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<a class="navbar-brand" href="DecisionTrees-bs.html">Data Analysis and Machine Learning: From Decision Trees to Forests and all that</a>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs001.html#___sec0" style="font-size: 80%;">Decision trees, overarching aims</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs002.html#___sec1" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs003.html#___sec2" style="font-size: 80%;">General Features</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs004.html#___sec3" style="font-size: 80%;">How do we set it up?</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs005.html#___sec4" style="font-size: 80%;">Decision trees and Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs006.html#___sec5" style="font-size: 80%;">Building a tree, regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs007.html#___sec6" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs008.html#___sec7" style="font-size: 80%;">Making a tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs009.html#___sec8" style="font-size: 80%;">Pruning the tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs010.html#___sec9" style="font-size: 80%;">Cost complexity pruning</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs011.html#___sec10" style="font-size: 80%;">Schematic Regression Procedure</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs012.html#___sec11" style="font-size: 80%;">A Classification Tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs013.html#___sec12" style="font-size: 80%;">Growing a classification tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs014.html#___sec13" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs015.html#___sec14" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs016.html#___sec15" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs017.html#___sec16" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs018.html#___sec17" style="font-size: 80%;">The CART algorithm for Classification</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs019.html#___sec18" style="font-size: 80%;">The CART algorithm for Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs020.html#___sec19" style="font-size: 80%;">Computing the Gini index</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs021.html#___sec20" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs022.html#___sec21" style="font-size: 80%;">Computing the Gini Factor</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs023.html#___sec22" style="font-size: 80%;">Entropy and the ID3 algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs024.html#___sec23" style="font-size: 80%;">Implementing the ID3 Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs025.html#___sec24" style="font-size: 80%;">Cancer Data again now with Decision Trees and other Methods</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs026.html#___sec25" style="font-size: 80%;">Another example, the moons again</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs027.html#___sec26" style="font-size: 80%;">Playing around with regions</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs028.html#___sec27" style="font-size: 80%;">Regression trees</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs029.html#___sec28" style="font-size: 80%;">Final regressor code</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs030.html#___sec29" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs031.html#___sec30" style="font-size: 80%;">Disadvantages</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs032.html#___sec31" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs033.html#___sec32" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs034.html#___sec33" style="font-size: 80%;">Bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs035.html#___sec34" style="font-size: 80%;">More bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs036.html#___sec35" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs037.html#___sec36" style="font-size: 80%;">Using the Voting Classifier</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs038.html#___sec37" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs039.html#___sec38" style="font-size: 80%;">Now Bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs040.html#___sec39" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs041.html#___sec40" style="font-size: 80%;">Random forests</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs042.html#___sec41" style="font-size: 80%;">Random Forest Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs043.html#___sec42" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs044.html#___sec43" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling, or iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Classification</a></li>
<!-- navigation toc: --> <li><a href="#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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<h2 id="___sec57" class="anchor">XGBoost: Extreme Gradient Boosting </h2>
<p>
<a href="https://github.com/dmlc/xgboost" target="_self">XGBoost</a> or Extreme Gradient
Boosting, is an optimized distributed gradient boosting library
designed to be highly efficient, flexible and portable. It implements
machine learning algorithms under the Gradient Boosting
framework. XGBoost provides a parallel tree boosting that solve many
data science problems in a fast and accurate way. See the <a href="https://arxiv.org/abs/1603.02754" target="_self">article by Chen and Guestrin</a>.
<p>
The authors design and build a highly scalable end-to-end tree
boosting system. It has a theoretically justified weighted quantile
sketch for efficient proposal calculation. It introduces a novel sparsity-aware algorithm for parallel tree learning and an effective cache-aware block structure for out-of-core tree learning.
<p>
It is now the algorithm which wins essentially all ML competitions!!!
<p>
<p>
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs001.html#___sec0" style="font-size: 80%;">Decision trees, overarching aims</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs002.html#___sec1" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs003.html#___sec2" style="font-size: 80%;">General Features</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs004.html#___sec3" style="font-size: 80%;">How do we set it up?</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs005.html#___sec4" style="font-size: 80%;">Decision trees and Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs006.html#___sec5" style="font-size: 80%;">Building a tree, regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs007.html#___sec6" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs008.html#___sec7" style="font-size: 80%;">Making a tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs009.html#___sec8" style="font-size: 80%;">Pruning the tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs010.html#___sec9" style="font-size: 80%;">Cost complexity pruning</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs011.html#___sec10" style="font-size: 80%;">Schematic Regression Procedure</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs012.html#___sec11" style="font-size: 80%;">A Classification Tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs013.html#___sec12" style="font-size: 80%;">Growing a classification tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs014.html#___sec13" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs015.html#___sec14" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs016.html#___sec15" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs017.html#___sec16" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs018.html#___sec17" style="font-size: 80%;">The CART algorithm for Classification</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs019.html#___sec18" style="font-size: 80%;">The CART algorithm for Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs020.html#___sec19" style="font-size: 80%;">Computing the Gini index</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs021.html#___sec20" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs022.html#___sec21" style="font-size: 80%;">Computing the Gini Factor</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs023.html#___sec22" style="font-size: 80%;">Entropy and the ID3 algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs024.html#___sec23" style="font-size: 80%;">Implementing the ID3 Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs025.html#___sec24" style="font-size: 80%;">Cancer Data again now with Decision Trees and other Methods</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs026.html#___sec25" style="font-size: 80%;">Another example, the moons again</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs027.html#___sec26" style="font-size: 80%;">Playing around with regions</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs028.html#___sec27" style="font-size: 80%;">Regression trees</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs029.html#___sec28" style="font-size: 80%;">Final regressor code</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs030.html#___sec29" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs031.html#___sec30" style="font-size: 80%;">Disadvantages</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs032.html#___sec31" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs033.html#___sec32" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs034.html#___sec33" style="font-size: 80%;">Bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs035.html#___sec34" style="font-size: 80%;">More bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs036.html#___sec35" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs037.html#___sec36" style="font-size: 80%;">Using the Voting Classifier</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs038.html#___sec37" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs039.html#___sec38" style="font-size: 80%;">Now Bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs040.html#___sec39" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs041.html#___sec40" style="font-size: 80%;">Random forests</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs042.html#___sec41" style="font-size: 80%;">Random Forest Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs043.html#___sec42" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs044.html#___sec43" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling, or iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Classification</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="#___sec58" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs060.html#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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<h2 id="___sec58" class="anchor">Regression Case </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">xgboost</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">xgb</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> StandardScaler
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.metrics</span> <span style="color: #008000; font-weight: bold">import</span> mean_squared_error
n <span style="color: #666666">=</span> <span style="color: #666666">100</span>
maxdegree <span style="color: #666666">=</span> <span style="color: #666666">6</span>
<span style="color: #408080; font-style: italic"># Make data set.</span>
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">-3</span>, <span style="color: #666666">3</span>, n)<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)
y <span style="color: #666666">=</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>x<span style="color: #666666">**2</span>) <span style="color: #666666">+</span> <span style="color: #666666">1.5</span> <span style="color: #666666">*</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>(x<span style="color: #666666">-2</span>)<span style="color: #666666">**2</span>)<span style="color: #666666">+</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>normal(<span style="color: #666666">0</span>, <span style="color: #666666">0.1</span>, x<span style="color: #666666">.</span>shape)
error <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
bias <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
variance <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
polydegree <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdegree)
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(x, y, test_size<span style="color: #666666">=0.2</span>)
scaler <span style="color: #666666">=</span> StandardScaler()
scaler<span style="color: #666666">.</span>fit(X_train)
X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_train)
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(maxdegree):
model <span style="color: #666666">=</span> xgb<span style="color: #666666">.</span>XGBRegressor(objective <span style="color: #666666">=</span><span style="color: #BA2121">&#39;reg:squarederror&#39;</span>, colsaobjective <span style="color: #666666">=</span><span style="color: #BA2121">&#39;reg:squarederror&#39;</span>, colsample_bytree <span style="color: #666666">=</span> <span style="color: #666666">0.3</span>, learning_rate <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>,max_depth <span style="color: #666666">=</span> degree, alpha <span style="color: #666666">=</span> <span style="color: #666666">10</span>, n_estimators <span style="color: #666666">=</span> <span style="color: #666666">200</span>)
model<span style="color: #666666">.</span>fit(X_train_scaled,y_train)
y_pred <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(X_test_scaled)
polydegree[degree] <span style="color: #666666">=</span> degree
error[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( np<span style="color: #666666">.</span>mean((y_test <span style="color: #666666">-</span> y_pred)<span style="color: #666666">**2</span>) )
bias[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( (y_test <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(y_pred))<span style="color: #666666">**2</span> )
variance[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( np<span style="color: #666666">.</span>var(y_pred) )
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Max depth:&#39;</span>, degree)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Error:&#39;</span>, error[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Bias^2:&#39;</span>, bias[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Var:&#39;</span>, variance[degree])
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;{} &gt;= {} + {} = {}&#39;</span><span style="color: #666666">.</span>format(error[degree], bias[degree], variance[degree], bias[degree]<span style="color: #666666">+</span>variance[degree]))
plt<span style="color: #666666">.</span>xlim(<span style="color: #666666">1</span>,maxdegree<span style="color: #666666">-1</span>)
plt<span style="color: #666666">.</span>plot(polydegree, error, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Error&#39;</span>)
plt<span style="color: #666666">.</span>plot(polydegree, bias, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;bias&#39;</span>)
plt<span style="color: #666666">.</span>plot(polydegree, variance, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Variance&#39;</span>)
plt<span style="color: #666666">.</span>legend()
plt<span style="color: #666666">.</span>show()
</pre></div>
<p>
<p>
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('Gradient Boosting, Examples of Classification',
2,
None,
'___sec56'),
('XGBoost: Extreme Gradient Boosting', 2, None, '___sec57'),
('Regression Case', 2, None, '___sec58'),
('Xgboost on the Cancer Data', 2, None, '___sec59')]}
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<!-- navigation toc: --> <li><a href="._DecisionTrees-bs001.html#___sec0" style="font-size: 80%;">Decision trees, overarching aims</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs002.html#___sec1" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs003.html#___sec2" style="font-size: 80%;">General Features</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs004.html#___sec3" style="font-size: 80%;">How do we set it up?</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs005.html#___sec4" style="font-size: 80%;">Decision trees and Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs006.html#___sec5" style="font-size: 80%;">Building a tree, regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs007.html#___sec6" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs008.html#___sec7" style="font-size: 80%;">Making a tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs009.html#___sec8" style="font-size: 80%;">Pruning the tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs010.html#___sec9" style="font-size: 80%;">Cost complexity pruning</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs011.html#___sec10" style="font-size: 80%;">Schematic Regression Procedure</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs012.html#___sec11" style="font-size: 80%;">A Classification Tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs013.html#___sec12" style="font-size: 80%;">Growing a classification tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs014.html#___sec13" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs015.html#___sec14" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs016.html#___sec15" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs017.html#___sec16" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs018.html#___sec17" style="font-size: 80%;">The CART algorithm for Classification</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs019.html#___sec18" style="font-size: 80%;">The CART algorithm for Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs020.html#___sec19" style="font-size: 80%;">Computing the Gini index</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs021.html#___sec20" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs022.html#___sec21" style="font-size: 80%;">Computing the Gini Factor</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs023.html#___sec22" style="font-size: 80%;">Entropy and the ID3 algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs024.html#___sec23" style="font-size: 80%;">Implementing the ID3 Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs025.html#___sec24" style="font-size: 80%;">Cancer Data again now with Decision Trees and other Methods</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs026.html#___sec25" style="font-size: 80%;">Another example, the moons again</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs027.html#___sec26" style="font-size: 80%;">Playing around with regions</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs028.html#___sec27" style="font-size: 80%;">Regression trees</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs029.html#___sec28" style="font-size: 80%;">Final regressor code</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs030.html#___sec29" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs031.html#___sec30" style="font-size: 80%;">Disadvantages</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs032.html#___sec31" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs033.html#___sec32" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs034.html#___sec33" style="font-size: 80%;">Bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs035.html#___sec34" style="font-size: 80%;">More bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs036.html#___sec35" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs037.html#___sec36" style="font-size: 80%;">Using the Voting Classifier</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs038.html#___sec37" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs039.html#___sec38" style="font-size: 80%;">Now Bagging</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs040.html#___sec39" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs041.html#___sec40" style="font-size: 80%;">Random forests</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs042.html#___sec41" style="font-size: 80%;">Random Forest Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs043.html#___sec42" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs044.html#___sec43" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs045.html#___sec44" style="font-size: 80%;">Boosting, a Bird'e Eye</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs046.html#___sec45" style="font-size: 80%;">What is boosting? Additive Modelling, or iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs047.html#___sec46" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs048.html#___sec47" style="font-size: 80%;">Iterative Fitting, Classification, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs049.html#___sec48" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs050.html#___sec49" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs051.html#___sec50" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs052.html#___sec51" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs053.html#___sec52" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs054.html#___sec53" style="font-size: 80%;">Gradient boosting: Basics</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs055.html#___sec54" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs056.html#___sec55" style="font-size: 80%;">Gradient Boosting, Examples of Regression</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs057.html#___sec56" style="font-size: 80%;">Gradient Boosting, Examples of Classification</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs058.html#___sec57" style="font-size: 80%;">XGBoost: Extreme Gradient Boosting</a></li>
<!-- navigation toc: --> <li><a href="._DecisionTrees-bs059.html#___sec58" style="font-size: 80%;">Regression Case</a></li>
<!-- navigation toc: --> <li><a href="#___sec59" style="font-size: 80%;">Xgboost on the Cancer Data</a></li>
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<h2 id="___sec59" class="anchor">Xgboost on the Cancer Data </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_breast_cancer
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> LabelEncoder
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> cross_validate
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">xgboost</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">xgb</span>
<span style="color: #408080; font-style: italic"># Load the data</span>
cancer <span style="color: #666666">=</span> load_breast_cancer()
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(cancer<span style="color: #666666">.</span>data,cancer<span style="color: #666666">.</span>target,random_state<span style="color: #666666">=0</span>)
<span style="color: #008000; font-weight: bold">print</span>(X_train<span style="color: #666666">.</span>shape)
<span style="color: #008000; font-weight: bold">print</span>(X_test<span style="color: #666666">.</span>shape)
<span style="color: #408080; font-style: italic">#now scale the data</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> StandardScaler
scaler <span style="color: #666666">=</span> StandardScaler()
scaler<span style="color: #666666">.</span>fit(X_train)
X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_train)
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
xg_clf <span style="color: #666666">=</span> xgb<span style="color: #666666">.</span>XGBClassifier()
xg_clf<span style="color: #666666">.</span>fit(X_train_scaled,y_train)
y_test <span style="color: #666666">=</span> xg_clf<span style="color: #666666">.</span>predict(X_test_scaled)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy with Random Forests and scaled data: {:.2f}&quot;</span><span style="color: #666666">.</span>format(xg_clf<span style="color: #666666">.</span>score(X_test_scaled,y_test)))
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
y_pred <span style="color: #666666">=</span> xg_clf<span style="color: #666666">.</span>predict(X_test_scaled)
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_confusion_matrix(y_test, y_pred, normalize<span style="color: #666666">=</span><span style="color: #008000">True</span>)
plt<span style="color: #666666">.</span>show()
y_probas <span style="color: #666666">=</span> xg_clf<span style="color: #666666">.</span>predict_proba(X_test_scaled)
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_roc(y_test, y_probas)
plt<span style="color: #666666">.</span>show()
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_cumulative_gain(y_test, y_probas)
plt<span style="color: #666666">.</span>show()
xgb<span style="color: #666666">.</span>plot_tree(xg_clf,num_trees<span style="color: #666666">=0</span>)
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">&#39;figure.figsize&#39;</span>] <span style="color: #666666">=</span> [<span style="color: #666666">50</span>, <span style="color: #666666">10</span>]
plt<span style="color: #666666">.</span>show()
xgb<span style="color: #666666">.</span>plot_importance(xg_clf)
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">&#39;figure.figsize&#39;</span>] <span style="color: #666666">=</span> [<span style="color: #666666">5</span>, <span style="color: #666666">5</span>]
plt<span style="color: #666666">.</span>show()
</pre></div>
<p>
<p>
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