Morten Hjorth-Jensen
1627 lines
159 KiB
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1627 lines
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Applied Data Analysis and Machine Learning
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About the course
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Teachers and Grading
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Review of Statistics with Resampling Techniques and Linear Algebra
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1. Elements of Probability Theory and Statistical Data Analysis
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2. Linear Algebra, Handling of Arrays and more Python Features
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From Regression to Support Vector Machines
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3. Linear Regression
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4. Ridge and Lasso Regression
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5. Resampling Methods
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6. Logistic Regression
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7. Optimization, the central part of any Machine Learning algortithm
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<a class="reference internal" href="chapter5.html">
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8. Support Vector Machines, overarching aims
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<p aria-level="2" class="caption" role="heading">
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Decision Trees, Ensemble Methods and Boosting
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9. Decision trees, overarching aims
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10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
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Dimensionality Reduction
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11. Basic ideas of the Principal Component Analysis (PCA)
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12. Clustering and Unsupervised Learning
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Deep Learning Methods
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13. Neural networks
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14. Building a Feed Forward Neural Network
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15. Solving Differential Equations with Deep Learning
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16. Convolutional Neural Networks
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17. Recurrent neural networks: Overarching view
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Weekly material, notes and exercises
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Exercises week 34
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Week 34: Introduction to the course, Logistics and Practicalities
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Exercises week 35
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Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
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Exercises week 36
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Week 36: Linear Rgeression and Statistical interpretations
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<a class="reference internal nav-link" href="#an-overview-of-ensemble-methods">
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10.1. An Overview of Ensemble Methods
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<a class="reference internal nav-link" href="#bagging">
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10.2. Bagging
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10.3. Bagging Examples
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10.3.1. Making your own Bootstrap: Changing the Level of the Decision Tree
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10.4. Random forests
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<a class="reference internal nav-link" href="#compare-bagging-on-trees-with-random-forests">
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10.4.1. Compare Bagging on Trees with Random Forests
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10.5. Boosting, a Bird’s Eye View
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<a class="reference internal nav-link" href="#iterative-fitting-regression-and-squared-error-cost-function">
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10.5.1. Iterative Fitting, Regression and Squared-error Cost Function
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<li class="toc-h3 nav-item toc-entry">
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<a class="reference internal nav-link" href="#iterative-fitting-classification-and-adaboost">
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10.5.2. Iterative Fitting, Classification and AdaBoost
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<a class="reference internal nav-link" href="#adaptive-boosting-adaboost-basic-algorithm">
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10.5.3. Adaptive boosting: AdaBoost, Basic Algorithm
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</ul>
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<a class="reference internal nav-link" href="#gradient-boosting-basics-with-steepest-descent-functional-gradient-descent">
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10.6. Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent
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<a class="reference internal nav-link" href="#gradient-boosting-examples-of-regression">
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10.7. Gradient Boosting, Examples of Regression
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10.8. Gradient Boosting, Classification Example
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<a class="reference internal nav-link" href="#xgboost-extreme-gradient-boosting">
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10.9. XGBoost: Extreme Gradient Boosting
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10.10. Regression Case
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<h1>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</h1>
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<h2> Contents </h2>
|
||
</div>
|
||
<nav aria-label="Page">
|
||
<ul class="visible nav section-nav flex-column">
|
||
<li class="toc-h2 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#an-overview-of-ensemble-methods">
|
||
10.1. An Overview of Ensemble Methods
|
||
</a>
|
||
</li>
|
||
<li class="toc-h2 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#bagging">
|
||
10.2. Bagging
|
||
</a>
|
||
</li>
|
||
<li class="toc-h2 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#bagging-examples">
|
||
10.3. Bagging Examples
|
||
</a>
|
||
<ul class="nav section-nav flex-column">
|
||
<li class="toc-h3 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#making-your-own-bootstrap-changing-the-level-of-the-decision-tree">
|
||
10.3.1. Making your own Bootstrap: Changing the Level of the Decision Tree
|
||
</a>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="toc-h2 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#random-forests">
|
||
10.4. Random forests
|
||
</a>
|
||
<ul class="nav section-nav flex-column">
|
||
<li class="toc-h3 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#compare-bagging-on-trees-with-random-forests">
|
||
10.4.1. Compare Bagging on Trees with Random Forests
|
||
</a>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="toc-h2 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#boosting-a-bird-s-eye-view">
|
||
10.5. Boosting, a Bird’s Eye View
|
||
</a>
|
||
<ul class="nav section-nav flex-column">
|
||
<li class="toc-h3 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#iterative-fitting-regression-and-squared-error-cost-function">
|
||
10.5.1. Iterative Fitting, Regression and Squared-error Cost Function
|
||
</a>
|
||
</li>
|
||
<li class="toc-h3 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#iterative-fitting-classification-and-adaboost">
|
||
10.5.2. Iterative Fitting, Classification and AdaBoost
|
||
</a>
|
||
</li>
|
||
<li class="toc-h3 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#adaptive-boosting-adaboost-basic-algorithm">
|
||
10.5.3. Adaptive boosting: AdaBoost, Basic Algorithm
|
||
</a>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="toc-h2 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#gradient-boosting-basics-with-steepest-descent-functional-gradient-descent">
|
||
10.6. Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent
|
||
</a>
|
||
</li>
|
||
<li class="toc-h2 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#gradient-boosting-examples-of-regression">
|
||
10.7. Gradient Boosting, Examples of Regression
|
||
</a>
|
||
</li>
|
||
<li class="toc-h2 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#gradient-boosting-classification-example">
|
||
10.8. Gradient Boosting, Classification Example
|
||
</a>
|
||
</li>
|
||
<li class="toc-h2 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#xgboost-extreme-gradient-boosting">
|
||
10.9. XGBoost: Extreme Gradient Boosting
|
||
</a>
|
||
</li>
|
||
<li class="toc-h2 nav-item toc-entry">
|
||
<a class="reference internal nav-link" href="#regression-case">
|
||
10.10. Regression Case
|
||
</a>
|
||
</li>
|
||
</ul>
|
||
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
<div>
|
||
|
||
<div class="tex2jax_ignore mathjax_ignore section" id="ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods">
|
||
<h1><span class="section-number">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods<a class="headerlink" href="#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" title="Permalink to this headline">¶</a></h1>
|
||
<p>As stated previously and seen in many of the examples discussed in the previous chapter about
|
||
a single decision tree, we often end up overfitting our training
|
||
data. This normally means that we have a high variance. Can we reduce
|
||
the variance of a statistical learning method?</p>
|
||
<p>This leads us to a set of different methods that can combine different
|
||
machine learning algorithms or just use one of them to construct
|
||
forests and jungles of trees, homogeneous ones or heterogenous
|
||
ones. These methods are recognized by different names which we will
|
||
try to explain here. These are</p>
|
||
<ol class="simple">
|
||
<li><p>Voting classifiers</p></li>
|
||
<li><p>Bagging and Pasting</p></li>
|
||
<li><p>Random forests</p></li>
|
||
<li><p>Boosting methods, from adaptive to Extreme Gradient Boosting (XGBoost)</p></li>
|
||
</ol>
|
||
<p>We discuss these methods here.</p>
|
||
<div class="section" id="an-overview-of-ensemble-methods">
|
||
<h2><span class="section-number">10.1. </span>An Overview of Ensemble Methods<a class="headerlink" href="#an-overview-of-ensemble-methods" title="Permalink to this headline">¶</a></h2>
|
||
<!-- FIGURE: [DataFiles/ensembleoverview.png, width=600 frac=0.8] -->
|
||
</div>
|
||
<div class="section" id="bagging">
|
||
<h2><span class="section-number">10.2. </span>Bagging<a class="headerlink" href="#bagging" title="Permalink to this headline">¶</a></h2>
|
||
<p>The <strong>plain</strong> decision trees suffer from high
|
||
variance. This means that if we split the training data into two parts
|
||
at random, and fit a decision tree to both halves, the results that we
|
||
get could be quite different. In contrast, a procedure with low
|
||
variance will yield similar results if applied repeatedly to distinct
|
||
data sets; linear regression tends to have low variance, if the ratio
|
||
of <span class="math notranslate nohighlight">\(n\)</span> to <span class="math notranslate nohighlight">\(p\)</span> is moderately large.</p>
|
||
<p><strong>Bootstrap aggregation</strong>, or just <strong>bagging</strong>, is a
|
||
general-purpose procedure for reducing the variance of a statistical
|
||
learning method.</p>
|
||
<p>Bagging typically results in improved accuracy
|
||
over prediction using a single tree. Unfortunately, however, it can be
|
||
difficult to interpret the resulting model. Recall that one of the
|
||
advantages of decision trees is the attractive and easily interpreted
|
||
diagram that results.</p>
|
||
<p>However, when we bag a large number of trees, it is no longer
|
||
possible to represent the resulting statistical learning procedure
|
||
using a single tree, and it is no longer clear which variables are
|
||
most important to the procedure. Thus, bagging improves prediction
|
||
accuracy at the expense of interpretability. Although the collection
|
||
of bagged trees is much more difficult to interpret than a single
|
||
tree, one can obtain an overall summary of the importance of each
|
||
predictor using the MSE (for bagging regression trees) or the Gini
|
||
index (for bagging classification trees). In the case of bagging
|
||
regression trees, we can record the total amount that the MSE is
|
||
decreased due to splits over a given predictor, averaged over all <span class="math notranslate nohighlight">\(B\)</span> possible
|
||
trees. A large value indicates an important predictor. Similarly, in
|
||
the context of bagging classification trees, we can add up the total
|
||
amount that the Gini index is decreased by splits over a given
|
||
predictor, averaged over all <span class="math notranslate nohighlight">\(B\)</span> trees.</p>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">heads_proba</span> <span class="o">=</span> <span class="mf">0.51</span>
|
||
<span class="n">coin_tosses</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10000</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span> <span class="o"><</span> <span class="n">heads_proba</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span>
|
||
<span class="n">cumulative_heads_ratio</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">coin_tosses</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10001</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span><span class="mf">3.5</span><span class="p">))</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">cumulative_heads_ratio</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10000</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.51</span><span class="p">,</span> <span class="mf">0.51</span><span class="p">],</span> <span class="s2">"k--"</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"51%"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10000</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">],</span> <span class="s2">"k-"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"50%"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"Number of coin tosses"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"Heads ratio"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">"lower right"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10000</span><span class="p">,</span> <span class="mf">0.42</span><span class="p">,</span> <span class="mf">0.58</span><span class="p">])</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"votingsimple"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
<div class="cell_output docutils container">
|
||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
|
||
<span class="ne">NameError</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
|
||
<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">2</span>
|
||
<span class="g g-Whitespace"> </span><span class="mi">1</span> <span class="n">heads_proba</span> <span class="o">=</span> <span class="mf">0.51</span>
|
||
<span class="ne">----> </span><span class="mi">2</span> <span class="n">coin_tosses</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10000</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span> <span class="o"><</span> <span class="n">heads_proba</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span>
|
||
<span class="g g-Whitespace"> </span><span class="mi">3</span> <span class="n">cumulative_heads_ratio</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">coin_tosses</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10001</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
<span class="g g-Whitespace"> </span><span class="mi">4</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span><span class="mf">3.5</span><span class="p">))</span>
|
||
|
||
<span class="ne">NameError</span>: name 'np' is not defined
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_moons</span>
|
||
|
||
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">make_moons</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">500</span><span class="p">,</span> <span class="n">noise</span><span class="o">=</span><span class="mf">0.30</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
|
||
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">RandomForestClassifier</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">VotingClassifier</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <span class="n">SVC</span>
|
||
|
||
<span class="n">log_clf</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">solver</span><span class="o">=</span><span class="s2">"liblinear"</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">rnd_clf</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">svm_clf</span> <span class="o">=</span> <span class="n">SVC</span><span class="p">(</span><span class="n">gamma</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
|
||
<span class="n">voting_clf</span> <span class="o">=</span> <span class="n">VotingClassifier</span><span class="p">(</span>
|
||
<span class="n">estimators</span><span class="o">=</span><span class="p">[(</span><span class="s1">'lr'</span><span class="p">,</span> <span class="n">log_clf</span><span class="p">),</span> <span class="p">(</span><span class="s1">'rf'</span><span class="p">,</span> <span class="n">rnd_clf</span><span class="p">),</span> <span class="p">(</span><span class="s1">'svc'</span><span class="p">,</span> <span class="n">svm_clf</span><span class="p">)],</span>
|
||
<span class="n">voting</span><span class="o">=</span><span class="s1">'hard'</span><span class="p">)</span>
|
||
|
||
<span class="n">voting_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
|
||
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">accuracy_score</span>
|
||
|
||
<span class="k">for</span> <span class="n">clf</span> <span class="ow">in</span> <span class="p">(</span><span class="n">log_clf</span><span class="p">,</span> <span class="n">rnd_clf</span><span class="p">,</span> <span class="n">svm_clf</span><span class="p">,</span> <span class="n">voting_clf</span><span class="p">):</span>
|
||
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="vm">__name__</span><span class="p">,</span> <span class="n">accuracy_score</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">))</span>
|
||
|
||
<span class="n">log_clf</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">solver</span><span class="o">=</span><span class="s2">"liblinear"</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">rnd_clf</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">svm_clf</span> <span class="o">=</span> <span class="n">SVC</span><span class="p">(</span><span class="n">gamma</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">,</span> <span class="n">probability</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
|
||
<span class="n">voting_clf</span> <span class="o">=</span> <span class="n">VotingClassifier</span><span class="p">(</span>
|
||
<span class="n">estimators</span><span class="o">=</span><span class="p">[(</span><span class="s1">'lr'</span><span class="p">,</span> <span class="n">log_clf</span><span class="p">),</span> <span class="p">(</span><span class="s1">'rf'</span><span class="p">,</span> <span class="n">rnd_clf</span><span class="p">),</span> <span class="p">(</span><span class="s1">'svc'</span><span class="p">,</span> <span class="n">svm_clf</span><span class="p">)],</span>
|
||
<span class="n">voting</span><span class="o">=</span><span class="s1">'soft'</span><span class="p">)</span>
|
||
<span class="n">voting_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
|
||
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">accuracy_score</span>
|
||
|
||
<span class="k">for</span> <span class="n">clf</span> <span class="ow">in</span> <span class="p">(</span><span class="n">log_clf</span><span class="p">,</span> <span class="n">rnd_clf</span><span class="p">,</span> <span class="n">svm_clf</span><span class="p">,</span> <span class="n">voting_clf</span><span class="p">):</span>
|
||
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="vm">__name__</span><span class="p">,</span> <span class="n">accuracy_score</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">))</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_moons</span>
|
||
|
||
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">make_moons</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">500</span><span class="p">,</span> <span class="n">noise</span><span class="o">=</span><span class="mf">0.30</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">RandomForestClassifier</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">VotingClassifier</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <span class="n">SVC</span>
|
||
|
||
<span class="n">log_clf</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">rnd_clf</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">svm_clf</span> <span class="o">=</span> <span class="n">SVC</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
|
||
<span class="n">voting_clf</span> <span class="o">=</span> <span class="n">VotingClassifier</span><span class="p">(</span>
|
||
<span class="n">estimators</span><span class="o">=</span><span class="p">[(</span><span class="s1">'lr'</span><span class="p">,</span> <span class="n">log_clf</span><span class="p">),</span> <span class="p">(</span><span class="s1">'rf'</span><span class="p">,</span> <span class="n">rnd_clf</span><span class="p">),</span> <span class="p">(</span><span class="s1">'svc'</span><span class="p">,</span> <span class="n">svm_clf</span><span class="p">)],</span>
|
||
<span class="n">voting</span><span class="o">=</span><span class="s1">'hard'</span><span class="p">)</span>
|
||
<span class="n">voting_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">accuracy_score</span>
|
||
|
||
<span class="k">for</span> <span class="n">clf</span> <span class="ow">in</span> <span class="p">(</span><span class="n">log_clf</span><span class="p">,</span> <span class="n">rnd_clf</span><span class="p">,</span> <span class="n">svm_clf</span><span class="p">,</span> <span class="n">voting_clf</span><span class="p">):</span>
|
||
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="vm">__name__</span><span class="p">,</span> <span class="n">accuracy_score</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">))</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">log_clf</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">rnd_clf</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">svm_clf</span> <span class="o">=</span> <span class="n">SVC</span><span class="p">(</span><span class="n">probability</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
|
||
<span class="n">voting_clf</span> <span class="o">=</span> <span class="n">VotingClassifier</span><span class="p">(</span>
|
||
<span class="n">estimators</span><span class="o">=</span><span class="p">[(</span><span class="s1">'lr'</span><span class="p">,</span> <span class="n">log_clf</span><span class="p">),</span> <span class="p">(</span><span class="s1">'rf'</span><span class="p">,</span> <span class="n">rnd_clf</span><span class="p">),</span> <span class="p">(</span><span class="s1">'svc'</span><span class="p">,</span> <span class="n">svm_clf</span><span class="p">)],</span>
|
||
<span class="n">voting</span><span class="o">=</span><span class="s1">'soft'</span><span class="p">)</span>
|
||
<span class="n">voting_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">accuracy_score</span>
|
||
|
||
<span class="k">for</span> <span class="n">clf</span> <span class="ow">in</span> <span class="p">(</span><span class="n">log_clf</span><span class="p">,</span> <span class="n">rnd_clf</span><span class="p">,</span> <span class="n">svm_clf</span><span class="p">,</span> <span class="n">voting_clf</span><span class="p">):</span>
|
||
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="vm">__name__</span><span class="p">,</span> <span class="n">accuracy_score</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">))</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="section" id="bagging-examples">
|
||
<h2><span class="section-number">10.3. </span>Bagging Examples<a class="headerlink" href="#bagging-examples" title="Permalink to this headline">¶</a></h2>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">BaggingClassifier</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.tree</span> <span class="kn">import</span> <span class="n">DecisionTreeClassifier</span>
|
||
|
||
<span class="n">bag_clf</span> <span class="o">=</span> <span class="n">BaggingClassifier</span><span class="p">(</span>
|
||
<span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">),</span> <span class="n">n_estimators</span><span class="o">=</span><span class="mi">500</span><span class="p">,</span>
|
||
<span class="n">max_samples</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">bootstrap</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">bag_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">bag_clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">accuracy_score</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">accuracy_score</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">))</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">tree_clf</span> <span class="o">=</span> <span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">tree_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">y_pred_tree</span> <span class="o">=</span> <span class="n">tree_clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">accuracy_score</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred_tree</span><span class="p">))</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> inline
|
||
|
||
<span class="kn">from</span> <span class="nn">matplotlib.colors</span> <span class="kn">import</span> <span class="n">ListedColormap</span>
|
||
|
||
<span class="k">def</span> <span class="nf">plot_decision_boundary</span><span class="p">(</span><span class="n">clf</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">axes</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mf">1.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">contour</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
|
||
<span class="n">x1s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="mi">100</span><span class="p">)</span>
|
||
<span class="n">x2s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">axes</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="mi">100</span><span class="p">)</span>
|
||
<span class="n">x1</span><span class="p">,</span> <span class="n">x2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">x1s</span><span class="p">,</span> <span class="n">x2s</span><span class="p">)</span>
|
||
<span class="n">X_new</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">x1</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">x2</span><span class="o">.</span><span class="n">ravel</span><span class="p">()]</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_new</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x1</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
|
||
<span class="n">custom_cmap</span> <span class="o">=</span> <span class="n">ListedColormap</span><span class="p">([</span><span class="s1">'#fafab0'</span><span class="p">,</span><span class="s1">'#9898ff'</span><span class="p">,</span><span class="s1">'#a0faa0'</span><span class="p">])</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">contourf</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">custom_cmap</span><span class="p">)</span>
|
||
<span class="k">if</span> <span class="n">contour</span><span class="p">:</span>
|
||
<span class="n">custom_cmap2</span> <span class="o">=</span> <span class="n">ListedColormap</span><span class="p">([</span><span class="s1">'#7d7d58'</span><span class="p">,</span><span class="s1">'#4c4c7f'</span><span class="p">,</span><span class="s1">'#507d50'</span><span class="p">])</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">custom_cmap2</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">][</span><span class="n">y</span><span class="o">==</span><span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">][</span><span class="n">y</span><span class="o">==</span><span class="mi">0</span><span class="p">],</span> <span class="s2">"yo"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="n">alpha</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">][</span><span class="n">y</span><span class="o">==</span><span class="mi">1</span><span class="p">],</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">][</span><span class="n">y</span><span class="o">==</span><span class="mi">1</span><span class="p">],</span> <span class="s2">"bs"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="n">alpha</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="n">axes</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$x_1$"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">18</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$x_2$"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">18</span><span class="p">,</span> <span class="n">rotation</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">11</span><span class="p">,</span><span class="mi">4</span><span class="p">))</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
|
||
<span class="n">plot_decision_boundary</span><span class="p">(</span><span class="n">tree_clf</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Decision Tree"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">14</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
|
||
<span class="n">plot_decision_boundary</span><span class="p">(</span><span class="n">bag_clf</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Decision Trees with Bagging"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">14</span><span class="p">)</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"baggingtree"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="section" id="making-your-own-bootstrap-changing-the-level-of-the-decision-tree">
|
||
<h3><span class="section-number">10.3.1. </span>Making your own Bootstrap: Changing the Level of the Decision Tree<a class="headerlink" href="#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" title="Permalink to this headline">¶</a></h3>
|
||
<p>Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with
|
||
a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points <span class="math notranslate nohighlight">\(n\)</span>).</p>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.pipeline</span> <span class="kn">import</span> <span class="n">make_pipeline</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <span class="n">resample</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.tree</span> <span class="kn">import</span> <span class="n">DecisionTreeRegressor</span>
|
||
|
||
<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
|
||
<span class="n">n_boostraps</span> <span class="o">=</span> <span class="mi">100</span>
|
||
<span class="n">maxdepth</span> <span class="o">=</span> <span class="mi">8</span>
|
||
|
||
<span class="c1"># Make data set.</span>
|
||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
<span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="mf">1.5</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
|
||
<span class="n">error</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdepth</span><span class="p">)</span>
|
||
<span class="n">bias</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdepth</span><span class="p">)</span>
|
||
<span class="n">variance</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdepth</span><span class="p">)</span>
|
||
<span class="n">polydegree</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdepth</span><span class="p">)</span>
|
||
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
|
||
|
||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">StandardScaler</span>
|
||
<span class="n">scaler</span> <span class="o">=</span> <span class="n">StandardScaler</span><span class="p">()</span>
|
||
<span class="n">scaler</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_train_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_test_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
|
||
<span class="c1"># we produce a simple tree first as benchmark</span>
|
||
<span class="n">simpletree</span> <span class="o">=</span> <span class="n">DecisionTreeRegressor</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
|
||
<span class="n">simpletree</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">simpleprediction</span> <span class="o">=</span> <span class="n">simpletree</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
<span class="k">for</span> <span class="n">degree</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">maxdepth</span><span class="p">):</span>
|
||
<span class="n">model</span> <span class="o">=</span> <span class="n">DecisionTreeRegressor</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="n">degree</span><span class="p">)</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">y_test</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">n_boostraps</span><span class="p">))</span>
|
||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_boostraps</span><span class="p">):</span>
|
||
<span class="n">x_</span><span class="p">,</span> <span class="n">y_</span> <span class="o">=</span> <span class="n">resample</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">x_</span><span class="p">,</span> <span class="n">y_</span><span class="p">)</span>
|
||
<span class="n">y_pred</span><span class="p">[:,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span><span class="c1">#.ravel()</span>
|
||
|
||
<span class="n">polydegree</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">degree</span>
|
||
<span class="n">error</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">((</span><span class="n">y_test</span> <span class="o">-</span> <span class="n">y_pred</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> <span class="p">)</span>
|
||
<span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span> <span class="p">(</span><span class="n">y_test</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">y_pred</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span> <span class="p">)</span>
|
||
<span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">var</span><span class="p">(</span><span class="n">y_pred</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> <span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Polynomial degree:'</span><span class="p">,</span> <span class="n">degree</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Error:'</span><span class="p">,</span> <span class="n">error</span><span class="p">[</span><span class="n">degree</span><span class="p">])</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Bias^2:'</span><span class="p">,</span> <span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">])</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Var:'</span><span class="p">,</span> <span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">])</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="si">{}</span><span class="s1"> >= </span><span class="si">{}</span><span class="s1"> + </span><span class="si">{}</span><span class="s1"> = </span><span class="si">{}</span><span class="s1">'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">error</span><span class="p">[</span><span class="n">degree</span><span class="p">],</span> <span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">],</span> <span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">],</span> <span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span><span class="o">+</span><span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">]))</span>
|
||
|
||
<span class="n">mse_simpletree</span><span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">((</span><span class="n">y_test</span> <span class="o">-</span> <span class="n">simpleprediction</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">mse_simpletree</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">maxdepth</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">polydegree</span><span class="p">,</span> <span class="n">error</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'MSE'</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">polydegree</span><span class="p">,</span> <span class="n">bias</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'bias'</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">polydegree</span><span class="p">,</span> <span class="n">variance</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Variance'</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"baggingboot"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="section" id="random-forests">
|
||
<h2><span class="section-number">10.4. </span>Random forests<a class="headerlink" href="#random-forests" title="Permalink to this headline">¶</a></h2>
|
||
<p>Random forests provide an improvement over bagged trees by way of a
|
||
small tweak that decorrelates the trees.</p>
|
||
<p>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 <span class="math notranslate nohighlight">\(m\)</span> predictors is chosen as split
|
||
candidates from the full set of <span class="math notranslate nohighlight">\(p\)</span> predictors. The split is allowed to
|
||
use only one of those <span class="math notranslate nohighlight">\(m\)</span> predictors.</p>
|
||
<p>A fresh sample of <span class="math notranslate nohighlight">\(m\)</span> predictors is
|
||
taken at each split, and typically we choose</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
m\approx \sqrt{p}.
|
||
\]</div>
|
||
<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.</p>
|
||
<p>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 quantities. In particular, this means that bagging will
|
||
not lead to a substantial reduction in variance over a single tree in
|
||
this setting.</p>
|
||
<p>The algorithm described here can be applied to both classification and regression problems.</p>
|
||
<p>We will grow of forest of say <span class="math notranslate nohighlight">\(B\)</span> trees.</p>
|
||
<ol class="simple">
|
||
<li><p>For <span class="math notranslate nohighlight">\(b=1:B\)</span></p></li>
|
||
</ol>
|
||
<ul class="simple">
|
||
<li><p>Draw a bootstrap sample from the training data organized in our <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> matrix.</p></li>
|
||
<li><p>We grow then a random forest tree <span class="math notranslate nohighlight">\(T_b\)</span> based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached</p></li>
|
||
</ul>
|
||
<ol class="simple">
|
||
<li><p>we select <span class="math notranslate nohighlight">\(m \le p\)</span> variables at random from the <span class="math notranslate nohighlight">\(p\)</span> predictors/features</p></li>
|
||
<li><p>pick the best split point among the <span class="math notranslate nohighlight">\(m\)</span> features using for example the CART algorithm and create a new node</p></li>
|
||
<li><p>split the node into daughter nodes</p></li>
|
||
<li><p>Output then the ensemble of trees <span class="math notranslate nohighlight">\(\{T_b\}_1^{B}\)</span> and make predictions for either a regression type of problem or a classification type of problem.</p></li>
|
||
</ol>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_breast_cancer</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <span class="n">SVC</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.tree</span> <span class="kn">import</span> <span class="n">DecisionTreeClassifier</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">BaggingClassifier</span>
|
||
|
||
<span class="c1"># Load the data</span>
|
||
<span class="n">cancer</span> <span class="o">=</span> <span class="n">load_breast_cancer</span><span class="p">()</span>
|
||
|
||
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">cancer</span><span class="o">.</span><span class="n">data</span><span class="p">,</span><span class="n">cancer</span><span class="o">.</span><span class="n">target</span><span class="p">,</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">X_train</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">X_test</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
|
||
<span class="c1"># Logistic Regression</span>
|
||
<span class="n">logreg</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">solver</span><span class="o">=</span><span class="s1">'lbfgs'</span><span class="p">)</span>
|
||
<span class="n">logreg</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"Test set accuracy with Logistic Regression: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">logreg</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
|
||
<span class="c1"># Support vector machine</span>
|
||
<span class="n">svm</span> <span class="o">=</span> <span class="n">SVC</span><span class="p">(</span><span class="n">gamma</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="mi">100</span><span class="p">)</span>
|
||
<span class="n">svm</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"Test set accuracy with SVM: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">svm</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
|
||
<span class="c1"># Decision Trees</span>
|
||
<span class="n">deep_tree_clf</span> <span class="o">=</span> <span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span>
|
||
<span class="n">deep_tree_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"Test set accuracy with Decision Trees: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">deep_tree_clf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
|
||
<span class="c1">#now scale the data</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">StandardScaler</span>
|
||
<span class="n">scaler</span> <span class="o">=</span> <span class="n">StandardScaler</span><span class="p">()</span>
|
||
<span class="n">scaler</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_train_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_test_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
<span class="c1"># Logistic Regression</span>
|
||
<span class="n">logreg</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"Test set accuracy Logistic Regression with scaled data: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">logreg</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
|
||
<span class="c1"># Support Vector Machine</span>
|
||
<span class="n">svm</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"Test set accuracy SVM with scaled data: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">logreg</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
|
||
<span class="c1"># Decision Trees</span>
|
||
<span class="n">deep_tree_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"Test set accuracy with Decision Trees and scaled data: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">deep_tree_clf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
|
||
|
||
|
||
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">RandomForestClassifier</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">LabelEncoder</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">cross_validate</span>
|
||
<span class="c1"># Data set not specificied</span>
|
||
<span class="c1">#Instantiate the model with 500 trees and entropy as splitting criteria</span>
|
||
<span class="n">Random_Forest_model</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">500</span><span class="p">,</span><span class="n">criterion</span><span class="o">=</span><span class="s2">"entropy"</span><span class="p">)</span>
|
||
<span class="n">Random_Forest_model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="c1">#Cross validation</span>
|
||
<span class="n">accuracy</span> <span class="o">=</span> <span class="n">cross_validate</span><span class="p">(</span><span class="n">Random_Forest_model</span><span class="p">,</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">,</span><span class="n">cv</span><span class="o">=</span><span class="mi">10</span><span class="p">)[</span><span class="s1">'test_score'</span><span class="p">]</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">accuracy</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"Test set accuracy with Random Forests and scaled data: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">Random_Forest_model</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
|
||
|
||
|
||
<span class="kn">import</span> <span class="nn">scikitplot</span> <span class="k">as</span> <span class="nn">skplt</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">Random_Forest_model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_confusion_matrix</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">normalize</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
<span class="n">y_probas</span> <span class="o">=</span> <span class="n">Random_Forest_model</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_roc</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_cumulative_gain</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>Recall that the cumulative gains curve shows the percentage of the
|
||
overall number of cases in a given category <em>gained</em> by targeting a
|
||
percentage of the total number of cases.</p>
|
||
<p>Similarly, the receiver operating characteristic curve, or ROC curve,
|
||
displays the diagnostic ability of a binary classifier system as its
|
||
discrimination threshold is varied. It plots the true positive rate against the false positive rate.</p>
|
||
<div class="section" id="compare-bagging-on-trees-with-random-forests">
|
||
<h3><span class="section-number">10.4.1. </span>Compare Bagging on Trees with Random Forests<a class="headerlink" href="#compare-bagging-on-trees-with-random-forests" title="Permalink to this headline">¶</a></h3>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">bag_clf</span> <span class="o">=</span> <span class="n">BaggingClassifier</span><span class="p">(</span>
|
||
<span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">splitter</span><span class="o">=</span><span class="s2">"random"</span><span class="p">,</span> <span class="n">max_leaf_nodes</span><span class="o">=</span><span class="mi">16</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">),</span>
|
||
<span class="n">n_estimators</span><span class="o">=</span><span class="mi">500</span><span class="p">,</span> <span class="n">max_samples</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">bootstrap</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">bag_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">bag_clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">RandomForestClassifier</span>
|
||
<span class="n">rnd_clf</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">500</span><span class="p">,</span> <span class="n">max_leaf_nodes</span><span class="o">=</span><span class="mi">16</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">rnd_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">y_pred_rf</span> <span class="o">=</span> <span class="n">rnd_clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
<span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">y_pred</span> <span class="o">==</span> <span class="n">y_pred_rf</span><span class="p">)</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">y_pred</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="section" id="boosting-a-bird-s-eye-view">
|
||
<h2><span class="section-number">10.5. </span>Boosting, a Bird’s Eye View<a class="headerlink" href="#boosting-a-bird-s-eye-view" title="Permalink to this headline">¶</a></h2>
|
||
<p>The basic idea is to combine weak classifiers in order to create a good
|
||
classifier. With a weak classifier we often intend a classifier which
|
||
produces results which are only slightly better than we would get by
|
||
random guesses.</p>
|
||
<p>This is done by applying in an iterative way a weak (or a standard
|
||
classifier like decision trees) to modify the data. In each iteration
|
||
we emphasize those observations which are misclassified by weighting
|
||
them with a factor.</p>
|
||
<p>Boosting is a way of fitting an additive expansion in a set of
|
||
elementary basis functions like for example some simple polynomials.
|
||
Assume for example that we have a function</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||
\]</div>
|
||
<p>where <span class="math notranslate nohighlight">\(\beta_m\)</span> are the expansion parameters to be determined in a
|
||
minimization process and <span class="math notranslate nohighlight">\(b(x;\gamma_m)\)</span> are some simple functions of
|
||
the multivariable parameter <span class="math notranslate nohighlight">\(x\)</span> which is characterized by the
|
||
parameters <span class="math notranslate nohighlight">\(\gamma_m\)</span>.</p>
|
||
<p>As an example, consider the Sigmoid function we used in logistic
|
||
regression. In that case, we can translate the function
|
||
<span class="math notranslate nohighlight">\(b(x;\gamma_m)\)</span> into the Sigmoid function</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\sigma(t) = \frac{1}{1+\exp{(-t)}},
|
||
\]</div>
|
||
<p>where <span class="math notranslate nohighlight">\(t=\gamma_0+\gamma_1 x\)</span> and the parameters <span class="math notranslate nohighlight">\(\gamma_0\)</span> and
|
||
<span class="math notranslate nohighlight">\(\gamma_1\)</span> were determined by the Logistic Regression fitting
|
||
algorithm.</p>
|
||
<p>As another example, consider the cost function we defined for linear regression</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
C(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
|
||
\]</div>
|
||
<p>In this case the function <span class="math notranslate nohighlight">\(f(x)\)</span> was replaced by the design matrix
|
||
<span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> and the unknown linear regression parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>,
|
||
that is <span class="math notranslate nohighlight">\(\boldsymbol{f}=\boldsymbol{X}\boldsymbol{\beta}\)</span>. In linear regression we can
|
||
simply invert a matrix and obtain the parameters <span class="math notranslate nohighlight">\(\beta\)</span> by</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\boldsymbol{\beta}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}.
|
||
\]</div>
|
||
<p>In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters <span class="math notranslate nohighlight">\(\beta_m\)</span> and <span class="math notranslate nohighlight">\(\gamma_m\)</span>.</p>
|
||
<div class="section" id="iterative-fitting-regression-and-squared-error-cost-function">
|
||
<h3><span class="section-number">10.5.1. </span>Iterative Fitting, Regression and Squared-error Cost Function<a class="headerlink" href="#iterative-fitting-regression-and-squared-error-cost-function" title="Permalink to this headline">¶</a></h3>
|
||
<p>The way we proceed is as follows (here we specialize to the squared-error cost function)</p>
|
||
<ol class="simple">
|
||
<li><p>Establish a cost function, here <span class="math notranslate nohighlight">\(\cal{C}(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f_M(x_i))^2\)</span> with <span class="math notranslate nohighlight">\(f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m)\)</span>.</p></li>
|
||
<li><p>Initialize with a guess <span class="math notranslate nohighlight">\(f_0(x)\)</span>. It could be one or even zero or some random numbers.</p></li>
|
||
<li><p>For <span class="math notranslate nohighlight">\(m=1:M\)</span></p></li>
|
||
</ol>
|
||
<p>a. minimize <span class="math notranslate nohighlight">\(\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2\)</span> wrt <span class="math notranslate nohighlight">\(\gamma\)</span> and <span class="math notranslate nohighlight">\(\beta\)</span></p>
|
||
<p>b. This gives the optimal values <span class="math notranslate nohighlight">\(\beta_m\)</span> and <span class="math notranslate nohighlight">\(\gamma_m\)</span></p>
|
||
<p>c. Determine then the new values <span class="math notranslate nohighlight">\(f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m)\)</span></p>
|
||
<p>We could use any of the algorithms we have discussed till now. If we
|
||
use trees, <span class="math notranslate nohighlight">\(\gamma\)</span> parameterizes the split variables and split points
|
||
at the internal nodes, and the predictions at the terminal nodes.</p>
|
||
<p>To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.</p>
|
||
<p>For simplicity we assume also that our functions <span class="math notranslate nohighlight">\(b(x;\gamma)=1+\gamma x\)</span>.</p>
|
||
<p>This means that for every iteration <span class="math notranslate nohighlight">\(m\)</span>, we need to optimize</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
(\beta_m,\gamma_m) = \mathrm{argmin}_{\beta,\lambda}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2=\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(1+\gamma x_i))^2.
|
||
\]</div>
|
||
<p>We start our iteration by simply setting <span class="math notranslate nohighlight">\(f_0(x)=0\)</span>.
|
||
Taking the derivatives with respect to <span class="math notranslate nohighlight">\(\beta\)</span> and <span class="math notranslate nohighlight">\(\gamma\)</span> we obtain</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\frac{\partial \cal{C}}{\partial \beta} = -2\sum_{i}(1+\gamma x_i)(y_i-\beta(1+\gamma x_i))=0,
|
||
\]</div>
|
||
<p>and</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\frac{\partial \cal{C}}{\partial \gamma} =-2\sum_{i}\beta x_i(y_i-\beta(1+\gamma x_i))=0.
|
||
\]</div>
|
||
<p>We can then rewrite these equations as (defining <span class="math notranslate nohighlight">\(\boldsymbol{w}=\boldsymbol{e}+\gamma \boldsymbol{x})\)</span> with <span class="math notranslate nohighlight">\(\boldsymbol{e}\)</span> being the unit vector)</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\gamma \boldsymbol{w}^T(\boldsymbol{y}-\beta\gamma \boldsymbol{w})=0,
|
||
\]</div>
|
||
<p>which gives us <span class="math notranslate nohighlight">\(\beta = \boldsymbol{w}^T\boldsymbol{y}/(\boldsymbol{w}^T\boldsymbol{w})\)</span>. Similarly we have</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\beta\gamma \boldsymbol{x}^T(\boldsymbol{y}-\beta(1+\gamma \boldsymbol{x}))=0,
|
||
\]</div>
|
||
<p>which leads to <span class="math notranslate nohighlight">\(\gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\boldsymbol{e})/(\beta\boldsymbol{x}^T\boldsymbol{x})\)</span>. Inserting
|
||
for <span class="math notranslate nohighlight">\(\beta\)</span> gives us an equation for <span class="math notranslate nohighlight">\(\gamma\)</span>. This is a non-linear equation in the unknown <span class="math notranslate nohighlight">\(\gamma\)</span> and has to be solved numerically.</p>
|
||
<p>The solution to these two equations gives us in turn <span class="math notranslate nohighlight">\(\beta_1\)</span> and <span class="math notranslate nohighlight">\(\gamma_1\)</span> leading to the new expression for <span class="math notranslate nohighlight">\(f_1(x)\)</span> as
|
||
<span class="math notranslate nohighlight">\(f_1(x) = \beta_1(1+\gamma_1x)\)</span>. Doing this <span class="math notranslate nohighlight">\(M\)</span> times results in our final estimate for the function <span class="math notranslate nohighlight">\(f\)</span>.</p>
|
||
</div>
|
||
<div class="section" id="iterative-fitting-classification-and-adaboost">
|
||
<h3><span class="section-number">10.5.2. </span>Iterative Fitting, Classification and AdaBoost<a class="headerlink" href="#iterative-fitting-classification-and-adaboost" title="Permalink to this headline">¶</a></h3>
|
||
<p>Let us consider a binary classification problem with two outcomes <span class="math notranslate nohighlight">\(y_i \in \{-1,1\}\)</span> and <span class="math notranslate nohighlight">\(i=0,1,2,\dots,n-1\)</span> as our set of
|
||
observations. We define a classification function <span class="math notranslate nohighlight">\(G(x)\)</span> which produces a prediction taking one or the other of the two values
|
||
<span class="math notranslate nohighlight">\(\{-1,1\}\)</span>.</p>
|
||
<p>The error rate of the training sample is then</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i)).
|
||
\]</div>
|
||
<p>The iterative procedure starts with defining a weak classifier whose
|
||
error rate is barely better than random guessing. The iterative
|
||
procedure in boosting is to sequentially apply a weak
|
||
classification algorithm to repeatedly modified versions of the data
|
||
producing a sequence of weak classifiers <span class="math notranslate nohighlight">\(G_m(x)\)</span>.</p>
|
||
<p>Here we will express our function <span class="math notranslate nohighlight">\(f(x)\)</span> in terms of <span class="math notranslate nohighlight">\(G(x)\)</span>. That is</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||
\]</div>
|
||
<p>will be a function of</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
G_M(x) = \mathrm{sign} \sum_{i=1}^M \alpha_m G_m(x).
|
||
\]</div>
|
||
<p>In our iterative procedure we define thus</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
f_m(x) = f_{m-1}(x)+\beta_mG_m(x).
|
||
\]</div>
|
||
<p>The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the
|
||
exponential cost/loss function defined as</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{(-y_i(f_{m-1}(x_i)+\beta G(x_i))}.
|
||
\]</div>
|
||
<p>We optimize <span class="math notranslate nohighlight">\(\beta\)</span> and <span class="math notranslate nohighlight">\(G\)</span> for each value of <span class="math notranslate nohighlight">\(m=1:M\)</span> as we did in the regression case.
|
||
This is normally done in two steps. Let us however first rewrite the cost function as</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{(-y_i\beta G(x_i))},
|
||
\]</div>
|
||
<p>where we have defined <span class="math notranslate nohighlight">\(w_i^m= \exp{(-y_if_{m-1}(x_i))}\)</span>.</p>
|
||
<p>First, for any <span class="math notranslate nohighlight">\(\beta > 0\)</span>, we optimize <span class="math notranslate nohighlight">\(G\)</span> by setting</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)),
|
||
\]</div>
|
||
<p>which is the classifier that minimizes the weighted error rate in predicting <span class="math notranslate nohighlight">\(y\)</span>.</p>
|
||
<p>We can do this by rewriting</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\exp{-(\beta)}\sum_{y_i=G(x_i)}w_i^m+\exp{(\beta)}\sum_{y_i\ne G(x_i)}w_i^m,
|
||
\]</div>
|
||
<p>which can be rewritten as</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{(-\beta)}\sum_{i=0}^{n-1}w_i^m=0,
|
||
\]</div>
|
||
<p>which leads to</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\beta_m = \frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}},
|
||
\]</div>
|
||
<p>where we have redefined the error as</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\mathrm{\overline{err}}_m=\frac{1}{n}\frac{\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i)}{\sum_{i=0}^{n-1}w_i^m},
|
||
\]</div>
|
||
<p>which leads to an update of</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
f_m(x) = f_{m-1}(x) +\beta_m G_m(x).
|
||
\]</div>
|
||
<p>This leads to the new weights</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
w_i^{m+1} = w_i^m \exp{(-y_i\beta_m G_m(x_i))}
|
||
\]</div>
|
||
</div>
|
||
<div class="section" id="adaptive-boosting-adaboost-basic-algorithm">
|
||
<h3><span class="section-number">10.5.3. </span>Adaptive boosting: AdaBoost, Basic Algorithm<a class="headerlink" href="#adaptive-boosting-adaboost-basic-algorithm" title="Permalink to this headline">¶</a></h3>
|
||
<p>The algorithm here is rather straightforward. Assume that our weak
|
||
classifier is a decision tree and we consider a binary set of outputs
|
||
with <span class="math notranslate nohighlight">\(y_i \in \{-1,1\}\)</span> and <span class="math notranslate nohighlight">\(i=0,1,2,\dots,n-1\)</span> as our set of
|
||
observations. Our design matrix is given in terms of the
|
||
feature/predictor vectors
|
||
<span class="math notranslate nohighlight">\(\boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1}]\)</span>. Finally, we define also a
|
||
classifier determined by our data via a function <span class="math notranslate nohighlight">\(G(x)\)</span>. This function tells us how well we are able to classify our outputs/targets <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span>.</p>
|
||
<p>We have already defined the misclassification error <span class="math notranslate nohighlight">\(\mathrm{err}\)</span> as</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i)),
|
||
\]</div>
|
||
<p>where the function <span class="math notranslate nohighlight">\(I()\)</span> is one if we misclassify and zero if we classify correctly.</p>
|
||
<p>With the above definitions we are now ready to set up the algorithm for AdaBoost.
|
||
The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.</p>
|
||
<ol class="simple">
|
||
<li><p>We start by initializing all weights to <span class="math notranslate nohighlight">\(w_i = 1/n\)</span>, with <span class="math notranslate nohighlight">\(i=0,1,2,\dots n-1\)</span>. It is easy to see that we must have <span class="math notranslate nohighlight">\(\sum_{i=0}^{n-1}w_i = 1\)</span>.</p></li>
|
||
<li><p>We rewrite the misclassification error as</p></li>
|
||
</ol>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\mathrm{\overline{err}}_m=\frac{\sum_{i=0}^{n-1}w_i^m I(y_i\ne G(x_i))}{\sum_{i=0}^{n-1}w_i},
|
||
\]</div>
|
||
<ol class="simple">
|
||
<li><p>Then we start looping over all attempts at classifying, namely we start an iterative process for <span class="math notranslate nohighlight">\(m=1:M\)</span>, where <span class="math notranslate nohighlight">\(M\)</span> is the final number of classifications. Our given classifier could for example be a plain decision tree.</p></li>
|
||
</ol>
|
||
<p>a. Fit then a given classifier to the training set using the weights <span class="math notranslate nohighlight">\(w_i\)</span>.</p>
|
||
<p>b. Compute then <span class="math notranslate nohighlight">\(\mathrm{err}\)</span> and figure out which events are classified properly and which are classified wrongly.</p>
|
||
<p>c. Define a quantity <span class="math notranslate nohighlight">\(\alpha_{m} = \log{(1-\mathrm{\overline{err}}_m)/\mathrm{\overline{err}}_m}\)</span></p>
|
||
<p>d. Set the new weights to <span class="math notranslate nohighlight">\(w_i = w_i\times \exp{(\alpha_m I(y_i\ne G(x_i)}\)</span>.</p>
|
||
<ol class="simple">
|
||
<li><p>Compute the new classifier <span class="math notranslate nohighlight">\(G(x)= \sum_{i=0}^{n-1}\alpha_m I(y_i\ne G(x_i)\)</span>.</p></li>
|
||
</ol>
|
||
<p>For the iterations with <span class="math notranslate nohighlight">\(m \le 2\)</span> the weights are modified
|
||
individually at each steps. The observations which were misclassified
|
||
at iteration <span class="math notranslate nohighlight">\(m-1\)</span> have a weight which is larger than those which were
|
||
classified properly. As this proceeds, the observations which were
|
||
difficult to classifiy correctly are given a larger influence. Each
|
||
new classification step <span class="math notranslate nohighlight">\(m\)</span> is then forced to concentrate on those
|
||
observations that are missed in the previous iterations.</p>
|
||
<p>Using <strong>Scikit-Learn</strong> it is easy to apply the adaptive boosting algorithm, as done here.</p>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">AdaBoostClassifier</span>
|
||
|
||
<span class="n">ada_clf</span> <span class="o">=</span> <span class="n">AdaBoostClassifier</span><span class="p">(</span>
|
||
<span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span> <span class="n">n_estimators</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span>
|
||
<span class="n">algorithm</span><span class="o">=</span><span class="s2">"SAMME.R"</span><span class="p">,</span> <span class="n">learning_rate</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">ada_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
|
||
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">AdaBoostClassifier</span>
|
||
|
||
<span class="n">ada_clf</span> <span class="o">=</span> <span class="n">AdaBoostClassifier</span><span class="p">(</span>
|
||
<span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span> <span class="n">n_estimators</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span>
|
||
<span class="n">algorithm</span><span class="o">=</span><span class="s2">"SAMME.R"</span><span class="p">,</span> <span class="n">learning_rate</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
|
||
<span class="n">ada_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">ada_clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_confusion_matrix</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">normalize</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
<span class="n">y_probas</span> <span class="o">=</span> <span class="n">ada_clf</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_roc</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_cumulative_gain</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="section" id="gradient-boosting-basics-with-steepest-descent-functional-gradient-descent">
|
||
<h2><span class="section-number">10.6. </span>Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent<a class="headerlink" href="#gradient-boosting-basics-with-steepest-descent-functional-gradient-descent" title="Permalink to this headline">¶</a></h2>
|
||
<p>Gradient boosting is again a similar technique to Adaptive boosting,
|
||
it combines so-called weak classifiers or regressors into a strong
|
||
method via a series of iterations.</p>
|
||
<p>In order to understand the method, let us illustrate its basics by
|
||
bringing back the essential steps in linear regression, where our cost
|
||
function was the least squares function.</p>
|
||
<p>We start again with our cost function <span class="math notranslate nohighlight">\(\cal{C}(\boldsymbol{y}m\boldsymbol{f})=\sum_{i=0}^{n-1}\cal{L}(y_i, f(x_i))\)</span> where we want to minimize
|
||
This means that for every iteration, we need to optimize</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
(\hat{\boldsymbol{f}}) = \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
|
||
\]</div>
|
||
<p>We define a real function <span class="math notranslate nohighlight">\(h_m(x)\)</span> that defines our final function <span class="math notranslate nohighlight">\(f_M(x)\)</span> as</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
f_M(x) = \sum_{m=0}^M h_m(x).
|
||
\]</div>
|
||
<p>In the steepest decent approach we approximate <span class="math notranslate nohighlight">\(h_m(x) = -\rho_m g_m(x)\)</span>, where <span class="math notranslate nohighlight">\(\rho_m\)</span> is a scalar and <span class="math notranslate nohighlight">\(g_m(x)\)</span> the gradient defined as</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
g_m(x_i) = \left[ \frac{\partial \cal{L}(y_i, f(x_i))}{\partial f(x_i)}\right]_{f(x_i)=f_{m-1}(x_i)}.
|
||
\]</div>
|
||
<p>With the new gradient we can update <span class="math notranslate nohighlight">\(f_m(x) = f_{m-1}(x) -\rho_m g_m(x)\)</span>. Using the above squared-error function we see that
|
||
the gradient is <span class="math notranslate nohighlight">\(g_m(x_i) = -2(y_i-f(x_i))\)</span>.</p>
|
||
<p>Choosing <span class="math notranslate nohighlight">\(f_0(x)=0\)</span> we obtain <span class="math notranslate nohighlight">\(g_m(x) = -2y_i\)</span> and inserting this into the minimization problem for the cost function we have</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
(\rho_1) = \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2.
|
||
\]</div>
|
||
<p>Optimizing with respect to <span class="math notranslate nohighlight">\(\rho\)</span> we obtain (taking the derivative) that <span class="math notranslate nohighlight">\(\rho_1 = -1/2\)</span>. We have then that</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
f_1(x) = f_{0}(x) -\rho_1 g_1(x)=-y_i.
|
||
\]</div>
|
||
<p>We can then proceed and compute</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
g_2(x_i) = \left[ \frac{\partial \cal{L}(y_i, f(x_i))}{\partial f(x_i)}\right]_{f(x_i)=f_{1}(x_i)=y_i}=-4y_i,
|
||
\]</div>
|
||
<p>and find a new value for <span class="math notranslate nohighlight">\(\rho_2=-1/2\)</span> and continue till we have reached <span class="math notranslate nohighlight">\(m=M\)</span>. We can modify the steepest descent method, or steepest boosting, by introducing what is called <strong>gradient boosting</strong>.</p>
|
||
<p>Steepest descent is however not much used, since it only optimizes <span class="math notranslate nohighlight">\(f\)</span> at a fixed set of <span class="math notranslate nohighlight">\(n\)</span> points,
|
||
so we do not learn a function that can generalize. However, we can modify the algorithm by
|
||
fitting a weak learner to approximate the negative gradient signal.</p>
|
||
<p>Suppose we have a cost function <span class="math notranslate nohighlight">\(C(f)=\sum_{i=0}^{n-1}L(y_i, f(x_i))\)</span> where <span class="math notranslate nohighlight">\(y_i\)</span> is our target and <span class="math notranslate nohighlight">\(f(x_i)\)</span> the function which is meant to model <span class="math notranslate nohighlight">\(y_i\)</span>. The above cost function could be our standard squared-error function</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
C(\boldsymbol{y},\boldsymbol{f})=\sum_{i=0}^{n-1}(y_i-f(x_i))^2.
|
||
\]</div>
|
||
<p>The way we proceed in an iterative fashion is to</p>
|
||
<ol class="simple">
|
||
<li><p>Initialize our estimate <span class="math notranslate nohighlight">\(f_0(x)\)</span>.</p></li>
|
||
<li><p>For <span class="math notranslate nohighlight">\(m=1:M\)</span>, we</p></li>
|
||
</ol>
|
||
<p>a. compute the negative gradient vector <span class="math notranslate nohighlight">\(\boldsymbol{u}_m = -\partial C(\boldsymbol{y},\boldsymbol{f})/\partial \boldsymbol{f}(x)\)</span> at <span class="math notranslate nohighlight">\(f(x) = f_{m-1}(x)\)</span>;</p>
|
||
<p>b. fit the so-called base-learner to the negative gradient <span class="math notranslate nohighlight">\(h_m(u_m,x)\)</span>;</p>
|
||
<p>c. update the estimate <span class="math notranslate nohighlight">\(f_m(x) = f_{m-1}(x)+h_m(u_m,x)\)</span>;</p>
|
||
<ol class="simple">
|
||
<li><p>The final estimate is then <span class="math notranslate nohighlight">\(f_M(x) = \sum_{m=1}^M h_m(u_m,x)\)</span>.</p></li>
|
||
</ol>
|
||
</div>
|
||
<div class="section" id="gradient-boosting-examples-of-regression">
|
||
<h2><span class="section-number">10.7. </span>Gradient Boosting, Examples of Regression<a class="headerlink" href="#gradient-boosting-examples-of-regression" title="Permalink to this headline">¶</a></h2>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">GradientBoostingRegressor</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">StandardScaler</span>
|
||
<span class="kn">import</span> <span class="nn">scikitplot</span> <span class="k">as</span> <span class="nn">skplt</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">mean_squared_error</span>
|
||
|
||
<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
|
||
<span class="n">maxdegree</span> <span class="o">=</span> <span class="mi">6</span>
|
||
|
||
<span class="c1"># Make data set.</span>
|
||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
<span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="mf">1.5</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
|
||
|
||
<span class="n">error</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdegree</span><span class="p">)</span>
|
||
<span class="n">bias</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdegree</span><span class="p">)</span>
|
||
<span class="n">variance</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdegree</span><span class="p">)</span>
|
||
<span class="n">polydegree</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdegree</span><span class="p">)</span>
|
||
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
|
||
<span class="n">scaler</span> <span class="o">=</span> <span class="n">StandardScaler</span><span class="p">()</span>
|
||
<span class="n">scaler</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_train_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_test_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
|
||
<span class="k">for</span> <span class="n">degree</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">maxdegree</span><span class="p">):</span>
|
||
<span class="n">model</span> <span class="o">=</span> <span class="n">GradientBoostingRegressor</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="n">degree</span><span class="p">,</span> <span class="n">n_estimators</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">learning_rate</span><span class="o">=</span><span class="mf">1.0</span><span class="p">)</span>
|
||
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span><span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
<span class="n">polydegree</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">degree</span>
|
||
<span class="n">error</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">((</span><span class="n">y_test</span> <span class="o">-</span> <span class="n">y_pred</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="p">)</span>
|
||
<span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span> <span class="p">(</span><span class="n">y_test</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">y_pred</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span> <span class="p">)</span>
|
||
<span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">var</span><span class="p">(</span><span class="n">y_pred</span><span class="p">)</span> <span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Max depth:'</span><span class="p">,</span> <span class="n">degree</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Error:'</span><span class="p">,</span> <span class="n">error</span><span class="p">[</span><span class="n">degree</span><span class="p">])</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Bias^2:'</span><span class="p">,</span> <span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">])</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Var:'</span><span class="p">,</span> <span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">])</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="si">{}</span><span class="s1"> >= </span><span class="si">{}</span><span class="s1"> + </span><span class="si">{}</span><span class="s1"> = </span><span class="si">{}</span><span class="s1">'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">error</span><span class="p">[</span><span class="n">degree</span><span class="p">],</span> <span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">],</span> <span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">],</span> <span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span><span class="o">+</span><span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">]))</span>
|
||
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">maxdegree</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">polydegree</span><span class="p">,</span> <span class="n">error</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Error'</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">polydegree</span><span class="p">,</span> <span class="n">bias</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'bias'</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">polydegree</span><span class="p">,</span> <span class="n">variance</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Variance'</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"gdregression"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="section" id="gradient-boosting-classification-example">
|
||
<h2><span class="section-number">10.8. </span>Gradient Boosting, Classification Example<a class="headerlink" href="#gradient-boosting-classification-example" title="Permalink to this headline">¶</a></h2>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_breast_cancer</span>
|
||
<span class="kn">import</span> <span class="nn">scikitplot</span> <span class="k">as</span> <span class="nn">skplt</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">GradientBoostingClassifier</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">cross_validate</span>
|
||
|
||
<span class="c1"># Load the data</span>
|
||
<span class="n">cancer</span> <span class="o">=</span> <span class="n">load_breast_cancer</span><span class="p">()</span>
|
||
|
||
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">cancer</span><span class="o">.</span><span class="n">data</span><span class="p">,</span><span class="n">cancer</span><span class="o">.</span><span class="n">target</span><span class="p">,</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">X_train</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">X_test</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
|
||
<span class="c1">#now scale the data</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">StandardScaler</span>
|
||
<span class="n">scaler</span> <span class="o">=</span> <span class="n">StandardScaler</span><span class="p">()</span>
|
||
<span class="n">scaler</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_train_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_test_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
|
||
<span class="n">gd_clf</span> <span class="o">=</span> <span class="n">GradientBoostingClassifier</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">n_estimators</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">learning_rate</span><span class="o">=</span><span class="mf">1.0</span><span class="p">)</span>
|
||
<span class="n">gd_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
|
||
<span class="c1">#Cross validation</span>
|
||
<span class="n">accuracy</span> <span class="o">=</span> <span class="n">cross_validate</span><span class="p">(</span><span class="n">gd_clf</span><span class="p">,</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">,</span><span class="n">cv</span><span class="o">=</span><span class="mi">10</span><span class="p">)[</span><span class="s1">'test_score'</span><span class="p">]</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">accuracy</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"Test set accuracy with Random Forests and scaled data: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">gd_clf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
|
||
|
||
<span class="kn">import</span> <span class="nn">scikitplot</span> <span class="k">as</span> <span class="nn">skplt</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">gd_clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_confusion_matrix</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">normalize</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"gdclassiffierconfusion"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
<span class="n">y_probas</span> <span class="o">=</span> <span class="n">gd_clf</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_roc</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"gdclassiffierroc"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_cumulative_gain</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"gdclassiffiercgain"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="section" id="xgboost-extreme-gradient-boosting">
|
||
<h2><span class="section-number">10.9. </span>XGBoost: Extreme Gradient Boosting<a class="headerlink" href="#xgboost-extreme-gradient-boosting" title="Permalink to this headline">¶</a></h2>
|
||
<p><a class="reference external" href="https://github.com/dmlc/xgboost">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 class="reference external" href="https://arxiv.org/abs/1603.02754">article by Chen and Guestrin</a>.</p>
|
||
<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>
|
||
<p>It is now the algorithm which wins essentially all ML competitions!!!</p>
|
||
</div>
|
||
<div class="section" id="regression-case">
|
||
<h2><span class="section-number">10.10. </span>Regression Case<a class="headerlink" href="#regression-case" title="Permalink to this headline">¶</a></h2>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||
<span class="kn">import</span> <span class="nn">xgboost</span> <span class="k">as</span> <span class="nn">xgb</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">StandardScaler</span>
|
||
<span class="kn">import</span> <span class="nn">scikitplot</span> <span class="k">as</span> <span class="nn">skplt</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">mean_squared_error</span>
|
||
|
||
<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
|
||
<span class="n">maxdegree</span> <span class="o">=</span> <span class="mi">6</span>
|
||
|
||
<span class="c1"># Make data set.</span>
|
||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
<span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="mf">1.5</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
|
||
|
||
<span class="n">error</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdegree</span><span class="p">)</span>
|
||
<span class="n">bias</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdegree</span><span class="p">)</span>
|
||
<span class="n">variance</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdegree</span><span class="p">)</span>
|
||
<span class="n">polydegree</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">maxdegree</span><span class="p">)</span>
|
||
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
|
||
<span class="n">scaler</span> <span class="o">=</span> <span class="n">StandardScaler</span><span class="p">()</span>
|
||
<span class="n">scaler</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_train_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_test_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
|
||
<span class="k">for</span> <span class="n">degree</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">maxdegree</span><span class="p">):</span>
|
||
<span class="n">model</span> <span class="o">=</span> <span class="n">xgb</span><span class="o">.</span><span class="n">XGBRegressor</span><span class="p">(</span><span class="n">objective</span> <span class="o">=</span><span class="s1">'reg:squarederror'</span><span class="p">,</span> <span class="n">colsaobjective</span> <span class="o">=</span><span class="s1">'reg:squarederror'</span><span class="p">,</span> <span class="n">colsample_bytree</span> <span class="o">=</span> <span class="mf">0.3</span><span class="p">,</span> <span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">0.1</span><span class="p">,</span><span class="n">max_depth</span> <span class="o">=</span> <span class="n">degree</span><span class="p">,</span> <span class="n">alpha</span> <span class="o">=</span> <span class="mi">10</span><span class="p">,</span> <span class="n">n_estimators</span> <span class="o">=</span> <span class="mi">200</span><span class="p">)</span>
|
||
|
||
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span><span class="n">y_train</span><span class="p">)</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
<span class="n">polydegree</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">degree</span>
|
||
<span class="n">error</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">((</span><span class="n">y_test</span> <span class="o">-</span> <span class="n">y_pred</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="p">)</span>
|
||
<span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span> <span class="p">(</span><span class="n">y_test</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">y_pred</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span> <span class="p">)</span>
|
||
<span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">var</span><span class="p">(</span><span class="n">y_pred</span><span class="p">)</span> <span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Max depth:'</span><span class="p">,</span> <span class="n">degree</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Error:'</span><span class="p">,</span> <span class="n">error</span><span class="p">[</span><span class="n">degree</span><span class="p">])</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Bias^2:'</span><span class="p">,</span> <span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">])</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Var:'</span><span class="p">,</span> <span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">])</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="si">{}</span><span class="s1"> >= </span><span class="si">{}</span><span class="s1"> + </span><span class="si">{}</span><span class="s1"> = </span><span class="si">{}</span><span class="s1">'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">error</span><span class="p">[</span><span class="n">degree</span><span class="p">],</span> <span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">],</span> <span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">],</span> <span class="n">bias</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span><span class="o">+</span><span class="n">variance</span><span class="p">[</span><span class="n">degree</span><span class="p">]))</span>
|
||
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">maxdegree</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">polydegree</span><span class="p">,</span> <span class="n">error</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Error'</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">polydegree</span><span class="p">,</span> <span class="n">bias</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'bias'</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">polydegree</span><span class="p">,</span> <span class="n">variance</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Variance'</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>As you will see from the confusion matrix below, XGBoots does an excellent job on the Wisconsin cancer data and outperforms essentially all agorithms we have discussed till now.</p>
|
||
<div class="cell docutils container">
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_breast_cancer</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">LabelEncoder</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">cross_validate</span>
|
||
<span class="kn">import</span> <span class="nn">scikitplot</span> <span class="k">as</span> <span class="nn">skplt</span>
|
||
<span class="kn">import</span> <span class="nn">xgboost</span> <span class="k">as</span> <span class="nn">xgb</span>
|
||
<span class="c1"># Load the data</span>
|
||
<span class="n">cancer</span> <span class="o">=</span> <span class="n">load_breast_cancer</span><span class="p">()</span>
|
||
|
||
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">cancer</span><span class="o">.</span><span class="n">data</span><span class="p">,</span><span class="n">cancer</span><span class="o">.</span><span class="n">target</span><span class="p">,</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">X_train</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">X_test</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
|
||
<span class="c1">#now scale the data</span>
|
||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">StandardScaler</span>
|
||
<span class="n">scaler</span> <span class="o">=</span> <span class="n">StandardScaler</span><span class="p">()</span>
|
||
<span class="n">scaler</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_train_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
|
||
<span class="n">X_test_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||
|
||
<span class="n">xg_clf</span> <span class="o">=</span> <span class="n">xgb</span><span class="o">.</span><span class="n">XGBClassifier</span><span class="p">()</span>
|
||
<span class="n">xg_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span><span class="n">y_train</span><span class="p">)</span>
|
||
|
||
<span class="n">y_test</span> <span class="o">=</span> <span class="n">xg_clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"Test set accuracy with Random Forests and scaled data: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">xg_clf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
|
||
|
||
<span class="kn">import</span> <span class="nn">scikitplot</span> <span class="k">as</span> <span class="nn">skplt</span>
|
||
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">xg_clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_confusion_matrix</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">normalize</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"xdclassiffierconfusion"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
<span class="n">y_probas</span> <span class="o">=</span> <span class="n">xg_clf</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_roc</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"xdclassiffierroc"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_cumulative_gain</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"gdclassiffiercgain"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
|
||
|
||
<span class="n">xgb</span><span class="o">.</span><span class="n">plot_tree</span><span class="p">(</span><span class="n">xg_clf</span><span class="p">,</span><span class="n">num_trees</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">'figure.figsize'</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">50</span><span class="p">,</span> <span class="mi">10</span><span class="p">]</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"xgtree"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
|
||
<span class="n">xgb</span><span class="o">.</span><span class="n">plot_importance</span><span class="p">(</span><span class="n">xg_clf</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">'figure.figsize'</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span>
|
||
<span class="n">save_fig</span><span class="p">(</span><span class="s2">"xgparams"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</pre></div>
|
||
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