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<div class="sphx-glr-example-title section" id="feature-transformations-with-ensembles-of-trees">
<span id="sphx-glr-auto-examples-ensemble-plot-feature-transformation-py"></span><h1>Feature transformations with ensembles of trees<a class="headerlink" href="#feature-transformations-with-ensembles-of-trees" title="Permalink to this headline">¶</a></h1>
<p>Transform your features into a higher dimensional, sparse space. Then
train a linear model on these features.</p>
<p>First fit an ensemble of trees (totally random trees, a random
forest, or gradient boosted trees) on the training set. Then each leaf
of each tree in the ensemble is assigned a fixed arbitrary feature
index in a new feature space. These leaf indices are then encoded in a
one-hot fashion.</p>
<p>Each sample goes through the decisions of each tree of the ensemble
and ends up in one leaf per tree. The sample is encoded by setting
feature values for these leaves to 1 and the other feature values to 0.</p>
<p>The resulting transformer has then learned a supervised, sparse,
high-dimensional categorical embedding of the data.</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># Author: Tim Head <[email protected]></span>
<span class="c1">#</span>
<span class="c1"># License: BSD 3 clause</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">10</span><span class="p">)</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">from</span> <span class="nn">sklearn.datasets</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.datasets.make_classification.html#sklearn.datasets.make_classification" title="View documentation for sklearn.datasets.make_classification"><span class="n">make_classification</span></a>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="View documentation for sklearn.linear_model.LogisticRegression"><span class="n">LogisticRegression</span></a>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="k">import</span> <span class="p">(</span><a href="../../modules/generated/sklearn.ensemble.RandomTreesEmbedding.html#sklearn.ensemble.RandomTreesEmbedding" title="View documentation for sklearn.ensemble.RandomTreesEmbedding"><span class="n">RandomTreesEmbedding</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="View documentation for sklearn.ensemble.RandomForestClassifier"><span class="n">RandomForestClassifier</span></a><span class="p">,</span>
<a href="../../modules/generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="View documentation for sklearn.ensemble.GradientBoostingClassifier"><span class="n">GradientBoostingClassifier</span></a><span class="p">)</span>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.preprocessing.OneHotEncoder.html#sklearn.preprocessing.OneHotEncoder" title="View documentation for sklearn.preprocessing.OneHotEncoder"><span class="n">OneHotEncoder</span></a>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="View documentation for sklearn.model_selection.train_test_split"><span class="n">train_test_split</span></a>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.metrics.roc_curve.html#sklearn.metrics.roc_curve" title="View documentation for sklearn.metrics.roc_curve"><span class="n">roc_curve</span></a>
<span class="kn">from</span> <span class="nn">sklearn.pipeline</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="View documentation for sklearn.pipeline.make_pipeline"><span class="n">make_pipeline</span></a>
<span class="n">n_estimator</span> <span class="o">=</span> <span class="mi">10</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.make_classification.html#sklearn.datasets.make_classification" title="View documentation for sklearn.datasets.make_classification"><span class="n">make_classification</span></a><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">80000</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> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="View documentation for sklearn.model_selection.train_test_split"><span class="n">train_test_split</span></a><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">0.5</span><span class="p">)</span>
<span class="c1"># It is important to train the ensemble of trees on a different subset</span>
<span class="c1"># of the training data than the linear regression model to avoid</span>
<span class="c1"># overfitting, in particular if the total number of leaves is</span>
<span class="c1"># similar to the number of training samples</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_train_lr</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_train_lr</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="View documentation for sklearn.model_selection.train_test_split"><span class="n">train_test_split</span></a><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">test_size</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<span class="c1"># Unsupervised transformation based on totally random trees</span>
<span class="n">rt</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.RandomTreesEmbedding.html#sklearn.ensemble.RandomTreesEmbedding" title="View documentation for sklearn.ensemble.RandomTreesEmbedding"><span class="n">RandomTreesEmbedding</span></a><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="n">n_estimator</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="n">rt_lm</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="View documentation for sklearn.linear_model.LogisticRegression"><span class="n">LogisticRegression</span></a><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">max_iter</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span>
<span class="n">pipeline</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="View documentation for sklearn.pipeline.make_pipeline"><span class="n">make_pipeline</span></a><span class="p">(</span><span class="n">rt</span><span class="p">,</span> <span class="n">rt_lm</span><span class="p">)</span>
<span class="n">pipeline</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_rt</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)[:,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">fpr_rt_lm</span><span class="p">,</span> <span class="n">tpr_rt_lm</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.roc_curve.html#sklearn.metrics.roc_curve" title="View documentation for sklearn.metrics.roc_curve"><span class="n">roc_curve</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred_rt</span><span class="p">)</span>
<span class="c1"># Supervised transformation based on random forests</span>
<span class="n">rf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="View documentation for sklearn.ensemble.RandomForestClassifier"><span class="n">RandomForestClassifier</span></a><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="n">n_estimator</span><span class="p">)</span>
<span class="n">rf_enc</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.preprocessing.OneHotEncoder.html#sklearn.preprocessing.OneHotEncoder" title="View documentation for sklearn.preprocessing.OneHotEncoder"><span class="n">OneHotEncoder</span></a><span class="p">(</span><span class="n">categories</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span>
<span class="n">rf_lm</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="View documentation for sklearn.linear_model.LogisticRegression"><span class="n">LogisticRegression</span></a><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">max_iter</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span>
<span class="n">rf</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">rf_enc</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">rf</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">X_train</span><span class="p">))</span>
<span class="n">rf_lm</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">rf_enc</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">rf</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">X_train_lr</span><span class="p">)),</span> <span class="n">y_train_lr</span><span class="p">)</span>
<span class="n">y_pred_rf_lm</span> <span class="o">=</span> <span class="n">rf_lm</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">rf_enc</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">rf</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">X_test</span><span class="p">)))[:,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">fpr_rf_lm</span><span class="p">,</span> <span class="n">tpr_rf_lm</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.roc_curve.html#sklearn.metrics.roc_curve" title="View documentation for sklearn.metrics.roc_curve"><span class="n">roc_curve</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred_rf_lm</span><span class="p">)</span>
<span class="c1"># Supervised transformation based on gradient boosted trees</span>
<span class="n">grd</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="View documentation for sklearn.ensemble.GradientBoostingClassifier"><span class="n">GradientBoostingClassifier</span></a><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="n">n_estimator</span><span class="p">)</span>
<span class="n">grd_enc</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.preprocessing.OneHotEncoder.html#sklearn.preprocessing.OneHotEncoder" title="View documentation for sklearn.preprocessing.OneHotEncoder"><span class="n">OneHotEncoder</span></a><span class="p">(</span><span class="n">categories</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span>
<span class="n">grd_lm</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="View documentation for sklearn.linear_model.LogisticRegression"><span class="n">LogisticRegression</span></a><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">max_iter</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span>
<span class="n">grd</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">grd_enc</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">grd</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">X_train</span><span class="p">)[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">])</span>
<span class="n">grd_lm</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">grd_enc</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">grd</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">X_train_lr</span><span class="p">)[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">]),</span> <span class="n">y_train_lr</span><span class="p">)</span>
<span class="n">y_pred_grd_lm</span> <span class="o">=</span> <span class="n">grd_lm</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span>
<span class="n">grd_enc</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">grd</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">X_test</span><span class="p">)[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">]))[:,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">fpr_grd_lm</span><span class="p">,</span> <span class="n">tpr_grd_lm</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.roc_curve.html#sklearn.metrics.roc_curve" title="View documentation for sklearn.metrics.roc_curve"><span class="n">roc_curve</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred_grd_lm</span><span class="p">)</span>
<span class="c1"># The gradient boosted model by itself</span>
<span class="n">y_pred_grd</span> <span class="o">=</span> <span class="n">grd</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)[:,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">fpr_grd</span><span class="p">,</span> <span class="n">tpr_grd</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.roc_curve.html#sklearn.metrics.roc_curve" title="View documentation for sklearn.metrics.roc_curve"><span class="n">roc_curve</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred_grd</span><span class="p">)</span>
<span class="c1"># The random forest model by itself</span>
<span class="n">y_pred_rf</span> <span class="o">=</span> <span class="n">rf</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)[:,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">fpr_rf</span><span class="p">,</span> <span class="n">tpr_rf</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.roc_curve.html#sklearn.metrics.roc_curve" title="View documentation for sklearn.metrics.roc_curve"><span class="n">roc_curve</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred_rf</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="View documentation for matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'k--'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">fpr_rt_lm</span><span class="p">,</span> <span class="n">tpr_rt_lm</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'RT + LR'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">fpr_rf</span><span class="p">,</span> <span class="n">tpr_rf</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'RF'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">fpr_rf_lm</span><span class="p">,</span> <span class="n">tpr_rf_lm</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'RF + LR'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">fpr_grd</span><span class="p">,</span> <span class="n">tpr_grd</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'GBT'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">fpr_grd_lm</span><span class="p">,</span> <span class="n">tpr_grd_lm</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'GBT + LR'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s1">'False positive rate'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="View documentation for matplotlib.pyplot.ylabel"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s1">'True positive rate'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'ROC curve'</span><span class="p">)</span>
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<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="View documentation for matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="View documentation for matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlim.html#matplotlib.pyplot.xlim" title="View documentation for matplotlib.pyplot.xlim"><span class="n">plt</span><span class="o">.</span><span class="n">xlim</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylim.html#matplotlib.pyplot.ylim" title="View documentation for matplotlib.pyplot.ylim"><span class="n">plt</span><span class="o">.</span><span class="n">ylim</span></a><span class="p">(</span><span class="mf">0.8</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'k--'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">fpr_rt_lm</span><span class="p">,</span> <span class="n">tpr_rt_lm</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'RT + LR'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">fpr_rf</span><span class="p">,</span> <span class="n">tpr_rf</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'RF'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">fpr_rf_lm</span><span class="p">,</span> <span class="n">tpr_rf_lm</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'RF + LR'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">fpr_grd</span><span class="p">,</span> <span class="n">tpr_grd</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'GBT'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">fpr_grd_lm</span><span class="p">,</span> <span class="n">tpr_grd_lm</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'GBT + LR'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s1">'False positive rate'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="View documentation for matplotlib.pyplot.ylabel"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s1">'True positive rate'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'ROC curve (zoomed in at top left)'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="View documentation for matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">'best'</span><span class="p">)</span>
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