0.05 * np.random.randn(100)\n", + "\n", + "from sklearn.tree import DecisionTreeRegressor\n", + "\n", + "tree_reg1 = DecisionTreeRegressor(max_depth=2, random_state=42)\n", + "tree_reg1.fit(X, y)\n", + "\n", + "y2 = y - tree_reg1.predict(X)\n", + "tree_reg2 = DecisionTreeRegressor(max_depth=2, random_state=42)\n", + "tree_reg2.fit(X, y2)\n", + "\n", + "y3 = y2 - tree_reg2.predict(X)\n", + "tree_reg3 = DecisionTreeRegressor(max_depth=2, random_state=42)\n", + "tree_reg3.fit(X, y3)\n", + "\n", + "X_new = np.array([[0.8]])\n", + "y_pred = sum(tree.predict(X_new) for tree in (tree_reg1, tree_reg2, tree_reg3))\n", + "\n", + "def plot_predictions(regressors, X, y, axes, label=None, style=\"r-\", data_style=\"b.\", data_label=None):\n", + " x1 = np.linspace(axes[0], axes[1], 500)\n", + " y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n", + " plt.plot(X[:, 0], y, data_style, label=data_label)\n", + " plt.plot(x1, y_pred, style, linewidth=2, label=label)\n", + " if label or data_label:\n", + " plt.legend(loc=\"upper center\", fontsize=16)\n", + " plt.axis(axes)\n", + "\n", + "plt.figure(figsize=(11,11))\n", + "\n", + "plt.subplot(321)\n", + "plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h_1(x_1)$\", style=\"g-\", data_label=\"Training set\")\n", + "plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n", + "plt.title(\"Residuals and tree predictions\", fontsize=16)\n", + "\n", + "plt.subplot(322)\n", + "plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(x_1) = h_1(x_1)$\", data_label=\"Training set\")\n", + "plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n", + "plt.title(\"Ensemble predictions\", fontsize=16)\n", + "\n", + "plt.subplot(323)\n", + "plot_predictions([tree_reg2], X, y2, axes=[-0.5, 0.5, -0.5, 0.5], label=\"$h_2(x_1)$\", style=\"g-\", data_style=\"k+\", data_label=\"Residuals\")\n", + "plt.ylabel(\"$y - h_1(x_1)$\", fontsize=16)\n", + "\n", + "plt.subplot(324)\n", + "plot_predictions([tree_reg1, tree_reg2], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(x_1) = h_1(x_1) + h_2(x_1)$\")\n", + "plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n", + "\n", + "plt.subplot(325)\n", + "plot_predictions([tree_reg3], X, y3, axes=[-0.5, 0.5, -0.5, 0.5], label=\"$h_3(x_1)$\", style=\"g-\", data_style=\"k+\")\n", + "plt.ylabel(\"$y - h_1(x_1) - h_2(x_1)$\", fontsize=16)\n", + "plt.xlabel(\"$x_1$\", fontsize=16)\n", + "\n", + "plt.subplot(326)\n", + "plot_predictions([tree_reg1, tree_reg2, tree_reg3], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(x_1) = h_1(x_1) + h_2(x_1) + h_3(x_1)$\")\n", + "plt.xlabel(\"$x_1$\", fontsize=16)\n", + "plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n", + "\n", + "save_fig(\"gradient_boosting_plot\")\n", + "plt.show()\n", + "\n", + "from sklearn.ensemble import GradientBoostingRegressor\n", + "\n", + "gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=3, learning_rate=1.0, random_state=42)\n", + "gbrt.fit(X, y)\n", + "\n", + "gbrt_slow = GradientBoostingRegressor(max_depth=2, n_estimators=200, learning_rate=0.1, random_state=42)\n", + "gbrt_slow.fit(X, y)\n", + "\n", + "plt.figure(figsize=(11,4))\n", + "\n", + "plt.subplot(121)\n", + "plot_predictions([gbrt], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"Ensemble predictions\")\n", + "plt.title(\"learning_rate={}, n_estimators={}\".format(gbrt.learning_rate, gbrt.n_estimators), fontsize=14)\n", + "\n", + "plt.subplot(122)\n", + "plot_predictions([gbrt_slow], X, y, axes=[-0.5, 0.5, -0.1, 0.8])\n", + "plt.title(\"learning_rate={}, n_estimators={}\".format(gbrt_slow.learning_rate, gbrt_slow.n_estimators), fontsize=14)\n", + "\n", + "save_fig(\"gbrt_learning_rate_plot\")\n", + "plt.show()" + ] } ], "metadata": {}, diff --git a/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz b/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz index 52ccca5484fc59778e10a98ca4463ca983321dfd..63c74dc200b8f226f0815e93fab66efee4be6dfb 100644 GIT binary patch literal 194 zcmV;z06qU7iwFQE!@FGo1MSaE3WG2Z1z^{nVoo4Qjk+%AqKiT)ULe-7ray^IBGlVA zDzvM%D=CG1o5#RonAsQWd|O2JZiB@TLQ=+H%q&f&B&&IzP&d#xNz#l_#u6Yjj#Cx@ zS?;8l-dL{PDeVcRLHV}lYEAQD&-@BJ^G}qmFtFJTwp9|OvREl~h8z#V2qjC6Xd=-K wvVvNn85^MS)(efm^-K2|KNhnqN&6{`x1+^E~gn2SF>9T>uCG04QWvn*aa+ literal 194 zcmV;z06qU7iwFRb^SWIC1MSaC3c@fD2H>uHia9|^+9q8Kb>Tt~=><|dwegYEBn5kW z`v6_3t0F?a&CkHkFtcB;^6ffucNZ*%5W>?G#>_aIlEm{op~FBE#yHC;k0}tEB%B67 zmOJUCvrd@dl;(uWqI%mKYIXf#&-@BJ^G_6ww6NLruF(pVc35hCh8z#lO05cmXd~J7 ws)S0T9UEZq)=7gPR1c!6q#KIj61GMkjkww<{Pj+O3NK=Ti(n*o$!l){_-zNV~f2v)5 zv(aUqej4ijb?#uKnQr$62N=l)BwF`_am*{D)ze;e-n zd}B>IjeExbscpKs8wXz9-&mbaZ5znAk-z@PIJL98q+j>FCq&$9l?O^CQ*yi7(Z6rR zhwLh`!WOC^(Kp5jS(Nx%p=Hj8zmAh@iLFYffBOxK-R4U>%-F(>xS&W1VM|?k-AN@3 zMyAf&q{4=PUOpf1!&aA}B`4izEj^$(%~CYK(@QQk2S^(aN)=f=q=s zCnU;cveBZ-Y_Mf}s3*6F0LrEgf*GBTkNo|0N1L#3GvD&gzlQFa_S$Lgod5Iu#NX$B zyvkr9g{+EXQwiAQT$29_f4spCU{v~PcGEb(n^eUts`#Hyzts+&RrkF8f6wFLX5%Gl z#$kJG9K4kOxqEH;k*?umztj&vtl)698>iQsDo<}2@oU!*on7}-58+Z*yY{Nah@ES` z_tqC>x$;FN4ICLEqoJBovueJLbl)@RXp>4}M(b2%(gq(wAWLEMTm>H~gv<~N1->yB z&g0BcjNLLkQUE{GPdn99Gz{mb5MSMXW+G=?N|7mWpCzCSM$4i~5Z}U9@c#WdH4~^Y zSWhhjv$sYGn$O+bZh5m0$&;1>At?7uo5q`;)59gRRVgyfyt2D!$~#X;F@bHYT|NIk z3qHS+*HogEi1m}-0u_J6xlXrG3it~Iut9pE4PN=&3Ur_J@FfvEYqYl;=RjfG&dt;v z961}*$D5CB?T%9$Zg|;|pO)z^@-E*PtIz_Qo_9n8d6#3(DfYZD*xHY?3m&#kmr

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