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<li><a class="reference internal" href="#">Receiver Operating Characteristic (ROC) with cross validation</a><ul>
<li><a class="reference internal" href="#load-and-prepare-data">Load and prepare data</a><ul>
<li><a class="reference internal" href="#classification-and-roc-analysis">Classification and ROC analysis</a></li>
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<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#sphx-glr-download-auto-examples-model-selection-plot-roc-crossval-py"><span class="std std-ref">Go to the end</span></a>
to download the full example code or to run this example in your browser via JupyterLite or Binder</p>
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<section class="sphx-glr-example-title" id="receiver-operating-characteristic-roc-with-cross-validation">
<span id="sphx-glr-auto-examples-model-selection-plot-roc-crossval-py"></span><h1>Receiver Operating Characteristic (ROC) with cross validation<a class="headerlink" href="#receiver-operating-characteristic-roc-with-cross-validation" title="Link to this heading">¶</a></h1>
<p>This example presents how to estimate and visualize the variance of the Receiver
Operating Characteristic (ROC) metric using cross-validation.</p>
<p>ROC curves typically feature true positive rate (TPR) on the Y axis, and false
positive rate (FPR) on the X axis. This means that the top left corner of the
plot is the “ideal” point - a FPR of zero, and a TPR of one. This is not very
realistic, but it does mean that a larger Area Under the Curve (AUC) is usually
better. The “steepness” of ROC curves is also important, since it is ideal to
maximize the TPR while minimizing the FPR.</p>
<p>This example shows the ROC response of different datasets, created from K-fold
cross-validation. Taking all of these curves, it is possible to calculate the
mean AUC, and see the variance of the curve when the
training set is split into different subsets. This roughly shows how the
classifier output is affected by changes in the training data, and how different
the splits generated by K-fold cross-validation are from one another.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>See <a class="reference internal" href="plot_roc.html#sphx-glr-auto-examples-model-selection-plot-roc-py"><span class="std std-ref">Multiclass Receiver Operating Characteristic (ROC)</span></a> for a
complement of the present example explaining the averaging strategies to
generalize the metrics for multiclass classifiers.</p>
</div>
<section id="load-and-prepare-data">
<h2>Load and prepare data<a class="headerlink" href="#load-and-prepare-data" title="Link to this heading">¶</a></h2>
<p>We import the <a class="reference internal" href="../../datasets/toy_dataset.html#iris-dataset"><span class="std std-ref">Iris plants dataset</span></a> which contains 3 classes, each one
corresponding to a type of iris plant. One class is linearly separable from
the other 2; the latter are <strong>not</strong> linearly separable from each other.</p>
<p>In the following we binarize the dataset by dropping the “virginica” class
(<code class="docutils literal notranslate"><span class="pre">class_id=2</span></code>). This means that the “versicolor” class (<code class="docutils literal notranslate"><span class="pre">class_id=1</span></code>) is
regarded as the positive class and “setosa” as the negative class
(<code class="docutils literal notranslate"><span class="pre">class_id=0</span></code>).</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="sklearn.datasets.load_iris" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">load_iris</span></a>
<span class="n">iris</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="sklearn.datasets.load_iris" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">load_iris</span></a><span class="p">()</span>
<span class="n">target_names</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target_names</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">y</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">y</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">]</span>
<span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">shape</span>
</pre></div>
</div>
<p>We also add noisy features to make the problem harder.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">random_state</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/legacy.html#numpy.random.RandomState" title="numpy.random.RandomState" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span></a><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.concatenate.html#numpy.concatenate" title="numpy.concatenate" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span></a><span class="p">([</span><span class="n">X</span><span class="p">,</span> <span class="n">random_state</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="mi">200</span> <span class="o">*</span> <span class="n">n_features</span><span class="p">)],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<section id="classification-and-roc-analysis">
<h3>Classification and ROC analysis<a class="headerlink" href="#classification-and-roc-analysis" title="Link to this heading">¶</a></h3>
<p>Here we run a <a class="reference internal" href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="sklearn.svm.SVC"><code class="xref py py-class docutils literal notranslate"><span class="pre">SVC</span></code></a> classifier with cross-validation and
plot the ROC curves fold-wise. Notice that the baseline to define the chance
level (dashed ROC curve) is a classifier that would always predict the most
frequent class.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">svm</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">RocCurveDisplay</span><span class="p">,</span> <a href="../../modules/generated/sklearn.metrics.auc.html#sklearn.metrics.auc" title="sklearn.metrics.auc" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">auc</span></a>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.model_selection.StratifiedKFold.html#sklearn.model_selection.StratifiedKFold" title="sklearn.model_selection.StratifiedKFold" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StratifiedKFold</span></a>
<span class="n">n_splits</span> <span class="o">=</span> <span class="mi">6</span>
<span class="n">cv</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.StratifiedKFold.html#sklearn.model_selection.StratifiedKFold" title="sklearn.model_selection.StratifiedKFold" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StratifiedKFold</span></a><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="n">n_splits</span><span class="p">)</span>
<span class="n">classifier</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="sklearn.svm.SVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">svm</span><span class="o">.</span><span class="n">SVC</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"linear"</span><span class="p">,</span> <span class="n">probability</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="n">random_state</span><span class="p">)</span>
<span class="n">tprs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">aucs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">mean_fpr</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">linspace</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="mi">100</span><span class="p">)</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">))</span>
<span class="k">for</span> <span class="n">fold</span><span class="p">,</span> <span class="p">(</span><span class="n">train</span><span class="p">,</span> <span class="n">test</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">cv</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)):</span>
<span class="n">classifier</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">train</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">train</span><span class="p">])</span>
<span class="n">viz</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.RocCurveDisplay.html#sklearn.metrics.RocCurveDisplay.from_estimator" title="sklearn.metrics.RocCurveDisplay.from_estimator" class="sphx-glr-backref-module-sklearn-metrics-RocCurveDisplay sphx-glr-backref-type-py-method"><span class="n">RocCurveDisplay</span><span class="o">.</span><span class="n">from_estimator</span></a><span class="p">(</span>
<span class="n">classifier</span><span class="p">,</span>
<span class="n">X</span><span class="p">[</span><span class="n">test</span><span class="p">],</span>
<span class="n">y</span><span class="p">[</span><span class="n">test</span><span class="p">],</span>
<span class="n">name</span><span class="o">=</span><span class="sa">f</span><span class="s2">"ROC fold </span><span class="si">{</span><span class="n">fold</span><span class="si">}</span><span class="s2">"</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span>
<span class="n">lw</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">,</span>
<span class="n">plot_chance_level</span><span class="o">=</span><span class="p">(</span><span class="n">fold</span> <span class="o">==</span> <span class="n">n_splits</span> <span class="o">-</span> <span class="mi">1</span><span class="p">),</span>
<span class="p">)</span>
<span class="n">interp_tpr</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.interp.html#numpy.interp" title="numpy.interp" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">interp</span></a><span class="p">(</span><span class="n">mean_fpr</span><span class="p">,</span> <span class="n">viz</span><span class="o">.</span><span class="n">fpr</span><span class="p">,</span> <span class="n">viz</span><span class="o">.</span><span class="n">tpr</span><span class="p">)</span>
<span class="n">interp_tpr</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span>
<span class="n">tprs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">interp_tpr</span><span class="p">)</span>
<span class="n">aucs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">viz</span><span class="o">.</span><span class="n">roc_auc</span><span class="p">)</span>
<span class="n">mean_tpr</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.mean.html#numpy.mean" title="numpy.mean" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">mean</span></a><span class="p">(</span><span class="n">tprs</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">mean_tpr</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span>
<span class="n">mean_auc</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.auc.html#sklearn.metrics.auc" title="sklearn.metrics.auc" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">auc</span></a><span class="p">(</span><span class="n">mean_fpr</span><span class="p">,</span> <span class="n">mean_tpr</span><span class="p">)</span>
<span class="n">std_auc</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.std.html#numpy.std" title="numpy.std" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">std</span></a><span class="p">(</span><span class="n">aucs</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span>
<span class="n">mean_fpr</span><span class="p">,</span>
<span class="n">mean_tpr</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"b"</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"Mean ROC (AUC = </span><span class="si">%0.2f</span><span class="s2"> $\pm$ </span><span class="si">%0.2f</span><span class="s2">)"</span> <span class="o">%</span> <span class="p">(</span><span class="n">mean_auc</span><span class="p">,</span> <span class="n">std_auc</span><span class="p">),</span>
<span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">std_tpr</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.std.html#numpy.std" title="numpy.std" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">std</span></a><span class="p">(</span><span class="n">tprs</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">tprs_upper</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.minimum.html#numpy.minimum" title="numpy.minimum" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">minimum</span></a><span class="p">(</span><span class="n">mean_tpr</span> <span class="o">+</span> <span class="n">std_tpr</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">tprs_lower</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.maximum.html#numpy.maximum" title="numpy.maximum" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">maximum</span></a><span class="p">(</span><span class="n">mean_tpr</span> <span class="o">-</span> <span class="n">std_tpr</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span>
<span class="n">mean_fpr</span><span class="p">,</span>
<span class="n">tprs_lower</span><span class="p">,</span>
<span class="n">tprs_upper</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"grey"</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$\pm$ 1 std. dev."</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set</span><span class="p">(</span>
<span class="n">xlabel</span><span class="o">=</span><span class="s2">"False Positive Rate"</span><span class="p">,</span>
<span class="n">ylabel</span><span class="o">=</span><span class="s2">"True Positive Rate"</span><span class="p">,</span>
<span class="n">title</span><span class="o">=</span><span class="sa">f</span><span class="s2">"Mean ROC curve with variability</span><span class="se">\n</span><span class="s2">(Positive label '</span><span class="si">{</span><span class="n">target_names</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="s2">')"</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">"lower right"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
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<img src="../../_images/sphx_glr_plot_roc_crossval_001.png" srcset="../../_images/sphx_glr_plot_roc_crossval_001.png" alt="Mean ROC curve with variability (Positive label 'versicolor')" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 0.179 seconds)</p>
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