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<li class="toctree-l2"><a class="reference internal" href="../datasets/toy_dataset.html">7.1. Toy datasets</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../datasets/sample_generators.html">7.3. Generated datasets</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../computing/scaling_strategies.html">8.1. Strategies to scale computationally: bigger data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../computing/computational_performance.html">8.2. Computational Performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../computing/parallelism.html">8.3. Parallelism, resource management, and configuration</a></li>
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<li class="toctree-l2"><a class="reference internal" href="array_api.html">11.1. Array API support (experimental)</a></li>
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<section id="cross-validation-evaluating-estimator-performance">
<span id="cross-validation"></span><h1><span class="section-number">3.1. </span>Cross-validation: evaluating estimator performance<a class="headerlink" href="#cross-validation-evaluating-estimator-performance" title="Link to this heading">#</a></h1>
<p>Learning the parameters of a prediction function and testing it on the
same data is a methodological mistake: a model that would just repeat
the labels of the samples that it has just seen would have a perfect
score but would fail to predict anything useful on yet-unseen data.
This situation is called <strong>overfitting</strong>.
To avoid it, it is common practice when performing
a (supervised) machine learning experiment
to hold out part of the available data as a <strong>test set</strong> <code class="docutils literal notranslate"><span class="pre">X_test,</span> <span class="pre">y_test</span></code>.
Note that the word “experiment” is not intended
to denote academic use only,
because even in commercial settings
machine learning usually starts out experimentally.
Here is a flowchart of typical cross validation workflow in model training.
The best parameters can be determined by
<a class="reference internal" href="grid_search.html#grid-search"><span class="std std-ref">grid search</span></a> techniques.</p>
<a class="reference internal image-reference" href="../_images/grid_search_workflow.png"><img alt="Grid Search Workflow" class="align-center" src="../_images/grid_search_workflow.png" style="width: 400px; height: 240px;" />
</a>
<p>In scikit-learn a random split into training and test sets
can be quickly computed with the <a class="reference internal" href="generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="sklearn.model_selection.train_test_split"><code class="xref py py-func docutils literal notranslate"><span class="pre">train_test_split</span></code></a> helper function.
Let’s load the iris data set to fit a linear support vector machine on it:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">train_test_split</span>
<span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn</span><span class="w"> </span><span class="kn">import</span> <span class="n">datasets</span>
<span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn</span><span class="w"> </span><span class="kn">import</span> <span class="n">svm</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_iris</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">X</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">y</span><span class="o">.</span><span class="n">shape</span>
<span class="go">((150, 4), (150,))</span>
</pre></div>
</div>
<p>We can now quickly sample a training set while holding out 40% of the
data for testing (evaluating) our classifier:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </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> <span class="n">train_test_split</span><span class="p">(</span>
<span class="gp">... </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">0.4</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="gp">>>> </span><span class="n">X_train</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">y_train</span><span class="o">.</span><span class="n">shape</span>
<span class="go">((90, 4), (90,))</span>
<span class="gp">>>> </span><span class="n">X_test</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">y_test</span><span class="o">.</span><span class="n">shape</span>
<span class="go">((60, 4), (60,))</span>
<span class="gp">>>> </span><span class="n">clf</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="s1">'linear'</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="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="gp">>>> </span><span class="n">clf</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="go">0.96...</span>
</pre></div>
</div>
<p>When evaluating different settings (“hyperparameters”) for estimators,
such as the <code class="docutils literal notranslate"><span class="pre">C</span></code> setting that must be manually set for an SVM,
there is still a risk of overfitting <em>on the test set</em>
because the parameters can be tweaked until the estimator performs optimally.
This way, knowledge about the test set can “leak” into the model
and evaluation metrics no longer report on generalization performance.
To solve this problem, yet another part of the dataset can be held out
as a so-called “validation set”: training proceeds on the training set,
after which evaluation is done on the validation set,
and when the experiment seems to be successful,
final evaluation can be done on the test set.</p>
<p>However, by partitioning the available data into three sets,
we drastically reduce the number of samples
which can be used for learning the model,
and the results can depend on a particular random choice for the pair of
(train, validation) sets.</p>
<p>A solution to this problem is a procedure called
<a class="reference external" href="https://en.wikipedia.org/wiki/Cross-validation_(statistics)">cross-validation</a>
(CV for short).
A test set should still be held out for final evaluation,
but the validation set is no longer needed when doing CV.
In the basic approach, called <em>k</em>-fold CV,
the training set is split into <em>k</em> smaller sets
(other approaches are described below,
but generally follow the same principles).
The following procedure is followed for each of the <em>k</em> “folds”:</p>
<ul class="simple">
<li><p>A model is trained using <span class="math notranslate nohighlight">\(k-1\)</span> of the folds as training data;</p></li>
<li><p>the resulting model is validated on the remaining part of the data
(i.e., it is used as a test set to compute a performance measure
such as accuracy).</p></li>
</ul>
<p>The performance measure reported by <em>k</em>-fold cross-validation
is then the average of the values computed in the loop.
This approach can be computationally expensive,
but does not waste too much data
(as is the case when fixing an arbitrary validation set),
which is a major advantage in problems such as inverse inference
where the number of samples is very small.</p>
<a class="reference internal image-reference" href="../_images/grid_search_cross_validation.png"><img alt="A depiction of a 5 fold cross validation on a training set, while holding out a test set." class="align-center" src="../_images/grid_search_cross_validation.png" style="width: 500px; height: 300px;" />
</a>
<section id="computing-cross-validated-metrics">
<h2><span class="section-number">3.1.1. </span>Computing cross-validated metrics<a class="headerlink" href="#computing-cross-validated-metrics" title="Link to this heading">#</a></h2>
<p>The simplest way to use cross-validation is to call the
<a class="reference internal" href="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 function on the estimator and the dataset.</p>
<p>The following example demonstrates how to estimate the accuracy of a linear
kernel support vector machine on the iris dataset by splitting the data, fitting
a model and computing the score 5 consecutive times (with different splits each
time):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">cross_val_score</span>
<span class="gp">>>> </span><span class="n">clf</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="s1">'linear'</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">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">scores</span> <span class="o">=</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</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">scores</span>
<span class="go">array([0.96..., 1. , 0.96..., 0.96..., 1. ])</span>
</pre></div>
</div>
<p>The mean score and the standard deviation are hence given by:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="s2">"</span><span class="si">%0.2f</span><span class="s2"> accuracy with a standard deviation of </span><span class="si">%0.2f</span><span class="s2">"</span> <span class="o">%</span> <span class="p">(</span><span class="n">scores</span><span class="o">.</span><span class="n">mean</span><span class="p">(),</span> <span class="n">scores</span><span class="o">.</span><span class="n">std</span><span class="p">()))</span>
<span class="go">0.98 accuracy with a standard deviation of 0.02</span>
</pre></div>
</div>
<p>By default, the score computed at each CV iteration is the <code class="docutils literal notranslate"><span class="pre">score</span></code>
method of the estimator. It is possible to change this by using the
scoring parameter:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn</span><span class="w"> </span><span class="kn">import</span> <span class="n">metrics</span>
<span class="gp">>>> </span><span class="n">scores</span> <span class="o">=</span> <span class="n">cross_val_score</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">clf</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">cv</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">scoring</span><span class="o">=</span><span class="s1">'f1_macro'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">scores</span>
<span class="go">array([0.96..., 1. ..., 0.96..., 0.96..., 1. ])</span>
</pre></div>
</div>
<p>See <a class="reference internal" href="model_evaluation.html#scoring-parameter"><span class="std std-ref">The scoring parameter: defining model evaluation rules</span></a> for details.
In the case of the Iris dataset, the samples are balanced across target
classes hence the accuracy and the F1-score are almost equal.</p>
<p>When the <code class="docutils literal notranslate"><span class="pre">cv</span></code> argument is an integer, <a class="reference internal" href="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> uses the
<a class="reference internal" href="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> or <a class="reference internal" href="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> strategies by default, the latter
being used if the estimator derives from <a class="reference internal" href="generated/sklearn.base.ClassifierMixin.html#sklearn.base.ClassifierMixin" title="sklearn.base.ClassifierMixin"><code class="xref py py-class docutils literal notranslate"><span class="pre">ClassifierMixin</span></code></a>.</p>
<p>It is also possible to use other cross validation strategies by passing a cross
validation iterator instead, for instance:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">ShuffleSplit</span>
<span class="gp">>>> </span><span class="n">n_samples</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">0</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">cv</span> <span class="o">=</span> <span class="n">ShuffleSplit</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="n">test_size</span><span class="o">=</span><span class="mf">0.3</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="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</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="n">cv</span><span class="p">)</span>
<span class="go">array([0.977..., 0.977..., 1. ..., 0.955..., 1. ])</span>
</pre></div>
</div>
<p>Another option is to use an iterable yielding (train, test) splits as arrays of
indices, for example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">def</span><span class="w"> </span><span class="nf">custom_cv_2folds</span><span class="p">(</span><span class="n">X</span><span class="p">):</span>
<span class="gp">... </span> <span class="n">n</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">0</span><span class="p">]</span>
<span class="gp">... </span> <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span>
<span class="gp">... </span> <span class="k">while</span> <span class="n">i</span> <span class="o"><=</span> <span class="mi">2</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span> <span class="o">*</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="n">n</span> <span class="o">*</span> <span class="n">i</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">int</span><span class="p">)</span>
<span class="gp">... </span> <span class="k">yield</span> <span class="n">idx</span><span class="p">,</span> <span class="n">idx</span>
<span class="gp">... </span> <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="gp">...</span>
<span class="gp">>>> </span><span class="n">custom_cv</span> <span class="o">=</span> <span class="n">custom_cv_2folds</span><span class="p">(</span><span class="n">X</span><span class="p">)</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</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="n">custom_cv</span><span class="p">)</span>
<span class="go">array([1. , 0.973...])</span>
</pre></div>
</div>
<details class="sd-sphinx-override sd-dropdown sd-card sd-mb-3" id="data-transformation-with-held-out-data">
<summary class="sd-summary-title sd-card-header">
<span class="sd-summary-text">Data transformation with held-out data<a class="headerlink" href="#data-transformation-with-held-out-data" title="Link to this dropdown">#</a></span><span class="sd-summary-state-marker sd-summary-chevron-right"><svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-right" viewBox="0 0 24 24" aria-hidden="true"><path d="M8.72 18.78a.75.75 0 0 1 0-1.06L14.44 12 8.72 6.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018l6.25 6.25a.75.75 0 0 1 0 1.06l-6.25 6.25a.75.75 0 0 1-1.06 0Z"></path></svg></span></summary><div class="sd-summary-content sd-card-body docutils">
<p class="sd-card-text">Just as it is important to test a predictor on data held-out from
training, preprocessing (such as standardization, feature selection, etc.)
and similar <a class="reference internal" href="../data_transforms.html#data-transforms"><span class="std std-ref">data transformations</span></a> similarly should
be learnt from a training set and applied to held-out data for prediction:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn</span><span class="w"> </span><span class="kn">import</span> <span class="n">preprocessing</span>
<span class="gp">>>> </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> <span class="n">train_test_split</span><span class="p">(</span>
<span class="gp">... </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">0.4</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="gp">>>> </span><span class="n">scaler</span> <span class="o">=</span> <span class="n">preprocessing</span><span class="o">.</span><span class="n">StandardScaler</span><span class="p">()</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="gp">>>> </span><span class="n">X_train_transformed</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">clf</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="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_transformed</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">X_test_transformed</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</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_test_transformed</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)</span>
<span class="go">0.9333...</span>
</pre></div>
</div>
<p class="sd-card-text">A <a class="reference internal" href="generated/sklearn.pipeline.Pipeline.html#sklearn.pipeline.Pipeline" title="sklearn.pipeline.Pipeline"><code class="xref py py-class docutils literal notranslate"><span class="pre">Pipeline</span></code></a> makes it easier to compose
estimators, providing this behavior under 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="w"> </span><span class="nn">sklearn.pipeline</span><span class="w"> </span><span class="kn">import</span> <span class="n">make_pipeline</span>
<span class="gp">>>> </span><span class="n">clf</span> <span class="o">=</span> <span class="n">make_pipeline</span><span class="p">(</span><span class="n">preprocessing</span><span class="o">.</span><span class="n">StandardScaler</span><span class="p">(),</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="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</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="n">cv</span><span class="p">)</span>
<span class="go">array([0.977..., 0.933..., 0.955..., 0.933..., 0.977...])</span>
</pre></div>
</div>
<p class="sd-card-text">See <a class="reference internal" href="compose.html#combining-estimators"><span class="std std-ref">Pipelines and composite estimators</span></a>.</p>
</div>
</details><section id="the-cross-validate-function-and-multiple-metric-evaluation">
<span id="multimetric-cross-validation"></span><h3><span class="section-number">3.1.1.1. </span>The cross_validate function and multiple metric evaluation<a class="headerlink" href="#the-cross-validate-function-and-multiple-metric-evaluation" title="Link to this heading">#</a></h3>
<p>The <a class="reference internal" href="generated/sklearn.model_selection.cross_validate.html#sklearn.model_selection.cross_validate" title="sklearn.model_selection.cross_validate"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_validate</span></code></a> function differs from <a class="reference internal" href="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> in
two ways:</p>
<ul class="simple">
<li><p>It allows specifying multiple metrics for evaluation.</p></li>
<li><p>It returns a dict containing fit-times, score-times
(and optionally training scores, fitted estimators, train-test split indices)
in addition to the test score.</p></li>
</ul>
<p>For single metric evaluation, where the scoring parameter is a string,
callable or None, the keys will be - <code class="docutils literal notranslate"><span class="pre">['test_score',</span> <span class="pre">'fit_time',</span> <span class="pre">'score_time']</span></code></p>
<p>And for multiple metric evaluation, the return value is a dict with the
following keys -
<code class="docutils literal notranslate"><span class="pre">['test_<scorer1_name>',</span> <span class="pre">'test_<scorer2_name>',</span> <span class="pre">'test_<scorer...>',</span> <span class="pre">'fit_time',</span> <span class="pre">'score_time']</span></code></p>
<p><code class="docutils literal notranslate"><span class="pre">return_train_score</span></code> is set to <code class="docutils literal notranslate"><span class="pre">False</span></code> by default to save computation time.
To evaluate the scores on the training set as well you need to set it to
<code class="docutils literal notranslate"><span class="pre">True</span></code>. You may also retain the estimator fitted on each training set by
setting <code class="docutils literal notranslate"><span class="pre">return_estimator=True</span></code>. Similarly, you may set
<code class="docutils literal notranslate"><span class="pre">return_indices=True</span></code> to retain the training and testing indices used to split
the dataset into train and test sets for each cv split.</p>
<p>The multiple metrics can be specified either as a list, tuple or set of
predefined scorer names:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">cross_validate</span>
<span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.metrics</span><span class="w"> </span><span class="kn">import</span> <span class="n">recall_score</span>
<span class="gp">>>> </span><span class="n">scoring</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'precision_macro'</span><span class="p">,</span> <span class="s1">'recall_macro'</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">clf</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="s1">'linear'</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">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">scores</span> <span class="o">=</span> <span class="n">cross_validate</span><span class="p">(</span><span class="n">clf</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">scoring</span><span class="o">=</span><span class="n">scoring</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">sorted</span><span class="p">(</span><span class="n">scores</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span>
<span class="go">['fit_time', 'score_time', 'test_precision_macro', 'test_recall_macro']</span>
<span class="gp">>>> </span><span class="n">scores</span><span class="p">[</span><span class="s1">'test_recall_macro'</span><span class="p">]</span>
<span class="go">array([0.96..., 1. ..., 0.96..., 0.96..., 1. ])</span>
</pre></div>
</div>
<p>Or as a dict mapping scorer name to a predefined or custom scoring function:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.metrics</span><span class="w"> </span><span class="kn">import</span> <span class="n">make_scorer</span>
<span class="gp">>>> </span><span class="n">scoring</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'prec_macro'</span><span class="p">:</span> <span class="s1">'precision_macro'</span><span class="p">,</span>
<span class="gp">... </span> <span class="s1">'rec_macro'</span><span class="p">:</span> <span class="n">make_scorer</span><span class="p">(</span><span class="n">recall_score</span><span class="p">,</span> <span class="n">average</span><span class="o">=</span><span class="s1">'macro'</span><span class="p">)}</span>
<span class="gp">>>> </span><span class="n">scores</span> <span class="o">=</span> <span class="n">cross_validate</span><span class="p">(</span><span class="n">clf</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">scoring</span><span class="o">=</span><span class="n">scoring</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">cv</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">return_train_score</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">sorted</span><span class="p">(</span><span class="n">scores</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span>
<span class="go">['fit_time', 'score_time', 'test_prec_macro', 'test_rec_macro',</span>
<span class="go"> 'train_prec_macro', 'train_rec_macro']</span>
<span class="gp">>>> </span><span class="n">scores</span><span class="p">[</span><span class="s1">'train_rec_macro'</span><span class="p">]</span>
<span class="go">array([0.97..., 0.97..., 0.99..., 0.98..., 0.98...])</span>
</pre></div>
</div>
<p>Here is an example of <code class="docutils literal notranslate"><span class="pre">cross_validate</span></code> using a single metric:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">scores</span> <span class="o">=</span> <span class="n">cross_validate</span><span class="p">(</span><span class="n">clf</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="gp">... </span> <span class="n">scoring</span><span class="o">=</span><span class="s1">'precision_macro'</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">return_estimator</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">sorted</span><span class="p">(</span><span class="n">scores</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span>
<span class="go">['estimator', 'fit_time', 'score_time', 'test_score']</span>
</pre></div>
</div>
</section>
<section id="obtaining-predictions-by-cross-validation">
<h3><span class="section-number">3.1.1.2. </span>Obtaining predictions by cross-validation<a class="headerlink" href="#obtaining-predictions-by-cross-validation" title="Link to this heading">#</a></h3>
<p>The function <a class="reference internal" href="generated/sklearn.model_selection.cross_val_predict.html#sklearn.model_selection.cross_val_predict" title="sklearn.model_selection.cross_val_predict"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_predict</span></code></a> has a similar interface to
<a class="reference internal" href="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>, but returns, for each element in the input, the
prediction that was obtained for that element when it was in the test set. Only
cross-validation strategies that assign all elements to a test set exactly once
can be used (otherwise, an exception is raised).</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>Note on inappropriate usage of cross_val_predict</p>
<p>The result of <a class="reference internal" href="generated/sklearn.model_selection.cross_val_predict.html#sklearn.model_selection.cross_val_predict" title="sklearn.model_selection.cross_val_predict"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_predict</span></code></a> may be different from those
obtained using <a class="reference internal" href="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> as the elements are grouped in
different ways. The function <a class="reference internal" href="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> takes an average
over cross-validation folds, whereas <a class="reference internal" href="generated/sklearn.model_selection.cross_val_predict.html#sklearn.model_selection.cross_val_predict" title="sklearn.model_selection.cross_val_predict"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_predict</span></code></a> simply
returns the labels (or probabilities) from several distinct models
undistinguished. Thus, <a class="reference internal" href="generated/sklearn.model_selection.cross_val_predict.html#sklearn.model_selection.cross_val_predict" title="sklearn.model_selection.cross_val_predict"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_predict</span></code></a> is not an appropriate
measure of generalization error.</p>
</div>
<dl class="simple">
<dt>The function <a class="reference internal" href="generated/sklearn.model_selection.cross_val_predict.html#sklearn.model_selection.cross_val_predict" title="sklearn.model_selection.cross_val_predict"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_predict</span></code></a> is appropriate for:</dt><dd><ul class="simple">
<li><p>Visualization of predictions obtained from different models.</p></li>
<li><p>Model blending: When predictions of one supervised estimator are used to
train another estimator in ensemble methods.</p></li>
</ul>
</dd>
</dl>
<p>The available cross validation iterators are introduced in the following
section.</p>
<p class="rubric">Examples</p>
<ul class="simple">
<li><p><a class="reference internal" href="../auto_examples/model_selection/plot_roc_crossval.html#sphx-glr-auto-examples-model-selection-plot-roc-crossval-py"><span class="std std-ref">Receiver Operating Characteristic (ROC) with cross validation</span></a>,</p></li>
<li><p><a class="reference internal" href="../auto_examples/feature_selection/plot_rfe_with_cross_validation.html#sphx-glr-auto-examples-feature-selection-plot-rfe-with-cross-validation-py"><span class="std std-ref">Recursive feature elimination with cross-validation</span></a>,</p></li>
<li><p><a class="reference internal" href="../auto_examples/model_selection/plot_grid_search_digits.html#sphx-glr-auto-examples-model-selection-plot-grid-search-digits-py"><span class="std std-ref">Custom refit strategy of a grid search with cross-validation</span></a>,</p></li>
<li><p><a class="reference internal" href="../auto_examples/model_selection/plot_grid_search_text_feature_extraction.html#sphx-glr-auto-examples-model-selection-plot-grid-search-text-feature-extraction-py"><span class="std std-ref">Sample pipeline for text feature extraction and evaluation</span></a>,</p></li>
<li><p><a class="reference internal" href="../auto_examples/model_selection/plot_cv_predict.html#sphx-glr-auto-examples-model-selection-plot-cv-predict-py"><span class="std std-ref">Plotting Cross-Validated Predictions</span></a>,</p></li>
<li><p><a class="reference internal" href="../auto_examples/model_selection/plot_nested_cross_validation_iris.html#sphx-glr-auto-examples-model-selection-plot-nested-cross-validation-iris-py"><span class="std std-ref">Nested versus non-nested cross-validation</span></a>.</p></li>
</ul>
</section>
</section>
<section id="cross-validation-iterators">
<h2><span class="section-number">3.1.2. </span>Cross validation iterators<a class="headerlink" href="#cross-validation-iterators" title="Link to this heading">#</a></h2>
<p>The following sections list utilities to generate indices
that can be used to generate dataset splits according to different cross
validation strategies.</p>
<section id="cross-validation-iterators-for-i-i-d-data">
<span id="iid-cv"></span><h3><span class="section-number">3.1.2.1. </span>Cross-validation iterators for i.i.d. data<a class="headerlink" href="#cross-validation-iterators-for-i-i-d-data" title="Link to this heading">#</a></h3>
<p>Assuming that some data is Independent and Identically Distributed (i.i.d.) is
making the assumption that all samples stem from the same generative process
and that the generative process is assumed to have no memory of past generated
samples.</p>
<p>The following cross-validators can be used in such cases.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>While i.i.d. data is a common assumption in machine learning theory, it rarely
holds in practice. If one knows that the samples have been generated using a
time-dependent process, it is safer to
use a <a class="reference internal" href="#timeseries-cv"><span class="std std-ref">time-series aware cross-validation scheme</span></a>.
Similarly, if we know that the generative process has a group structure
(samples collected from different subjects, experiments, measurement
devices), it is safer to use <a class="reference internal" href="#group-cv"><span class="std std-ref">group-wise cross-validation</span></a>.</p>
</div>
<section id="k-fold">
<span id="id2"></span><h4><span class="section-number">3.1.2.1.1. </span>K-fold<a class="headerlink" href="#k-fold" title="Link to this heading">#</a></h4>
<p><a class="reference internal" href="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> divides all the samples in <span class="math notranslate nohighlight">\(k\)</span> groups of samples,
called folds (if <span class="math notranslate nohighlight">\(k = n\)</span>, this is equivalent to the <em>Leave One
Out</em> strategy), of equal sizes (if possible). The prediction function is
learned using <span class="math notranslate nohighlight">\(k - 1\)</span> folds, and the fold left out is used for test.</p>
<p>Example of 2-fold cross-validation on a dataset with 4 samples:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">KFold</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">"b"</span><span class="p">,</span> <span class="s2">"c"</span><span class="p">,</span> <span class="s2">"d"</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">kf</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">2</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">kf</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="s2">"</span><span class="si">%s</span><span class="s2"> </span><span class="si">%s</span><span class="s2">"</span> <span class="o">%</span> <span class="p">(</span><span class="n">train</span><span class="p">,</span> <span class="n">test</span><span class="p">))</span>
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