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<a class="navbar-brand" href="week44-bs.html">Week 44: Dimensionality Reduction, PCA and Clustering. Decision Trees</a>
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<!-- navigation toc: --> <li><a href="._week44-bs001.html#overview-of-week-44" style="font-size: 80%;">Overview of week 44</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs002.html#digression-first" style="font-size: 80%;">Digression First</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs018.html#wrapping-it-up" style="font-size: 80%;">Wrapping it up</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs019.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs023.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs024.html#general-features" style="font-size: 80%;">General Features</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs025.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs026.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs027.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs028.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs041.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs042.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs043.html#computing-the-gini-index" style="font-size: 80%;">Computing the Gini index</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs044.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs045.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs046.html#entropy-and-the-id3-algorithm" style="font-size: 80%;">Entropy and the ID3 algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs047.html#cancer-data-again-now-with-decision-trees-and-other-methods" style="font-size: 80%;">Cancer Data again now with Decision Trees and other Methods</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs048.html#another-example-the-moons-again" style="font-size: 80%;">Another example, the moons again</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs050.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs051.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs052.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs053.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs054.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs055.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs056.html#bagging" style="font-size: 80%;">Bagging</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs057.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs058.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs059.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs060.html#please-not-the-moons-again-voting-and-bagging" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs062.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
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<!-- !split -->
<h2 id="bagging-examples" class="anchor">Bagging Examples </h2>
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<pre style="line-height: 125%;"><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> BaggingClassifier
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.tree</span> <span style="color: #008000; font-weight: bold">import</span> DecisionTreeClassifier
bag_clf <span style="color: #666666">=</span> BaggingClassifier(
DecisionTreeClassifier(random_state<span style="color: #666666">=42</span>), n_estimators<span style="color: #666666">=500</span>,
max_samples<span style="color: #666666">=100</span>, bootstrap<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>, n_jobs<span style="color: #666666">=-1</span>, random_state<span style="color: #666666">=42</span>)
bag_clf<span style="color: #666666">.</span>fit(X_train, y_train)
y_pred <span style="color: #666666">=</span> bag_clf<span style="color: #666666">.</span>predict(X_test)
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<pre style="line-height: 125%;"><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.metrics</span> <span style="color: #008000; font-weight: bold">import</span> accuracy_score
<span style="color: #008000">print</span>(accuracy_score(y_test, y_pred))
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<pre style="line-height: 125%;">tree_clf <span style="color: #666666">=</span> DecisionTreeClassifier(random_state<span style="color: #666666">=42</span>)
tree_clf<span style="color: #666666">.</span>fit(X_train, y_train)
y_pred_tree <span style="color: #666666">=</span> tree_clf<span style="color: #666666">.</span>predict(X_test)
<span style="color: #008000">print</span>(accuracy_score(y_test, y_pred_tree))
</pre>
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<pre style="line-height: 125%;"><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">matplotlib.colors</span> <span style="color: #008000; font-weight: bold">import</span> ListedColormap
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">plot_decision_boundary</span>(clf, X, y, axes<span style="color: #666666">=</span>[<span style="color: #666666">-1.5</span>, <span style="color: #666666">2.5</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">1.5</span>], alpha<span style="color: #666666">=0.5</span>, contour<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>):
x1s <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(axes[<span style="color: #666666">0</span>], axes[<span style="color: #666666">1</span>], <span style="color: #666666">100</span>)
x2s <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(axes[<span style="color: #666666">2</span>], axes[<span style="color: #666666">3</span>], <span style="color: #666666">100</span>)
x1, x2 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>meshgrid(x1s, x2s)
X_new <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[x1<span style="color: #666666">.</span>ravel(), x2<span style="color: #666666">.</span>ravel()]
y_pred <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(X_new)<span style="color: #666666">.</span>reshape(x1<span style="color: #666666">.</span>shape)
custom_cmap <span style="color: #666666">=</span> ListedColormap([<span style="color: #BA2121">&#39;#fafab0&#39;</span>,<span style="color: #BA2121">&#39;#9898ff&#39;</span>,<span style="color: #BA2121">&#39;#a0faa0&#39;</span>])
plt<span style="color: #666666">.</span>contourf(x1, x2, y_pred, alpha<span style="color: #666666">=0.3</span>, cmap<span style="color: #666666">=</span>custom_cmap)
<span style="color: #008000; font-weight: bold">if</span> contour:
custom_cmap2 <span style="color: #666666">=</span> ListedColormap([<span style="color: #BA2121">&#39;#7d7d58&#39;</span>,<span style="color: #BA2121">&#39;#4c4c7f&#39;</span>,<span style="color: #BA2121">&#39;#507d50&#39;</span>])
plt<span style="color: #666666">.</span>contour(x1, x2, y_pred, cmap<span style="color: #666666">=</span>custom_cmap2, alpha<span style="color: #666666">=0.8</span>)
plt<span style="color: #666666">.</span>plot(X[:, <span style="color: #666666">0</span>][y<span style="color: #666666">==0</span>], X[:, <span style="color: #666666">1</span>][y<span style="color: #666666">==0</span>], <span style="color: #BA2121">&quot;yo&quot;</span>, alpha<span style="color: #666666">=</span>alpha)
plt<span style="color: #666666">.</span>plot(X[:, <span style="color: #666666">0</span>][y<span style="color: #666666">==1</span>], X[:, <span style="color: #666666">1</span>][y<span style="color: #666666">==1</span>], <span style="color: #BA2121">&quot;bs&quot;</span>, alpha<span style="color: #666666">=</span>alpha)
plt<span style="color: #666666">.</span>axis(axes)
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">r&quot;$x_1$&quot;</span>, fontsize<span style="color: #666666">=18</span>)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">r&quot;$x_2$&quot;</span>, fontsize<span style="color: #666666">=18</span>, rotation<span style="color: #666666">=0</span>)
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>,<span style="color: #666666">4</span>))
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">121</span>)
plot_decision_boundary(tree_clf, X, y)
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;Decision Tree&quot;</span>, fontsize<span style="color: #666666">=14</span>)
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">122</span>)
plot_decision_boundary(bag_clf, X, y)
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;Decision Trees with Bagging&quot;</span>, fontsize<span style="color: #666666">=14</span>)
save_fig(<span style="color: #BA2121">&quot;baggingtree&quot;</span>)
plt<span style="color: #666666">.</span>show()
</pre>
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<a class="navbar-brand" href="week44-bs.html">Week 44: Dimensionality Reduction, PCA and Clustering. Decision Trees</a>
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<!-- navigation toc: --> <li><a href="._week44-bs001.html#overview-of-week-44" style="font-size: 80%;">Overview of week 44</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs002.html#digression-first" style="font-size: 80%;">Digression First</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs006.html#basic-idea-of-the-k-means-clustering-algorithm" style="font-size: 80%;">Basic Idea of the \( k \)-means Clustering Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs012.html#the-k-means-clustering-algorithm" style="font-size: 80%;">The \( k \)-means Clustering Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs013.html#summarizing" style="font-size: 80%;">Summarizing</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs014.html#writing-our-own-code-the-data-set" style="font-size: 80%;">Writing our own Code, the Data Set</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs025.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs043.html#computing-the-gini-index" style="font-size: 80%;">Computing the Gini index</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs044.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs045.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs046.html#entropy-and-the-id3-algorithm" style="font-size: 80%;">Entropy and the ID3 algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs047.html#cancer-data-again-now-with-decision-trees-and-other-methods" style="font-size: 80%;">Cancer Data again now with Decision Trees and other Methods</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs048.html#another-example-the-moons-again" style="font-size: 80%;">Another example, the moons again</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs050.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs051.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs052.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs055.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs059.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs060.html#please-not-the-moons-again-voting-and-bagging" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
<!-- navigation toc: --> <li><a href="._week44-bs061.html#bagging-examples" style="font-size: 80%;">Bagging Examples</a></li>
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<h2 id="making-your-own-bootstrap-changing-the-level-of-the-decision-tree" class="anchor">Making your own Bootstrap: Changing the Level of the Decision Tree </h2>
<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 \( n \)).
</p>
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<pre style="line-height: 125%;"><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.pipeline</span> <span style="color: #008000; font-weight: bold">import</span> make_pipeline
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.utils</span> <span style="color: #008000; font-weight: bold">import</span> resample
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.tree</span> <span style="color: #008000; font-weight: bold">import</span> DecisionTreeRegressor
n <span style="color: #666666">=</span> <span style="color: #666666">100</span>
n_boostraps <span style="color: #666666">=</span> <span style="color: #666666">100</span>
maxdepth <span style="color: #666666">=</span> <span style="color: #666666">8</span>
<span style="color: #408080; font-style: italic"># Make data set.</span>
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">-3</span>, <span style="color: #666666">3</span>, n)<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)
y <span style="color: #666666">=</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>x<span style="color: #666666">**2</span>) <span style="color: #666666">+</span> <span style="color: #666666">1.5</span> <span style="color: #666666">*</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>(x<span style="color: #666666">-2</span>)<span style="color: #666666">**2</span>)<span style="color: #666666">+</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>normal(<span style="color: #666666">0</span>, <span style="color: #666666">0.1</span>, x<span style="color: #666666">.</span>shape)
error <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdepth)
bias <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdepth)
variance <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdepth)
polydegree <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(maxdepth)
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(x, y, test_size<span style="color: #666666">=0.2</span>)
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> StandardScaler
scaler <span style="color: #666666">=</span> StandardScaler()
scaler<span style="color: #666666">.</span>fit(X_train)
X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_train)
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># we produce a simple tree first as benchmark</span>
simpletree <span style="color: #666666">=</span> DecisionTreeRegressor(max_depth<span style="color: #666666">=3</span>)
simpletree<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
simpleprediction <span style="color: #666666">=</span> simpletree<span style="color: #666666">.</span>predict(X_test_scaled)
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>,maxdepth):
model <span style="color: #666666">=</span> DecisionTreeRegressor(max_depth<span style="color: #666666">=</span>degree)
y_pred <span style="color: #666666">=</span> np<span style="color: #666666">.</span>empty((y_test<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>], n_boostraps))
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(n_boostraps):
x_, y_ <span style="color: #666666">=</span> resample(X_train_scaled, y_train)
model<span style="color: #666666">.</span>fit(x_, y_)
y_pred[:, i] <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(X_test_scaled)<span style="color: #408080; font-style: italic">#.ravel()</span>
polydegree[degree] <span style="color: #666666">=</span> degree
error[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( np<span style="color: #666666">.</span>mean((y_test <span style="color: #666666">-</span> y_pred)<span style="color: #666666">**2</span>, axis<span style="color: #666666">=1</span>, keepdims<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>) )
bias[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( (y_test <span style="color: #666666">-</span> np<span style="color: #666666">.</span>mean(y_pred, axis<span style="color: #666666">=1</span>, keepdims<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>))<span style="color: #666666">**2</span> )
variance[degree] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( np<span style="color: #666666">.</span>var(y_pred, axis<span style="color: #666666">=1</span>, keepdims<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>) )
<span style="color: #008000">print</span>(<span style="color: #BA2121">&#39;Polynomial degree:&#39;</span>, degree)
<span style="color: #008000">print</span>(<span style="color: #BA2121">&#39;Error:&#39;</span>, error[degree])
<span style="color: #008000">print</span>(<span style="color: #BA2121">&#39;Bias^2:&#39;</span>, bias[degree])
<span style="color: #008000">print</span>(<span style="color: #BA2121">&#39;Var:&#39;</span>, variance[degree])
<span style="color: #008000">print</span>(<span style="color: #BA2121">&#39;</span><span style="color: #BB6688; font-weight: bold">{}</span><span style="color: #BA2121"> &gt;= </span><span style="color: #BB6688; font-weight: bold">{}</span><span style="color: #BA2121"> + </span><span style="color: #BB6688; font-weight: bold">{}</span><span style="color: #BA2121"> = </span><span style="color: #BB6688; font-weight: bold">{}</span><span style="color: #BA2121">&#39;</span><span style="color: #666666">.</span>format(error[degree], bias[degree], variance[degree], bias[degree]<span style="color: #666666">+</span>variance[degree]))
mse_simpletree<span style="color: #666666">=</span> np<span style="color: #666666">.</span>mean( np<span style="color: #666666">.</span>mean((y_test <span style="color: #666666">-</span> simpleprediction)<span style="color: #666666">**2</span>)
<span style="color: #008000">print</span>(mse_simpletree)
plt<span style="color: #666666">.</span>xlim(<span style="color: #666666">1</span>,maxdepth)
plt<span style="color: #666666">.</span>plot(polydegree, error, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;MSE&#39;</span>)
plt<span style="color: #666666">.</span>plot(polydegree, bias, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;bias&#39;</span>)
plt<span style="color: #666666">.</span>plot(polydegree, variance, label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;Variance&#39;</span>)
plt<span style="color: #666666">.</span>legend()
save_fig(<span style="color: #BA2121">&quot;baggingboot&quot;</span>)
plt<span style="color: #666666">.</span>show()
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