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<li><a class="reference internal" href="#">Model selection: choosing estimators and their parameters</a><ul>
<li><a class="reference internal" href="#score-and-cross-validated-scores">Score, and cross-validated scores</a></li>
<li><a class="reference internal" href="#cross-validation-generators">Cross-validation generators</a></li>
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<li><a class="reference internal" href="#cross-validated-estimators">Cross-validated estimators</a></li>
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<section id="model-selection-choosing-estimators-and-their-parameters">
<span id="model-selection-tut"></span><h1>Model selection: choosing estimators and their parameters<a class="headerlink" href="#model-selection-choosing-estimators-and-their-parameters" title="Link to this heading">¶</a></h1>
<section id="score-and-cross-validated-scores">
<h2>Score, and cross-validated scores<a class="headerlink" href="#score-and-cross-validated-scores" title="Link to this heading">¶</a></h2>
<p>As we have seen, every estimator exposes a <code class="docutils literal notranslate"><span class="pre">score</span></code> method that can judge
the quality of the fit (or the prediction) on new data. <strong>Bigger is
better</strong>.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">svm</span>
<span class="gp">>>> </span><span class="n">X_digits</span><span class="p">,</span> <span class="n">y_digits</span> <span class="o">=</span> <span class="n">datasets</span><span class="o">.</span><span class="n">load_digits</span><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">svc</span> <span class="o">=</span> <span class="n">svm</span><span class="o">.</span><span class="n">SVC</span><span class="p">(</span><span class="n">C</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">kernel</span><span class="o">=</span><span class="s1">'linear'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">svc</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_digits</span><span class="p">[:</span><span class="o">-</span><span class="mi">100</span><span class="p">],</span> <span class="n">y_digits</span><span class="p">[:</span><span class="o">-</span><span class="mi">100</span><span class="p">])</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_digits</span><span class="p">[</span><span class="o">-</span><span class="mi">100</span><span class="p">:],</span> <span class="n">y_digits</span><span class="p">[</span><span class="o">-</span><span class="mi">100</span><span class="p">:])</span>
<span class="go">0.98</span>
</pre></div>
</div>
<p>To get a better measure of prediction accuracy (which we can use as a
proxy for goodness of fit of the model), we can successively split the
data in <em>folds</em> that we use for training and testing:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="n">X_folds</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array_split</span><span class="p">(</span><span class="n">X_digits</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y_folds</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array_split</span><span class="p">(</span><span class="n">y_digits</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">scores</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="gp">>>> </span><span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">):</span>
<span class="gp">... </span> <span class="c1"># We use 'list' to copy, in order to 'pop' later on</span>
<span class="gp">... </span> <span class="n">X_train</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">X_folds</span><span class="p">)</span>
<span class="gp">... </span> <span class="n">X_test</span> <span class="o">=</span> <span class="n">X_train</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">k</span><span class="p">)</span>
<span class="gp">... </span> <span class="n">X_train</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="gp">... </span> <span class="n">y_train</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">y_folds</span><span class="p">)</span>
<span class="gp">... </span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">y_train</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">k</span><span class="p">)</span>
<span class="gp">... </span> <span class="n">y_train</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">y_train</span><span class="p">)</span>
<span class="gp">... </span> <span class="n">scores</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">svc</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="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">))</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">scores</span><span class="p">)</span>
<span class="go">[0.934..., 0.956..., 0.939...]</span>
</pre></div>
</div>
<p>This is called a <a class="reference internal" href="../../modules/generated/sklearn.model_selection.KFold.html#sklearn.model_selection.KFold" title="sklearn.model_selection.KFold"><code class="xref py py-class docutils literal notranslate"><span class="pre">KFold</span></code></a> cross-validation.</p>
</section>
<section id="cross-validation-generators">
<span id="cv-generators-tut"></span><h2>Cross-validation generators<a class="headerlink" href="#cross-validation-generators" title="Link to this heading">¶</a></h2>
<p>Scikit-learn has a collection of classes which can be used to generate lists of
train/test indices for popular cross-validation strategies.</p>
<p>They expose a <code class="docutils literal notranslate"><span class="pre">split</span></code> method which accepts the input
dataset to be split and yields the train/test set indices for each iteration
of the chosen cross-validation strategy.</p>
<p>This example shows an example usage of the <code class="docutils literal notranslate"><span class="pre">split</span></code> method.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">KFold</span><span class="p">,</span> <span class="n">cross_val_score</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"a"</span><span class="p">,</span> <span class="s2">"a"</span><span class="p">,</span> <span class="s2">"a"</span><span class="p">,</span> <span class="s2">"b"</span><span class="p">,</span> <span class="s2">"b"</span><span class="p">,</span> <span class="s2">"c"</span><span class="p">,</span> <span class="s2">"c"</span><span class="p">,</span> <span class="s2">"c"</span><span class="p">,</span> <span class="s2">"c"</span><span class="p">,</span> <span class="s2">"c"</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">k_fold</span> <span class="o">=</span> <span class="n">KFold</span><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
<span class="gp">>>> </span><span class="k">for</span> <span class="n">train_indices</span><span class="p">,</span> <span class="n">test_indices</span> <span class="ow">in</span> <span class="n">k_fold</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="gp">... </span> <span class="nb">print</span><span class="p">(</span><span class="s1">'Train: </span><span class="si">%s</span><span class="s1"> | test: </span><span class="si">%s</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="n">train_indices</span><span class="p">,</span> <span class="n">test_indices</span><span class="p">))</span>
<span class="go">Train: [2 3 4 5 6 7 8 9] | test: [0 1]</span>
<span class="go">Train: [0 1 4 5 6 7 8 9] | test: [2 3]</span>
<span class="go">Train: [0 1 2 3 6 7 8 9] | test: [4 5]</span>
<span class="go">Train: [0 1 2 3 4 5 8 9] | test: [6 7]</span>
<span class="go">Train: [0 1 2 3 4 5 6 7] | test: [8 9]</span>
</pre></div>
</div>
<p>The cross-validation can then be performed easily:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="p">[</span><span class="n">svc</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_digits</span><span class="p">[</span><span class="n">train</span><span class="p">],</span> <span class="n">y_digits</span><span class="p">[</span><span class="n">train</span><span class="p">])</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_digits</span><span class="p">[</span><span class="n">test</span><span class="p">],</span> <span class="n">y_digits</span><span class="p">[</span><span class="n">test</span><span class="p">])</span>
<span class="gp">... </span> <span class="k">for</span> <span class="n">train</span><span class="p">,</span> <span class="n">test</span> <span class="ow">in</span> <span class="n">k_fold</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">X_digits</span><span class="p">)]</span>
<span class="go">[0.963..., 0.922..., 0.963..., 0.963..., 0.930...]</span>
</pre></div>
</div>
<p>The cross-validation score can be directly calculated using the
<a class="reference internal" href="../../modules/generated/sklearn.model_selection.cross_val_score.html#sklearn.model_selection.cross_val_score" title="sklearn.model_selection.cross_val_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_score</span></code></a> helper. Given an estimator, the cross-validation object
and the input dataset, the <a class="reference internal" href="../../modules/generated/sklearn.model_selection.cross_val_score.html#sklearn.model_selection.cross_val_score" title="sklearn.model_selection.cross_val_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_score</span></code></a> splits the data repeatedly into
a training and a testing set, trains the estimator using the training set and
computes the scores based on the testing set for each iteration of cross-validation.</p>
<p>By default the estimator’s <code class="docutils literal notranslate"><span class="pre">score</span></code> method is used to compute the individual scores.</p>
<p>Refer the <a class="reference internal" href="../../modules/metrics.html#metrics"><span class="std std-ref">metrics module</span></a> to learn more on the available scoring
methods.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">cross_val_score</span><span class="p">(</span><span class="n">svc</span><span class="p">,</span> <span class="n">X_digits</span><span class="p">,</span> <span class="n">y_digits</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="n">k_fold</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="go">array([0.96388889, 0.92222222, 0.9637883 , 0.9637883 , 0.93036212])</span>
</pre></div>
</div>
<p><code class="docutils literal notranslate"><span class="pre">n_jobs=-1</span></code> means that the computation will be dispatched on all the CPUs
of the computer.</p>
<p>Alternatively, the <code class="docutils literal notranslate"><span class="pre">scoring</span></code> argument can be provided to specify an alternative
scoring method.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">cross_val_score</span><span class="p">(</span><span class="n">svc</span><span class="p">,</span> <span class="n">X_digits</span><span class="p">,</span> <span class="n">y_digits</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="n">k_fold</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">scoring</span><span class="o">=</span><span class="s1">'precision_macro'</span><span class="p">)</span>
<span class="go">array([0.96578289, 0.92708922, 0.96681476, 0.96362897, 0.93192644])</span>
</pre></div>
</div>
<p><strong>Cross-validation generators</strong></p>
<table class="docutils align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.KFold.html#sklearn.model_selection.KFold" title="sklearn.model_selection.KFold"><code class="xref py py-class docutils literal notranslate"><span class="pre">KFold</span></code></a> <strong>(n_splits, shuffle, random_state)</strong></p></td>
<td><p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.StratifiedKFold.html#sklearn.model_selection.StratifiedKFold" title="sklearn.model_selection.StratifiedKFold"><code class="xref py py-class docutils literal notranslate"><span class="pre">StratifiedKFold</span></code></a> <strong>(n_splits, shuffle, random_state)</strong></p></td>
<td><p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.GroupKFold.html#sklearn.model_selection.GroupKFold" title="sklearn.model_selection.GroupKFold"><code class="xref py py-class docutils literal notranslate"><span class="pre">GroupKFold</span></code></a> <strong>(n_splits)</strong></p></td>
</tr>
<tr class="row-even"><td><p>Splits it into K folds, trains on K-1 and then tests on the left-out.</p></td>
<td><p>Same as K-Fold but preserves the class distribution within each fold.</p></td>
<td><p>Ensures that the same group is not in both testing and training sets.</p></td>
</tr>
</tbody>
</table>
<table class="docutils align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.ShuffleSplit.html#sklearn.model_selection.ShuffleSplit" title="sklearn.model_selection.ShuffleSplit"><code class="xref py py-class docutils literal notranslate"><span class="pre">ShuffleSplit</span></code></a> <strong>(n_splits, test_size, train_size, random_state)</strong></p></td>
<td><p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.StratifiedShuffleSplit.html#sklearn.model_selection.StratifiedShuffleSplit" title="sklearn.model_selection.StratifiedShuffleSplit"><code class="xref py py-class docutils literal notranslate"><span class="pre">StratifiedShuffleSplit</span></code></a></p></td>
<td><p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.GroupShuffleSplit.html#sklearn.model_selection.GroupShuffleSplit" title="sklearn.model_selection.GroupShuffleSplit"><code class="xref py py-class docutils literal notranslate"><span class="pre">GroupShuffleSplit</span></code></a></p></td>
</tr>
<tr class="row-even"><td><p>Generates train/test indices based on random permutation.</p></td>
<td><p>Same as shuffle split but preserves the class distribution within each iteration.</p></td>
<td><p>Ensures that the same group is not in both testing and training sets.</p></td>
</tr>
</tbody>
</table>
<table class="docutils align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.LeaveOneGroupOut.html#sklearn.model_selection.LeaveOneGroupOut" title="sklearn.model_selection.LeaveOneGroupOut"><code class="xref py py-class docutils literal notranslate"><span class="pre">LeaveOneGroupOut</span></code></a> <strong>()</strong></p></td>
<td><p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.LeavePGroupsOut.html#sklearn.model_selection.LeavePGroupsOut" title="sklearn.model_selection.LeavePGroupsOut"><code class="xref py py-class docutils literal notranslate"><span class="pre">LeavePGroupsOut</span></code></a> <strong>(n_groups)</strong></p></td>
<td><p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.LeaveOneOut.html#sklearn.model_selection.LeaveOneOut" title="sklearn.model_selection.LeaveOneOut"><code class="xref py py-class docutils literal notranslate"><span class="pre">LeaveOneOut</span></code></a> <strong>()</strong></p></td>
</tr>
<tr class="row-even"><td><p>Takes a group array to group observations.</p></td>
<td><p>Leave P groups out.</p></td>
<td><p>Leave one observation out.</p></td>
</tr>
</tbody>
</table>
<table class="docutils align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.LeavePOut.html#sklearn.model_selection.LeavePOut" title="sklearn.model_selection.LeavePOut"><code class="xref py py-class docutils literal notranslate"><span class="pre">LeavePOut</span></code></a> <strong>(p)</strong></p></td>
<td><p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.PredefinedSplit.html#sklearn.model_selection.PredefinedSplit" title="sklearn.model_selection.PredefinedSplit"><code class="xref py py-class docutils literal notranslate"><span class="pre">PredefinedSplit</span></code></a></p></td>
</tr>
<tr class="row-even"><td><p>Leave P observations out.</p></td>
<td><p>Generates train/test indices based on predefined splits.</p></td>
</tr>
</tbody>
</table>
<aside class="topic">
<p class="topic-title"><strong>Exercise</strong></p>
<p>On the digits dataset, plot the cross-validation score of 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>
estimator with a linear kernel as a function of parameter <code class="docutils literal notranslate"><span class="pre">C</span></code> (use a
logarithmic grid of points, from 1 to 10).</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">svm</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">cross_val_score</span>
<span class="gp">>>> </span><span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">datasets</span><span class="o">.</span><span class="n">load_digits</span><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">svc</span> <span class="o">=</span> <span class="n">svm</span><span class="o">.</span><span class="n">SVC</span><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"linear"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">C_s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">logspace</span><span class="p">(</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">scores</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">scores_std</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
</pre></div>
</div>
<p><details id="summary-anchor">
<summary class="btn btn-light">
<strong>Solution</strong>
<span class="tooltiptext">Click for more details</span>
<a class="headerlink" href="#summary-anchor" title="Permalink to this heading">¶</a>
</summary>
<div class="card"></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</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">svm</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">cross_val_score</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">datasets</span><span class="o">.</span><span class="n">load_digits</span><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">svc</span> <span class="o">=</span> <span class="n">svm</span><span class="o">.</span><span class="n">SVC</span><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_s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">logspace</span><span class="p">(</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="n">scores</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">scores_std</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="k">for</span> <span class="n">C</span> <span class="ow">in</span> <span class="n">C_s</span><span class="p">:</span>
<span class="n">svc</span><span class="o">.</span><span class="n">C</span> <span class="o">=</span> <span class="n">C</span>
<span class="n">this_scores</span> <span class="o">=</span> <span class="n">cross_val_score</span><span class="p">(</span><span class="n">svc</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">n_jobs</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">scores</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">this_scores</span><span class="p">))</span>
<span class="n">scores_std</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">this_scores</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="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">semilogx</span><span class="p">(</span><span class="n">C_s</span><span class="p">,</span> <span class="n">scores</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">semilogx</span><span class="p">(</span><span class="n">C_s</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">scores</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">scores_std</span><span class="p">),</span> <span class="s2">"b--"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">semilogx</span><span class="p">(</span><span class="n">C_s</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">scores</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">scores_std</span><span class="p">),</span> <span class="s2">"b--"</span><span class="p">)</span>
<span class="n">locs</span><span class="p">,</span> <span class="n">labels</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">yticks</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">yticks</span><span class="p">(</span><span class="n">locs</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="s2">"</span><span class="si">%g</span><span class="s2">"</span> <span class="o">%</span> <span class="n">x</span><span class="p">,</span> <span class="n">locs</span><span class="p">)))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"CV score"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"Parameter C"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<figure class="align-center">
<img alt="../../_images/model_selection-1.png" class="plot-directive" src="../../_images/model_selection-1.png" />
</figure>
<p></div>
</details></p>
</aside>
</section>
<section id="grid-search-and-cross-validated-estimators">
<h2>Grid-search and cross-validated estimators<a class="headerlink" href="#grid-search-and-cross-validated-estimators" title="Link to this heading">¶</a></h2>
<section id="grid-search">
<h3>Grid-search<a class="headerlink" href="#grid-search" title="Link to this heading">¶</a></h3>
<p>scikit-learn provides an object that, given data, computes the score
during the fit of an estimator on a parameter grid and chooses the
parameters to maximize the cross-validation score. This object takes an
estimator during the construction and exposes an estimator API:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">GridSearchCV</span><span class="p">,</span> <span class="n">cross_val_score</span>
<span class="gp">>>> </span><span class="n">Cs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">logspace</span><span class="p">(</span><span class="o">-</span><span class="mi">6</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">clf</span> <span class="o">=</span> <span class="n">GridSearchCV</span><span class="p">(</span><span class="n">estimator</span><span class="o">=</span><span class="n">svc</span><span class="p">,</span> <span class="n">param_grid</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">C</span><span class="o">=</span><span class="n">Cs</span><span class="p">),</span>
<span class="gp">... </span> <span class="n">n_jobs</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_digits</span><span class="p">[:</span><span class="mi">1000</span><span class="p">],</span> <span class="n">y_digits</span><span class="p">[:</span><span class="mi">1000</span><span class="p">])</span>
<span class="go">GridSearchCV(cv=None,...</span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">best_score_</span>
<span class="go">0.925...</span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">best_estimator_</span><span class="o">.</span><span class="n">C</span>
<span class="go">0.0077...</span>
<span class="gp">>>> </span><span class="c1"># Prediction performance on test set is not as good as on train set</span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_digits</span><span class="p">[</span><span class="mi">1000</span><span class="p">:],</span> <span class="n">y_digits</span><span class="p">[</span><span class="mi">1000</span><span class="p">:])</span>
<span class="go">0.943...</span>
</pre></div>
</div>
<p>By default, the <a class="reference internal" href="../../modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a> uses a 5-fold cross-validation. However,
if it detects that a classifier is passed, rather than a regressor, it uses
a stratified 5-fold.</p>
<aside class="topic">
<p class="topic-title">Nested cross-validation</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">cross_val_score</span><span class="p">(</span><span class="n">clf</span><span class="p">,</span> <span class="n">X_digits</span><span class="p">,</span> <span class="n">y_digits</span><span class="p">)</span>
<span class="go">array([0.938..., 0.963..., 0.944...])</span>
</pre></div>
</div>
<p>Two cross-validation loops are performed in parallel: one by the
<a class="reference internal" href="../../modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a> estimator to set <code class="docutils literal notranslate"><span class="pre">gamma</span></code> and the other one by
<code class="docutils literal notranslate"><span class="pre">cross_val_score</span></code> to measure the prediction performance of the
estimator. The resulting scores are unbiased estimates of the
prediction score on new data.</p>
</aside>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>You cannot nest objects with parallel computing (<code class="docutils literal notranslate"><span class="pre">n_jobs</span></code> different
than 1).</p>
</div>
</section>
<section id="cross-validated-estimators">
<span id="cv-estimators-tut"></span><h3>Cross-validated estimators<a class="headerlink" href="#cross-validated-estimators" title="Link to this heading">¶</a></h3>
<p>Cross-validation to set a parameter can be done more efficiently on an
algorithm-by-algorithm basis. This is why, for certain estimators,
scikit-learn exposes <a class="reference internal" href="../../modules/cross_validation.html#cross-validation"><span class="std std-ref">Cross-validation: evaluating estimator performance</span></a> estimators that set their
parameter automatically by cross-validation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">linear_model</span><span class="p">,</span> <span class="n">datasets</span>
<span class="gp">>>> </span><span class="n">lasso</span> <span class="o">=</span> <span class="n">linear_model</span><span class="o">.</span><span class="n">LassoCV</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">X_diabetes</span><span class="p">,</span> <span class="n">y_diabetes</span> <span class="o">=</span> <span class="n">datasets</span><span class="o">.</span><span class="n">load_diabetes</span><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">lasso</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_diabetes</span><span class="p">,</span> <span class="n">y_diabetes</span><span class="p">)</span>
<span class="go">LassoCV()</span>
<span class="gp">>>> </span><span class="c1"># The estimator chose automatically its lambda:</span>
<span class="gp">>>> </span><span class="n">lasso</span><span class="o">.</span><span class="n">alpha_</span>
<span class="go">0.00375...</span>
</pre></div>
</div>
<p>These estimators are called similarly to their counterparts, with ‘CV’
appended to their name.</p>
<aside class="topic">
<p class="topic-title"><strong>Exercise</strong></p>
<p>On the diabetes dataset, find the optimal regularization parameter
alpha.</p>
<p><strong>Bonus</strong>: How much can you trust the selection of alpha?</p>
<div class="highlight-default 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</span> <span class="kn">import</span> <span class="n">datasets</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">Lasso</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">GridSearchCV</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">datasets</span><span class="o">.</span><span class="n">load_diabetes</span><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:</span><span class="mi">150</span><span class="p">]</span>
</pre></div>
</div>
<p><strong>Solution:</strong> <a class="reference internal" href="../../auto_examples/exercises/plot_cv_diabetes.html#sphx-glr-auto-examples-exercises-plot-cv-diabetes-py"><span class="std std-ref">Cross-validation on diabetes Dataset Exercise</span></a></p>
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