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<li><a class="reference internal" href="#">Plot classification probability</a></li>
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<p><a class="reference internal" href="#sphx-glr-download-auto-examples-classification-plot-classification-probability-py"><span class="std std-ref">Go to the end</span></a>
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<section class="sphx-glr-example-title" id="plot-classification-probability">
<span id="sphx-glr-auto-examples-classification-plot-classification-probability-py"></span><h1>Plot classification probability<a class="headerlink" href="#plot-classification-probability" title="Link to this heading">¶</a></h1>
<p>Plot the classification probability for different classifiers. We use a 3 class
dataset, and we classify it with a Support Vector classifier, L1 and L2
penalized logistic regression with either a One-Vs-Rest or multinomial setting,
and Gaussian process classification.</p>
<p>Linear SVC is not a probabilistic classifier by default but it has a built-in
calibration option enabled in this example (<code class="docutils literal notranslate"><span class="pre">probability=True</span></code>).</p>
<p>The logistic regression with One-Vs-Rest is not a multiclass classifier out of
the box. As a result it has more trouble in separating class 2 and 3 than the
other estimators.</p>
<img src="../../_images/sphx_glr_plot_classification_probability_001.png" srcset="../../_images/sphx_glr_plot_classification_probability_001.png" alt="Class 0, Class 1, Class 2, Class 0, Class 1, Class 2, Class 0, Class 1, Class 2, Class 0, Class 1, Class 2, Class 0, Class 1, Class 2, Probability" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Accuracy (train) for L1 logistic: 83.3%
Accuracy (train) for L2 logistic (Multinomial): 82.7%
Accuracy (train) for L2 logistic (OvR): 79.3%
Accuracy (train) for Linear SVC: 82.0%
Accuracy (train) for GPC: 82.7%
</pre></div>
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<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Alexandre Gramfort <[email protected]></span>
<span class="c1"># License: BSD 3 clause</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">cm</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span>
<span class="kn">from</span> <span class="nn">sklearn.gaussian_process</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.gaussian_process.GaussianProcessClassifier.html#sklearn.gaussian_process.GaussianProcessClassifier" title="sklearn.gaussian_process.GaussianProcessClassifier" class="sphx-glr-backref-module-sklearn-gaussian_process sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GaussianProcessClassifier</span></a>
<span class="kn">from</span> <span class="nn">sklearn.gaussian_process.kernels</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.gaussian_process.kernels.RBF.html#sklearn.gaussian_process.kernels.RBF" title="sklearn.gaussian_process.kernels.RBF" class="sphx-glr-backref-module-sklearn-gaussian_process-kernels sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RBF</span></a>
<span class="kn">from</span> <span class="nn">sklearn.inspection</span> <span class="kn">import</span> <span class="n">DecisionBoundaryDisplay</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="sklearn.linear_model.LogisticRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LogisticRegression</span></a>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.metrics.accuracy_score.html#sklearn.metrics.accuracy_score" title="sklearn.metrics.accuracy_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">accuracy_score</span></a>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</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">SVC</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">datasets</span><span class="o">.</span><span class="n">load_iris</span></a><span class="p">()</span>
<span class="n">X</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="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span> <span class="c1"># we only take the first two features for visualization</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</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><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">C</span> <span class="o">=</span> <span class="mi">10</span>
<span class="n">kernel</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">*</span> <a href="../../modules/generated/sklearn.gaussian_process.kernels.RBF.html#sklearn.gaussian_process.kernels.RBF" title="sklearn.gaussian_process.kernels.RBF" class="sphx-glr-backref-module-sklearn-gaussian_process-kernels sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RBF</span></a><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">])</span> <span class="c1"># for GPC</span>
<span class="c1"># Create different classifiers.</span>
<span class="n">classifiers</span> <span class="o">=</span> <span class="p">{</span>
<span class="s2">"L1 logistic"</span><span class="p">:</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="sklearn.linear_model.LogisticRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LogisticRegression</span></a><span class="p">(</span>
<span class="n">C</span><span class="o">=</span><span class="n">C</span><span class="p">,</span> <span class="n">penalty</span><span class="o">=</span><span class="s2">"l1"</span><span class="p">,</span> <span class="n">solver</span><span class="o">=</span><span class="s2">"saga"</span><span class="p">,</span> <span class="n">multi_class</span><span class="o">=</span><span class="s2">"multinomial"</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">10000</span>
<span class="p">),</span>
<span class="s2">"L2 logistic (Multinomial)"</span><span class="p">:</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="sklearn.linear_model.LogisticRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LogisticRegression</span></a><span class="p">(</span>
<span class="n">C</span><span class="o">=</span><span class="n">C</span><span class="p">,</span> <span class="n">penalty</span><span class="o">=</span><span class="s2">"l2"</span><span class="p">,</span> <span class="n">solver</span><span class="o">=</span><span class="s2">"saga"</span><span class="p">,</span> <span class="n">multi_class</span><span class="o">=</span><span class="s2">"multinomial"</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">10000</span>
<span class="p">),</span>
<span class="s2">"L2 logistic (OvR)"</span><span class="p">:</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="sklearn.linear_model.LogisticRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LogisticRegression</span></a><span class="p">(</span>
<span class="n">C</span><span class="o">=</span><span class="n">C</span><span class="p">,</span> <span class="n">penalty</span><span class="o">=</span><span class="s2">"l2"</span><span class="p">,</span> <span class="n">solver</span><span class="o">=</span><span class="s2">"saga"</span><span class="p">,</span> <span class="n">multi_class</span><span class="o">=</span><span class="s2">"ovr"</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">10000</span>
<span class="p">),</span>
<span class="s2">"Linear SVC"</span><span class="p">:</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">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">C</span><span class="o">=</span><span class="n">C</span><span class="p">,</span> <span class="n">probability</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span>
<span class="s2">"GPC"</span><span class="p">:</span> <a href="../../modules/generated/sklearn.gaussian_process.GaussianProcessClassifier.html#sklearn.gaussian_process.GaussianProcessClassifier" title="sklearn.gaussian_process.GaussianProcessClassifier" class="sphx-glr-backref-module-sklearn-gaussian_process sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GaussianProcessClassifier</span></a><span class="p">(</span><span class="n">kernel</span><span class="p">),</span>
<span class="p">}</span>
<span class="n">n_classifiers</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">classifiers</span><span class="p">)</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axes</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">nrows</span><span class="o">=</span><span class="n">n_classifiers</span><span class="p">,</span>
<span class="n">ncols</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">iris</span><span class="o">.</span><span class="n">target_names</span><span class="p">),</span>
<span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="mi">2</span><span class="p">,</span> <span class="n">n_classifiers</span> <span class="o">*</span> <span class="mi">2</span><span class="p">),</span>
<span class="p">)</span>
<span class="k">for</span> <span class="n">classifier_idx</span><span class="p">,</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">classifier</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">classifiers</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
<span class="n">y_pred</span> <span class="o">=</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">y</span><span class="p">)</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">accuracy</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.accuracy_score.html#sklearn.metrics.accuracy_score" title="sklearn.metrics.accuracy_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">accuracy_score</span></a><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Accuracy (train) for </span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">accuracy</span><span class="si">:</span><span class="s2">0.1%</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="k">for</span> <span class="n">label</span> <span class="ow">in</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.unique.html#numpy.unique" title="numpy.unique" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">unique</span></a><span class="p">(</span><span class="n">y</span><span class="p">):</span>
<span class="c1"># plot the probability estimate provided by the classifier</span>
<span class="n">disp</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.inspection.DecisionBoundaryDisplay.html#sklearn.inspection.DecisionBoundaryDisplay.from_estimator" title="sklearn.inspection.DecisionBoundaryDisplay.from_estimator" class="sphx-glr-backref-module-sklearn-inspection-DecisionBoundaryDisplay sphx-glr-backref-type-py-method"><span class="n">DecisionBoundaryDisplay</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">response_method</span><span class="o">=</span><span class="s2">"predict_proba"</span><span class="p">,</span>
<span class="n">class_of_interest</span><span class="o">=</span><span class="n">label</span><span class="p">,</span>
<span class="n">ax</span><span class="o">=</span><span class="n">axes</span><span class="p">[</span><span class="n">classifier_idx</span><span class="p">,</span> <span class="n">label</span><span class="p">],</span>
<span class="n">vmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
<span class="n">vmax</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">axes</span><span class="p">[</span><span class="n">classifier_idx</span><span class="p">,</span> <span class="n">label</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Class </span><span class="si">{</span><span class="n">label</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="c1"># plot data predicted to belong to given class</span>
<span class="n">mask_y_pred</span> <span class="o">=</span> <span class="n">y_pred</span> <span class="o">==</span> <span class="n">label</span>
<span class="n">axes</span><span class="p">[</span><span class="n">classifier_idx</span><span class="p">,</span> <span class="n">label</span><span class="p">]</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<span class="n">X</span><span class="p">[</span><span class="n">mask_y_pred</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="n">mask_y_pred</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"o"</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s2">"w"</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s2">"k"</span>
<span class="p">)</span>
<span class="n">axes</span><span class="p">[</span><span class="n">classifier_idx</span><span class="p">,</span> <span class="n">label</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">xticks</span><span class="o">=</span><span class="p">(),</span> <span class="n">yticks</span><span class="o">=</span><span class="p">())</span>
<span class="n">axes</span><span class="p">[</span><span class="n">classifier_idx</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">name</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.axes.html#matplotlib.pyplot.axes" title="matplotlib.pyplot.axes" 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">axes</span></a><span class="p">([</span><span class="mf">0.15</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">])</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" 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">title</span></a><span class="p">(</span><span class="s2">"Probability"</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar" 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">colorbar</span></a><span class="p">(</span>
<a href="https://matplotlib.org/stable/api/cm_api.html#matplotlib.cm.ScalarMappable" title="matplotlib.cm.ScalarMappable" class="sphx-glr-backref-module-matplotlib-cm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cm</span><span class="o">.</span><span class="n">ScalarMappable</span></a><span class="p">(</span><span class="n">norm</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s2">"viridis"</span><span class="p">),</span> <span class="n">cax</span><span class="o">=</span><span class="n">ax</span><span class="p">,</span> <span class="n">orientation</span><span class="o">=</span><span class="s2">"horizontal"</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>
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