update week 45
This commit is contained in:
mhjensen
+68
-274
@@ -126,81 +126,74 @@ div { text-align: justify; text-justify: inter-word; }
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('An Overview of Ensemble Methods', 2, None, '___sec37'),
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('Bagging', 2, None, '___sec38'),
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('More bagging', 2, None, '___sec39'),
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('Simple Voting Example, head or tail', 2, None, '___sec40'),
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('Using the Voting Classifier', 2, None, '___sec41'),
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('Please, not the moons again! Voting and Bagging',
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2,
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None,
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'___sec42'),
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('Bagging Examples', 2, None, '___sec43'),
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('Making your own Bootstrap: Changing the Level of the Decision '
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'Tree',
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2,
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None,
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'___sec44'),
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('Why Voting?', 2, None, '___sec45'),
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('Tossing coins', 2, None, '___sec46'),
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('Standard imports first', 2, None, '___sec47'),
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('Simple Voting Example, head or tail', 2, None, '___sec48'),
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('Using the Voting Classifier', 2, None, '___sec49'),
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('Voting and Bagging', 2, None, '___sec50'),
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('Random forests', 2, None, '___sec51'),
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('Random Forest Algorithm', 2, None, '___sec52'),
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'___sec40'),
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('Why Voting?', 2, None, '___sec41'),
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('Tossing coins', 2, None, '___sec42'),
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('Standard imports first', 2, None, '___sec43'),
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('Simple Voting Example, head or tail', 2, None, '___sec44'),
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('Using the Voting Classifier', 2, None, '___sec45'),
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('Voting and Bagging', 2, None, '___sec46'),
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('Random forests', 2, None, '___sec47'),
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('Random Forest Algorithm', 2, None, '___sec48'),
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('Random Forests Compared with other Methods on the Cancer Data',
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2,
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None,
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'___sec53'),
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'___sec49'),
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('Compare Bagging on Trees with Random Forests',
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2,
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None,
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'___sec54'),
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("Boosting, a Bird's Eye View", 2, None, '___sec55'),
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'___sec50'),
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("Boosting, a Bird's Eye View", 2, None, '___sec51'),
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('What is boosting? Additive Modelling/Iterative Fitting',
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2,
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None,
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'___sec56'),
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'___sec52'),
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('Iterative Fitting, Regression and Squared-error Cost Function',
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2,
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None,
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'___sec57'),
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'___sec53'),
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('Squared-Error Example and Iterative Fitting',
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2,
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None,
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'___sec58'),
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'___sec54'),
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('Iterative Fitting, Classification and AdaBoost',
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2,
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None,
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'___sec59'),
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('Adaptive Boosting, AdaBoost', 2, None, '___sec60'),
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('Building up AdaBoost', 2, None, '___sec61'),
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'___sec55'),
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('Adaptive Boosting, AdaBoost', 2, None, '___sec56'),
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('Building up AdaBoost', 2, None, '___sec57'),
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('Adaptive boosting: AdaBoost, Basic Algorithm',
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2,
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None,
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'___sec62'),
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('Basic Steps of AdaBoost', 2, None, '___sec63'),
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('AdaBoost Examples', 2, None, '___sec64'),
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'___sec58'),
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('Basic Steps of AdaBoost', 2, None, '___sec59'),
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('AdaBoost Examples', 2, None, '___sec60'),
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('Gradient boosting: Basics with Steepest Descent/Functional '
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'Gradient Descent',
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2,
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None,
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'___sec65'),
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'___sec61'),
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('The Squared-Error again! Steepest Descent',
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2,
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None,
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'___sec66'),
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('Steepest Descent Example', 2, None, '___sec67'),
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('Gradient Boosting, algorithm', 2, None, '___sec68'),
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'___sec62'),
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('Steepest Descent Example', 2, None, '___sec63'),
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('Gradient Boosting, algorithm', 2, None, '___sec64'),
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('Gradient Boosting, Examples of Regression',
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2,
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None,
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'___sec69'),
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'___sec65'),
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('Gradient Boosting, Classification Example',
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2,
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None,
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'___sec70'),
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('XGBoost: Extreme Gradient Boosting', 2, None, '___sec71'),
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('Regression Case', 2, None, '___sec72'),
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('Xgboost on the Cancer Data', 2, None, '___sec73')]}
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'___sec66'),
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('XGBoost: Extreme Gradient Boosting', 2, None, '___sec67'),
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('Regression Case', 2, None, '___sec68'),
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('Xgboost on the Cancer Data', 2, None, '___sec69')]}
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end of tocinfo -->
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<body>
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@@ -1539,200 +1532,7 @@ predictor, averaged over all \( B \) trees.
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<p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="___sec40">Simple Voting Example, head or tail </h2>
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>heads_proba <span style="color: #666666">=</span> <span style="color: #666666">0.51</span>
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coin_tosses <span style="color: #666666">=</span> (np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(<span style="color: #666666">10000</span>, <span style="color: #666666">10</span>) <span style="color: #666666"><</span> heads_proba)<span style="color: #666666">.</span>astype(np<span style="color: #666666">.</span>int32)
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cumulative_heads_ratio <span style="color: #666666">=</span> np<span style="color: #666666">.</span>cumsum(coin_tosses, axis<span style="color: #666666">=0</span>) <span style="color: #666666">/</span> np<span style="color: #666666">.</span>arange(<span style="color: #666666">1</span>, <span style="color: #666666">10001</span>)<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)
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plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">8</span>,<span style="color: #666666">3.5</span>))
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plt<span style="color: #666666">.</span>plot(cumulative_heads_ratio)
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plt<span style="color: #666666">.</span>plot([<span style="color: #666666">0</span>, <span style="color: #666666">10000</span>], [<span style="color: #666666">0.51</span>, <span style="color: #666666">0.51</span>], <span style="color: #BA2121">"k--"</span>, linewidth<span style="color: #666666">=2</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"51%"</span>)
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plt<span style="color: #666666">.</span>plot([<span style="color: #666666">0</span>, <span style="color: #666666">10000</span>], [<span style="color: #666666">0.5</span>, <span style="color: #666666">0.5</span>], <span style="color: #BA2121">"k-"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"50%"</span>)
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plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">"Number of coin tosses"</span>)
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plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"Heads ratio"</span>)
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plt<span style="color: #666666">.</span>legend(loc<span style="color: #666666">=</span><span style="color: #BA2121">"lower right"</span>)
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plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0</span>, <span style="color: #666666">10000</span>, <span style="color: #666666">0.42</span>, <span style="color: #666666">0.58</span>])
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save_fig(<span style="color: #BA2121">"votingsimple"</span>)
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plt<span style="color: #666666">.</span>show()
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</pre></div>
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<p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="___sec41">Using the Voting Classifier </h2>
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></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
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> make_moons
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X, y <span style="color: #666666">=</span> make_moons(n_samples<span style="color: #666666">=500</span>, noise<span style="color: #666666">=0.30</span>, random_state<span style="color: #666666">=42</span>)
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X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(X, y, random_state<span style="color: #666666">=42</span>)
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<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> RandomForestClassifier
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<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> VotingClassifier
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LogisticRegression
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.svm</span> <span style="color: #008000; font-weight: bold">import</span> SVC
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log_clf <span style="color: #666666">=</span> LogisticRegression(solver<span style="color: #666666">=</span><span style="color: #BA2121">"liblinear"</span>, random_state<span style="color: #666666">=42</span>)
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rnd_clf <span style="color: #666666">=</span> RandomForestClassifier(n_estimators<span style="color: #666666">=10</span>, random_state<span style="color: #666666">=42</span>)
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svm_clf <span style="color: #666666">=</span> SVC(gamma<span style="color: #666666">=</span><span style="color: #BA2121">"auto"</span>, random_state<span style="color: #666666">=42</span>)
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voting_clf <span style="color: #666666">=</span> VotingClassifier(
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estimators<span style="color: #666666">=</span>[(<span style="color: #BA2121">'lr'</span>, log_clf), (<span style="color: #BA2121">'rf'</span>, rnd_clf), (<span style="color: #BA2121">'svc'</span>, svm_clf)],
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voting<span style="color: #666666">=</span><span style="color: #BA2121">'hard'</span>)
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voting_clf<span style="color: #666666">.</span>fit(X_train, y_train)
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<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
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<span style="color: #008000; font-weight: bold">for</span> clf <span style="color: #AA22FF; font-weight: bold">in</span> (log_clf, rnd_clf, svm_clf, voting_clf):
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clf<span style="color: #666666">.</span>fit(X_train, y_train)
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y_pred <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(X_test)
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<span style="color: #008000">print</span>(clf<span style="color: #666666">.</span><span style="color: #19177C">__class__</span><span style="color: #666666">.</span><span style="color: #19177C">__name__</span>, accuracy_score(y_test, y_pred))
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log_clf <span style="color: #666666">=</span> LogisticRegression(solver<span style="color: #666666">=</span><span style="color: #BA2121">"liblinear"</span>, random_state<span style="color: #666666">=42</span>)
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rnd_clf <span style="color: #666666">=</span> RandomForestClassifier(n_estimators<span style="color: #666666">=10</span>, random_state<span style="color: #666666">=42</span>)
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svm_clf <span style="color: #666666">=</span> SVC(gamma<span style="color: #666666">=</span><span style="color: #BA2121">"auto"</span>, probability<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>, random_state<span style="color: #666666">=42</span>)
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voting_clf <span style="color: #666666">=</span> VotingClassifier(
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estimators<span style="color: #666666">=</span>[(<span style="color: #BA2121">'lr'</span>, log_clf), (<span style="color: #BA2121">'rf'</span>, rnd_clf), (<span style="color: #BA2121">'svc'</span>, svm_clf)],
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voting<span style="color: #666666">=</span><span style="color: #BA2121">'soft'</span>)
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voting_clf<span style="color: #666666">.</span>fit(X_train, y_train)
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<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
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<span style="color: #008000; font-weight: bold">for</span> clf <span style="color: #AA22FF; font-weight: bold">in</span> (log_clf, rnd_clf, svm_clf, voting_clf):
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clf<span style="color: #666666">.</span>fit(X_train, y_train)
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y_pred <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(X_test)
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<span style="color: #008000">print</span>(clf<span style="color: #666666">.</span><span style="color: #19177C">__class__</span><span style="color: #666666">.</span><span style="color: #19177C">__name__</span>, accuracy_score(y_test, y_pred))
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</pre></div>
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<p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="___sec42">Please, not the moons again! Voting and Bagging </h2>
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></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
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> make_moons
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X, y <span style="color: #666666">=</span> make_moons(n_samples<span style="color: #666666">=500</span>, noise<span style="color: #666666">=0.30</span>, random_state<span style="color: #666666">=42</span>)
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X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(X, y, random_state<span style="color: #666666">=42</span>)
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<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> RandomForestClassifier
|
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<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> VotingClassifier
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LogisticRegression
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.svm</span> <span style="color: #008000; font-weight: bold">import</span> SVC
|
||||
|
||||
log_clf <span style="color: #666666">=</span> LogisticRegression(random_state<span style="color: #666666">=42</span>)
|
||||
rnd_clf <span style="color: #666666">=</span> RandomForestClassifier(random_state<span style="color: #666666">=42</span>)
|
||||
svm_clf <span style="color: #666666">=</span> SVC(random_state<span style="color: #666666">=42</span>)
|
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|
||||
voting_clf <span style="color: #666666">=</span> VotingClassifier(
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estimators<span style="color: #666666">=</span>[(<span style="color: #BA2121">'lr'</span>, log_clf), (<span style="color: #BA2121">'rf'</span>, rnd_clf), (<span style="color: #BA2121">'svc'</span>, svm_clf)],
|
||||
voting<span style="color: #666666">=</span><span style="color: #BA2121">'hard'</span>)
|
||||
voting_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
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</pre></div>
|
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<p>
|
||||
|
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.metrics</span> <span style="color: #008000; font-weight: bold">import</span> accuracy_score
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> clf <span style="color: #AA22FF; font-weight: bold">in</span> (log_clf, rnd_clf, svm_clf, voting_clf):
|
||||
clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
y_pred <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(X_test)
|
||||
<span style="color: #008000">print</span>(clf<span style="color: #666666">.</span><span style="color: #19177C">__class__</span><span style="color: #666666">.</span><span style="color: #19177C">__name__</span>, accuracy_score(y_test, y_pred))
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>log_clf <span style="color: #666666">=</span> LogisticRegression(random_state<span style="color: #666666">=42</span>)
|
||||
rnd_clf <span style="color: #666666">=</span> RandomForestClassifier(random_state<span style="color: #666666">=42</span>)
|
||||
svm_clf <span style="color: #666666">=</span> SVC(probability<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>, random_state<span style="color: #666666">=42</span>)
|
||||
|
||||
voting_clf <span style="color: #666666">=</span> VotingClassifier(
|
||||
estimators<span style="color: #666666">=</span>[(<span style="color: #BA2121">'lr'</span>, log_clf), (<span style="color: #BA2121">'rf'</span>, rnd_clf), (<span style="color: #BA2121">'svc'</span>, svm_clf)],
|
||||
voting<span style="color: #666666">=</span><span style="color: #BA2121">'soft'</span>)
|
||||
voting_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">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; font-weight: bold">for</span> clf <span style="color: #AA22FF; font-weight: bold">in</span> (log_clf, rnd_clf, svm_clf, voting_clf):
|
||||
clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
y_pred <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(X_test)
|
||||
<span style="color: #008000">print</span>(clf<span style="color: #666666">.</span><span style="color: #19177C">__class__</span><span style="color: #666666">.</span><span style="color: #19177C">__name__</span>, accuracy_score(y_test, y_pred))
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec43">Bagging Examples </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">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)
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">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))
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>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></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">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">'#fafab0'</span>,<span style="color: #BA2121">'#9898ff'</span>,<span style="color: #BA2121">'#a0faa0'</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">'#7d7d58'</span>,<span style="color: #BA2121">'#4c4c7f'</span>,<span style="color: #BA2121">'#507d50'</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">"yo"</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">"bs"</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"$x_1$"</span>, fontsize<span style="color: #666666">=18</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">r"$x_2$"</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">"Decision Tree"</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">"Decision Trees with Bagging"</span>, fontsize<span style="color: #666666">=14</span>)
|
||||
save_fig(<span style="color: #BA2121">"baggingtree"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec44">Making your own Bootstrap: Changing the Level of the Decision Tree </h2>
|
||||
<h2 id="___sec40">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
|
||||
@@ -1747,9 +1547,9 @@ a decision tree wth different depths and perform a bootstrap aggregate (in this
|
||||
<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 <span style="color: #666666">=</span> <span style="color: #666666">1000</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>
|
||||
maxdepth <span style="color: #666666">=</span> <span style="color: #666666">10</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>)
|
||||
@@ -1760,23 +1560,17 @@ variance <span style="color: #666666">=</span> np<span style="color: #666666">.<
|
||||
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>
|
||||
<span style="color: #408080; font-style: italic"># we produce a simple tree first as benchmark, no scaling</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)
|
||||
simpletree<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
simpleprediction <span style="color: #666666">=</span> simpletree<span style="color: #666666">.</span>predict(X_test)
|
||||
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<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)
|
||||
x_, y_ <span style="color: #666666">=</span> resample(X_train, 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>
|
||||
y_pred[:, i] <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(X_test)<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>) )
|
||||
@@ -1788,7 +1582,7 @@ simpleprediction <span style="color: #666666">=</span> simpletree<span style="co
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">'Var:'</span>, variance[degree])
|
||||
<span style="color: #008000">print</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"> + </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: #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>)
|
||||
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">'MSE'</span>)
|
||||
@@ -1801,7 +1595,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec45">Why Voting? </h2>
|
||||
<h2 id="___sec41">Why Voting? </h2>
|
||||
|
||||
<p>
|
||||
The idea behind boosting, and voting as well can be phrased as follows:
|
||||
@@ -1824,7 +1618,7 @@ Decision trees play an important role as our weak classifier. They serve as the
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec46">Tossing coins </h2>
|
||||
<h2 id="___sec42">Tossing coins </h2>
|
||||
|
||||
<p>
|
||||
The simplest case is a so-called voting ensemble. To illustrate this,
|
||||
@@ -1854,7 +1648,7 @@ numbers kicking in.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec47">Standard imports first </h2>
|
||||
<h2 id="___sec43">Standard imports first </h2>
|
||||
|
||||
<p>
|
||||
|
||||
@@ -1900,7 +1694,7 @@ DATA_ID <span style="color: #666666">=</span> <span style="color: #BA2121">"
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec48">Simple Voting Example, head or tail </h2>
|
||||
<h2 id="___sec44">Simple Voting Example, head or tail </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
@@ -1930,7 +1724,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec49">Using the Voting Classifier </h2>
|
||||
<h2 id="___sec45">Using the Voting Classifier </h2>
|
||||
|
||||
<p>
|
||||
We can use the voting classifier on other data sets, here the exciting binary case of two distinct objects using the make moons functionality of <b>Scikit-Learn</b>.
|
||||
@@ -1983,7 +1777,7 @@ voting_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec50">Voting and Bagging </h2>
|
||||
<h2 id="___sec46">Voting and Bagging </h2>
|
||||
|
||||
<p>
|
||||
|
||||
@@ -2042,7 +1836,7 @@ voting_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec51">Random forests </h2>
|
||||
<h2 id="___sec47">Random forests </h2>
|
||||
|
||||
<p>
|
||||
Random forests provide an improvement over bagged trees by way of a
|
||||
@@ -2086,7 +1880,7 @@ this setting.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec52">Random Forest Algorithm </h2>
|
||||
<h2 id="___sec48">Random Forest Algorithm </h2>
|
||||
The algorithm described here can be applied to both classification and regression problems.
|
||||
|
||||
<p>
|
||||
@@ -2112,7 +1906,7 @@ We will grow of forest of say \( B \) trees.
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec53">Random Forests Compared with other Methods on the Cancer Data </h2>
|
||||
<h2 id="___sec49">Random Forests Compared with other Methods on the Cancer Data </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
@@ -2196,7 +1990,7 @@ discrimination threshold is varied. It plots the true positive rate against the
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec54">Compare Bagging on Trees with Random Forests </h2>
|
||||
<h2 id="___sec50">Compare Bagging on Trees with Random Forests </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
@@ -2218,7 +2012,7 @@ np<span style="color: #666666">.</span>sum(y_pred <span style="color: #666666">=
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec55">Boosting, a Bird's Eye View </h2>
|
||||
<h2 id="___sec51">Boosting, a Bird's Eye View </h2>
|
||||
|
||||
<p>
|
||||
The basic idea is to combine weak classifiers in order to create a good
|
||||
@@ -2235,7 +2029,7 @@ them with a factor.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec56">What is boosting? Additive Modelling/Iterative Fitting </h2>
|
||||
<h2 id="___sec52">What is boosting? Additive Modelling/Iterative Fitting </h2>
|
||||
|
||||
<p>
|
||||
Boosting is a way of fitting an additive expansion in a set of
|
||||
@@ -2287,7 +2081,7 @@ In iterative fitting or additive modeling, we minimize the cost function with re
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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||||
|
||||
<h2 id="___sec57">Iterative Fitting, Regression and Squared-error Cost Function </h2>
|
||||
<h2 id="___sec53">Iterative Fitting, Regression and Squared-error Cost Function </h2>
|
||||
|
||||
<p>
|
||||
The way we proceed is as follows (here we specialize to the squared-error cost function)
|
||||
@@ -2312,7 +2106,7 @@ at the internal nodes, and the predictions at the terminal nodes.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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||||
|
||||
<h2 id="___sec58">Squared-Error Example and Iterative Fitting </h2>
|
||||
<h2 id="___sec54">Squared-Error Example and Iterative Fitting </h2>
|
||||
|
||||
<p>
|
||||
To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.
|
||||
@@ -2360,7 +2154,7 @@ The solution to these two equations gives us in turn \( \beta_1 \) and \( \gamma
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec59">Iterative Fitting, Classification and AdaBoost </h2>
|
||||
<h2 id="___sec55">Iterative Fitting, Classification and AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
|
||||
@@ -2395,7 +2189,7 @@ $$
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec60">Adaptive Boosting, AdaBoost </h2>
|
||||
<h2 id="___sec56">Adaptive Boosting, AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
In our iterative procedure we define thus
|
||||
@@ -2423,7 +2217,7 @@ where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \).
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec61">Building up AdaBoost </h2>
|
||||
<h2 id="___sec57">Building up AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
First, for any \( \beta > 0 \), we optimize \( G \) by setting
|
||||
@@ -2467,7 +2261,7 @@ $$
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec62">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
<h2 id="___sec58">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
|
||||
<p>
|
||||
The algorithm here is rather straightforward. Assume that our weak
|
||||
@@ -2489,7 +2283,7 @@ where the function \( I() \) is one if we misclassify and zero if we classify co
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec63">Basic Steps of AdaBoost </h2>
|
||||
<h2 id="___sec59">Basic Steps of AdaBoost </h2>
|
||||
|
||||
<p>
|
||||
With the above definitions we are now ready to set up the algorithm for AdaBoost.
|
||||
@@ -2529,7 +2323,7 @@ observations that are missed in the previous iterations.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec64">AdaBoost Examples </h2>
|
||||
<h2 id="___sec60">AdaBoost Examples </h2>
|
||||
|
||||
<p>
|
||||
Using <b>Scikit-Learn</b> it is easy to apply the adaptive boosting algorithm, as done here.
|
||||
@@ -2562,7 +2356,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec65">Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent </h2>
|
||||
<h2 id="___sec61">Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent </h2>
|
||||
|
||||
<p>
|
||||
Gradient boosting is again a similar technique to Adaptive boosting,
|
||||
@@ -2577,7 +2371,7 @@ function was the least squares function.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec66">The Squared-Error again! Steepest Descent </h2>
|
||||
<h2 id="___sec62">The Squared-Error again! Steepest Descent </h2>
|
||||
|
||||
<p>
|
||||
We start again with our cost function \( {\cal C}(\boldsymbol{y}m\boldsymbol{f})=\sum_{i=0}^{n-1}{\cal L}(y_i, f(x_i)) \) where we want to minimize
|
||||
@@ -2612,7 +2406,7 @@ $$
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec67">Steepest Descent Example </h2>
|
||||
<h2 id="___sec63">Steepest Descent Example </h2>
|
||||
|
||||
<p>
|
||||
Optimizing with respect to \( \rho \) we obtain (taking the derivative) that \( \rho_1 = -1/2 \). We have then that
|
||||
@@ -2630,7 +2424,7 @@ and find a new value for \( \rho_2=-1/2 \) and continue till we have reached \(
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec68">Gradient Boosting, algorithm </h2>
|
||||
<h2 id="___sec64">Gradient Boosting, algorithm </h2>
|
||||
|
||||
<p>
|
||||
Steepest descent is however not much used, since it only optimizes \( f \) at a fixed set of \( n \) points,
|
||||
@@ -2661,7 +2455,7 @@ The way we proceed in an iterative fashion is to
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec69">Gradient Boosting, Examples of Regression </h2>
|
||||
<h2 id="___sec65">Gradient Boosting, Examples of Regression </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
@@ -2715,7 +2509,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec70">Gradient Boosting, Classification Example </h2>
|
||||
<h2 id="___sec66">Gradient Boosting, Classification Example </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
@@ -2763,7 +2557,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec71">XGBoost: Extreme Gradient Boosting </h2>
|
||||
<h2 id="___sec67">XGBoost: Extreme Gradient Boosting </h2>
|
||||
|
||||
<p>
|
||||
<a href="https://github.com/dmlc/xgboost" target="_blank">XGBoost</a> or Extreme Gradient
|
||||
@@ -2784,7 +2578,7 @@ It is now the algorithm which wins essentially all ML competitions!!!
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec72">Regression Case </h2>
|
||||
<h2 id="___sec68">Regression Case </h2>
|
||||
|
||||
<p>
|
||||
|
||||
@@ -2839,7 +2633,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec73">Xgboost on the Cancer Data </h2>
|
||||
<h2 id="___sec69">Xgboost on the Cancer Data </h2>
|
||||
|
||||
<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.
|
||||
|
||||
Reference in New Issue
Block a user