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<li><a class="reference internal" href="#">3.1. Cross-validation: evaluating estimator performance</a><ul>
<li><a class="reference internal" href="#computing-cross-validated-metrics">3.1.1. Computing cross-validated metrics</a><ul>
<li><a class="reference internal" href="#the-cross-validate-function-and-multiple-metric-evaluation">3.1.1.1. The cross_validate function and multiple metric evaluation</a></li>
<li><a class="reference internal" href="#obtaining-predictions-by-cross-validation">3.1.1.2. Obtaining predictions by cross-validation</a></li>
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<li><a class="reference internal" href="#cross-validation-iterators">3.1.2. Cross validation iterators</a><ul>
<li><a class="reference internal" href="#cross-validation-iterators-for-i-i-d-data">3.1.2.1. Cross-validation iterators for i.i.d. data</a><ul>
<li><a class="reference internal" href="#k-fold">3.1.2.1.1. K-fold</a></li>
<li><a class="reference internal" href="#repeated-k-fold">3.1.2.1.2. Repeated K-Fold</a></li>
<li><a class="reference internal" href="#leave-one-out-loo">3.1.2.1.3. Leave One Out (LOO)</a></li>
<li><a class="reference internal" href="#leave-p-out-lpo">3.1.2.1.4. Leave P Out (LPO)</a></li>
<li><a class="reference internal" href="#random-permutations-cross-validation-a-k-a-shuffle-split">3.1.2.1.5. Random permutations cross-validation a.k.a. Shuffle & Split</a></li>
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<li><a class="reference internal" href="#cross-validation-iterators-with-stratification-based-on-class-labels">3.1.2.2. Cross-validation iterators with stratification based on class labels.</a><ul>
<li><a class="reference internal" href="#stratified-k-fold">3.1.2.2.1. Stratified k-fold</a></li>
<li><a class="reference internal" href="#stratified-shuffle-split">3.1.2.2.2. Stratified Shuffle Split</a></li>
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<li><a class="reference internal" href="#cross-validation-iterators-for-grouped-data">3.1.2.3. Cross-validation iterators for grouped data</a><ul>
<li><a class="reference internal" href="#group-k-fold">3.1.2.3.1. Group k-fold</a></li>
<li><a class="reference internal" href="#stratifiedgroupkfold">3.1.2.3.2. StratifiedGroupKFold</a></li>
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<li><a class="reference internal" href="#leave-p-groups-out">3.1.2.3.4. Leave P Groups Out</a></li>
<li><a class="reference internal" href="#group-shuffle-split">3.1.2.3.5. Group Shuffle Split</a></li>
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<li><a class="reference internal" href="#predefined-fold-splits-validation-sets">3.1.2.4. Predefined Fold-Splits / Validation-Sets</a></li>
<li><a class="reference internal" href="#using-cross-validation-iterators-to-split-train-and-test">3.1.2.5. Using cross-validation iterators to split train and test</a></li>
<li><a class="reference internal" href="#cross-validation-of-time-series-data">3.1.2.6. Cross validation of time series data</a><ul>
<li><a class="reference internal" href="#time-series-split">3.1.2.6.1. Time Series Split</a></li>
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<li><a class="reference internal" href="#a-note-on-shuffling">3.1.3. A note on shuffling</a></li>
<li><a class="reference internal" href="#cross-validation-and-model-selection">3.1.4. Cross validation and model selection</a></li>
<li><a class="reference internal" href="#permutation-test-score">3.1.5. Permutation test score</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="Permalink 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="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.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</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="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn</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>
<blockquote>
<div><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>
</div></blockquote>
<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="../_images/grid_search_cross_validation.png" 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="Permalink 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="nn">sklearn.model_selection</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="nn">sklearn</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="nn">sklearn.model_selection</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="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>
<aside class="topic">
<p class="topic-title">Data transformation with held out data</p>
<p>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="nn">sklearn</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>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="nn">sklearn.pipeline</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>See <a class="reference internal" href="compose.html#combining-estimators"><span class="std std-ref">Pipelines and composite estimators</span></a>.</p>
</aside>
<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="Permalink 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 as well as fitted estimators) 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>.</p>
<p>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>.</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="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">cross_validate</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.metrics</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="nn">sklearn.metrics</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="Permalink 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>
<aside class="topic">
<p class="topic-title">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/grid_search_text_feature_extraction.html#sphx-glr-auto-examples-model-selection-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>
</aside>
</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="Permalink 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="Permalink 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="Permalink 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="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.model_selection</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>
<span class="go">[2 3] [0 1]</span>
<span class="go">[0 1] [2 3]</span>
</pre></div>
</div>
<p>Here is a visualization of the cross-validation behavior. Note that
<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> is not affected by classes or groups.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/model_selection/plot_cv_indices.html"><img alt="../_images/sphx_glr_plot_cv_indices_006.png" src="../_images/sphx_glr_plot_cv_indices_006.png" style="width: 450.0px; height: 225.0px;" /></a>
</figure>
<p>Each fold is constituted by two arrays: the first one is related to the
<em>training set</em>, and the second one to the <em>test set</em>.
Thus, one can create the training/test sets using numpy indexing:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">X</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="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">1.</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">y</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="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="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">X</span><span class="p">[</span><span class="n">train</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="n">test</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">train</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">test</span><span class="p">]</span>
</pre></div>
</div>
</section>
<section id="repeated-k-fold">
<span id="id3"></span><h4><span class="section-number">3.1.2.1.2. </span>Repeated K-Fold<a class="headerlink" href="#repeated-k-fold" title="Permalink to this heading">¶</a></h4>
<p><a class="reference internal" href="generated/sklearn.model_selection.RepeatedKFold.html#sklearn.model_selection.RepeatedKFold" title="sklearn.model_selection.RepeatedKFold"><code class="xref py py-class docutils literal notranslate"><span class="pre">RepeatedKFold</span></code></a> repeats K-Fold n times. It can be used when one
requires to run <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> n times, producing different splits in
each repetition.</p>
<p>Example of 2-fold K-Fold repeated 2 times:</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.model_selection</span> <span class="kn">import</span> <span class="n">RepeatedKFold</span>
<span class="gp">>>> </span><span class="n">X</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="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">random_state</span> <span class="o">=</span> <span class="mi">12883823</span>
<span class="gp">>>> </span><span class="n">rkf</span> <span class="o">=</span> <span class="n">RepeatedKFold</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="n">n_repeats</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="n">random_state</span><span class="p">)</span>
<span class="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">rkf</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>
<span class="gp">...</span>
<span class="go">[2 3] [0 1]</span>
<span class="go">[0 1] [2 3]</span>
<span class="go">[0 2] [1 3]</span>
<span class="go">[1 3] [0 2]</span>
</pre></div>
</div>
<p>Similarly, <a class="reference internal" href="generated/sklearn.model_selection.RepeatedStratifiedKFold.html#sklearn.model_selection.RepeatedStratifiedKFold" title="sklearn.model_selection.RepeatedStratifiedKFold"><code class="xref py py-class docutils literal notranslate"><span class="pre">RepeatedStratifiedKFold</span></code></a> repeats Stratified K-Fold n times
with different randomization in each repetition.</p>
</section>
<section id="leave-one-out-loo">
<span id="leave-one-out"></span><h4><span class="section-number">3.1.2.1.3. </span>Leave One Out (LOO)<a class="headerlink" href="#leave-one-out-loo" title="Permalink to this heading">¶</a></h4>
<p><a class="reference internal" href="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> (or LOO) is a simple cross-validation. Each learning
set is created by taking all the samples except one, the test set being
the sample left out. Thus, for <span class="math notranslate nohighlight">\(n\)</span> samples, we have <span class="math notranslate nohighlight">\(n\)</span> different
training sets and <span class="math notranslate nohighlight">\(n\)</span> different tests set. This cross-validation
procedure does not waste much data as only one sample is removed from the
training set:</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">LeaveOneOut</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">loo</span> <span class="o">=</span> <span class="n">LeaveOneOut</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">loo</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>
<span class="go">[1 2 3] [0]</span>
<span class="go">[0 2 3] [1]</span>
<span class="go">[0 1 3] [2]</span>
<span class="go">[0 1 2] [3]</span>
</pre></div>
</div>
<p>Potential users of LOO for model selection should weigh a few known caveats.
When compared with <span class="math notranslate nohighlight">\(k\)</span>-fold cross validation, one builds <span class="math notranslate nohighlight">\(n\)</span> models
from <span class="math notranslate nohighlight">\(n\)</span> samples instead of <span class="math notranslate nohighlight">\(k\)</span> models, where <span class="math notranslate nohighlight">\(n > k\)</span>.
Moreover, each is trained on <span class="math notranslate nohighlight">\(n - 1\)</span> samples rather than
<span class="math notranslate nohighlight">\((k-1) n / k\)</span>. In both ways, assuming <span class="math notranslate nohighlight">\(k\)</span> is not too large
and <span class="math notranslate nohighlight">\(k < n\)</span>, LOO is more computationally expensive than <span class="math notranslate nohighlight">\(k\)</span>-fold
cross validation.</p>
<p>In terms of accuracy, LOO often results in high variance as an estimator for the
test error. Intuitively, since <span class="math notranslate nohighlight">\(n - 1\)</span> of
the <span class="math notranslate nohighlight">\(n\)</span> samples are used to build each model, models constructed from
folds are virtually identical to each other and to the model built from the
entire training set.</p>
<p>However, if the learning curve is steep for the training size in question,
then 5- or 10- fold cross validation can overestimate the generalization error.</p>
<p>As a general rule, most authors, and empirical evidence, suggest that 5- or 10-
fold cross validation should be preferred to LOO.</p>
<aside class="topic">
<p class="topic-title">References:</p>
<ul class="simple">
<li><p><a class="reference external" href="http://www.faqs.org/faqs/ai-faq/neural-nets/part3/section-12.html">http://www.faqs.org/faqs/ai-faq/neural-nets/part3/section-12.html</a>;</p></li>
<li><p>T. Hastie, R. Tibshirani, J. Friedman, <a class="reference external" href="https://web.stanford.edu/~hastie/ElemStatLearn/">The Elements of Statistical Learning</a>, Springer 2009</p></li>
<li><p>L. Breiman, P. Spector <a class="reference external" href="http://digitalassets.lib.berkeley.edu/sdtr/ucb/text/197.pdf">Submodel selection and evaluation in regression: The X-random case</a>, International Statistical Review 1992;</p></li>
<li><p>R. Kohavi, <a class="reference external" href="https://www.ijcai.org/Proceedings/95-2/Papers/016.pdf">A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection</a>, Intl. Jnt. Conf. AI</p></li>
<li><p>R. Bharat Rao, G. Fung, R. Rosales, <a class="reference external" href="https://people.csail.mit.edu/romer/papers/CrossVal_SDM08.pdf">On the Dangers of Cross-Validation. An Experimental Evaluation</a>, SIAM 2008;</p></li>
<li><p>G. James, D. Witten, T. Hastie, R Tibshirani, <a class="reference external" href="https://www-bcf.usc.edu/~gareth/ISL/">An Introduction to
Statistical Learning</a>, Springer 2013.</p></li>
</ul>
</aside>
</section>
<section id="leave-p-out-lpo">
<span id="leave-p-out"></span><h4><span class="section-number">3.1.2.1.4. </span>Leave P Out (LPO)<a class="headerlink" href="#leave-p-out-lpo" title="Permalink to this heading">¶</a></h4>
<p><a class="reference internal" href="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> is very similar to <a class="reference internal" href="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> as it creates all
the possible training/test sets by removing <span class="math notranslate nohighlight">\(p\)</span> samples from the complete
set. For <span class="math notranslate nohighlight">\(n\)</span> samples, this produces <span class="math notranslate nohighlight">\({n \choose p}\)</span> train-test
pairs. Unlike <a class="reference internal" href="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> and <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>, the test sets will
overlap for <span class="math notranslate nohighlight">\(p > 1\)</span>.</p>
<p>Example of Leave-2-Out 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">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">LeavePOut</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">lpo</span> <span class="o">=</span> <span class="n">LeavePOut</span><span class="p">(</span><span class="n">p</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">lpo</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>
<span class="go">[2 3] [0 1]</span>
<span class="go">[1 3] [0 2]</span>
<span class="go">[1 2] [0 3]</span>
<span class="go">[0 3] [1 2]</span>
<span class="go">[0 2] [1 3]</span>
<span class="go">[0 1] [2 3]</span>
</pre></div>
</div>
</section>
<section id="random-permutations-cross-validation-a-k-a-shuffle-split">
<span id="shufflesplit"></span><h4><span class="section-number">3.1.2.1.5. </span>Random permutations cross-validation a.k.a. Shuffle & Split<a class="headerlink" href="#random-permutations-cross-validation-a-k-a-shuffle-split" title="Permalink to this heading">¶</a></h4>
<p>The <a class="reference internal" href="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> iterator will generate a user defined number of
independent train / test dataset splits. Samples are first shuffled and
then split into a pair of train and test sets.</p>
<p>It is possible to control the randomness for reproducibility of the
results by explicitly seeding the <code class="docutils literal notranslate"><span class="pre">random_state</span></code> pseudo random number
generator.</p>
<p>Here is a usage example:</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">ShuffleSplit</span>
<span class="gp">>>> </span><span class="n">X</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="mi">10</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">ss</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">0.25</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="k">for</span> <span class="n">train_index</span><span class="p">,</span> <span class="n">test_index</span> <span class="ow">in</span> <span class="n">ss</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_index</span><span class="p">,</span> <span class="n">test_index</span><span class="p">))</span>
<span class="go">[9 1 6 7 3 0 5] [2 8 4]</span>
<span class="go">[2 9 8 0 6 7 4] [3 5 1]</span>
<span class="go">[4 5 1 0 6 9 7] [2 3 8]</span>
<span class="go">[2 7 5 8 0 3 4] [6 1 9]</span>
<span class="go">[4 1 0 6 8 9 3] [5 2 7]</span>
</pre></div>
</div>
<p>Here is a visualization of the cross-validation behavior. Note that
<a class="reference internal" href="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> is not affected by classes or groups.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/model_selection/plot_cv_indices.html"><img alt="../_images/sphx_glr_plot_cv_indices_008.png" src="../_images/sphx_glr_plot_cv_indices_008.png" style="width: 450.0px; height: 225.0px;" /></a>
</figure>
<p><a class="reference internal" href="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> is thus a good alternative to <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> cross
validation that allows a finer control on the number of iterations and
the proportion of samples on each side of the train / test split.</p>
</section>
</section>
<section id="cross-validation-iterators-with-stratification-based-on-class-labels">
<span id="stratification"></span><h3><span class="section-number">3.1.2.2. </span>Cross-validation iterators with stratification based on class labels.<a class="headerlink" href="#cross-validation-iterators-with-stratification-based-on-class-labels" title="Permalink to this heading">¶</a></h3>
<p>Some classification problems can exhibit a large imbalance in the distribution
of the target classes: for instance there could be several times more negative
samples than positive samples. In such cases it is recommended to use
stratified sampling as implemented in <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> and
<a class="reference internal" href="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> to ensure that relative class frequencies is
approximately preserved in each train and validation fold.</p>
<section id="stratified-k-fold">
<span id="id4"></span><h4><span class="section-number">3.1.2.2.1. </span>Stratified k-fold<a class="headerlink" href="#stratified-k-fold" title="Permalink to this heading">¶</a></h4>
<p><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> is a variation of <em>k-fold</em> which returns <em>stratified</em>
folds: each set contains approximately the same percentage of samples of each
target class as the complete set.</p>
<p>Here is an example of stratified 3-fold cross-validation on a dataset with 50 samples from
two unbalanced classes. We show the number of samples in each class and compare with
<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>.</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">StratifiedKFold</span><span class="p">,</span> <span class="n">KFold</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</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">50</span><span class="p">,</span> <span class="mi">1</span><span class="p">)),</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">(([</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">45</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">skf</span> <span class="o">=</span> <span class="n">StratifiedKFold</span><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="mi">3</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">skf</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="gp">... </span> <span class="nb">print</span><span class="p">(</span><span class="s1">'train - </span><span class="si">{}</span><span class="s1"> | test - </span><span class="si">{}</span><span class="s1">'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">np</span><span class="o">.</span><span class="n">bincount</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="n">train</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">bincount</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="n">test</span><span class="p">])))</span>
<span class="go">train - [30 3] | test - [15 2]</span>
<span class="go">train - [30 3] | test - [15 2]</span>
<span class="go">train - [30 4] | test - [15 1]</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">3</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="n">y</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">{}</span><span class="s1"> | test - </span><span class="si">{}</span><span class="s1">'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">np</span><span class="o">.</span><span class="n">bincount</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="n">train</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">bincount</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="n">test</span><span class="p">])))</span>
<span class="go">train - [28 5] | test - [17]</span>
<span class="go">train - [28 5] | test - [17]</span>
<span class="go">train - [34] | test - [11 5]</span>
</pre></div>
</div>
<p>We can see that <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> preserves the class ratios
(approximately 1 / 10) in both train and test dataset.</p>
<p>Here is a visualization of the cross-validation behavior.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/model_selection/plot_cv_indices.html"><img alt="../_images/sphx_glr_plot_cv_indices_009.png" src="../_images/sphx_glr_plot_cv_indices_009.png" style="width: 450.0px; height: 225.0px;" /></a>
</figure>
<p><a class="reference internal" href="generated/sklearn.model_selection.RepeatedStratifiedKFold.html#sklearn.model_selection.RepeatedStratifiedKFold" title="sklearn.model_selection.RepeatedStratifiedKFold"><code class="xref py py-class docutils literal notranslate"><span class="pre">RepeatedStratifiedKFold</span></code></a> can be used to repeat Stratified K-Fold n times
with different randomization in each repetition.</p>
</section>
<section id="stratified-shuffle-split">
<span id="id5"></span><h4><span class="section-number">3.1.2.2.2. </span>Stratified Shuffle Split<a class="headerlink" href="#stratified-shuffle-split" title="Permalink to this heading">¶</a></h4>
<p><a class="reference internal" href="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> is a variation of <em>ShuffleSplit</em>, which returns
stratified splits, <em>i.e</em> which creates splits by preserving the same
percentage for each target class as in the complete set.</p>
<p>Here is a visualization of the cross-validation behavior.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/model_selection/plot_cv_indices.html"><img alt="../_images/sphx_glr_plot_cv_indices_012.png" src="../_images/sphx_glr_plot_cv_indices_012.png" style="width: 450.0px; height: 225.0px;" /></a>
</figure>
</section>
</section>
<section id="cross-validation-iterators-for-grouped-data">
<span id="group-cv"></span><h3><span class="section-number">3.1.2.3. </span>Cross-validation iterators for grouped data<a class="headerlink" href="#cross-validation-iterators-for-grouped-data" title="Permalink to this heading">¶</a></h3>
<p>The i.i.d. assumption is broken if the underlying generative process yield
groups of dependent samples.</p>
<p>Such a grouping of data is domain specific. An example would be when there is
medical data collected from multiple patients, with multiple samples taken from
each patient. And such data is likely to be dependent on the individual group.
In our example, the patient id for each sample will be its group identifier.</p>
<p>In this case we would like to know if a model trained on a particular set of
groups generalizes well to the unseen groups. To measure this, we need to
ensure that all the samples in the validation fold come from groups that are
not represented at all in the paired training fold.</p>
<p>The following cross-validation splitters can be used to do that.
The grouping identifier for the samples is specified via the <code class="docutils literal notranslate"><span class="pre">groups</span></code>
parameter.</p>
<section id="group-k-fold">
<span id="id6"></span><h4><span class="section-number">3.1.2.3.1. </span>Group k-fold<a class="headerlink" href="#group-k-fold" title="Permalink to this heading">¶</a></h4>
<p><a class="reference internal" href="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> is a variation of k-fold which ensures that the same group is
not represented in both testing and training sets. For example if the data is
obtained from different subjects with several samples per-subject and if the
model is flexible enough to learn from highly person specific features it
could fail to generalize to new subjects. <a class="reference internal" href="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> makes it possible
to detect this kind of overfitting situations.</p>
<p>Imagine you have three subjects, each with an associated number from 1 to 3:</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">GroupKFold</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">2.2</span><span class="p">,</span> <span class="mf">2.4</span><span class="p">,</span> <span class="mf">2.3</span><span class="p">,</span> <span class="mf">4.55</span><span class="p">,</span> <span class="mf">5.8</span><span class="p">,</span> <span class="mf">8.8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">y</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">"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">"d"</span><span class="p">,</span> <span class="s2">"d"</span><span class="p">,</span> <span class="s2">"d"</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">groups</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">gkf</span> <span class="o">=</span> <span class="n">GroupKFold</span><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="mi">3</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">gkf</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">groups</span><span class="o">=</span><span class="n">groups</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>
<span class="go">[0 1 2 3 4 5] [6 7 8 9]</span>
<span class="go">[0 1 2 6 7 8 9] [3 4 5]</span>
<span class="go">[3 4 5 6 7 8 9] [0 1 2]</span>
</pre></div>
</div>
<p>Each subject is in a different testing fold, and the same subject is never in
both testing and training. Notice that the folds do not have exactly the same
size due to the imbalance in the data. If class proportions must be balanced
across folds, <a class="reference internal" href="generated/sklearn.model_selection.StratifiedGroupKFold.html#sklearn.model_selection.StratifiedGroupKFold" title="sklearn.model_selection.StratifiedGroupKFold"><code class="xref py py-class docutils literal notranslate"><span class="pre">StratifiedGroupKFold</span></code></a> is a better option.</p>
<p>Here is a visualization of the cross-validation behavior.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/model_selection/plot_cv_indices.html"><img alt="../_images/sphx_glr_plot_cv_indices_007.png" src="../_images/sphx_glr_plot_cv_indices_007.png" style="width: 450.0px; height: 225.0px;" /></a>
</figure>
<p>Similar to <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>, the test sets from <a class="reference internal" href="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> will form a
complete partition of all the data. Unlike <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>, <a class="reference internal" href="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>
is not randomized at all, whereas <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> is randomized when
<code class="docutils literal notranslate"><span class="pre">shuffle=True</span></code>.</p>
</section>
<section id="stratifiedgroupkfold">
<span id="stratified-group-k-fold"></span><h4><span class="section-number">3.1.2.3.2. </span>StratifiedGroupKFold<a class="headerlink" href="#stratifiedgroupkfold" title="Permalink to this heading">¶</a></h4>
<p><a class="reference internal" href="generated/sklearn.model_selection.StratifiedGroupKFold.html#sklearn.model_selection.StratifiedGroupKFold" title="sklearn.model_selection.StratifiedGroupKFold"><code class="xref py py-class docutils literal notranslate"><span class="pre">StratifiedGroupKFold</span></code></a> is a cross-validation scheme that combines both
<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> and <a class="reference internal" href="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>. The idea is to try to
preserve the distribution of classes in each split while keeping each group
within a single split. That might be useful when you have an unbalanced
dataset so that using just <a class="reference internal" href="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> might produce skewed splits.</p>
<p>Example:</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">StratifiedGroupKFold</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">18</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="mi">6</span> <span class="o">+</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">12</span>
<span class="gp">>>> </span><span class="n">groups</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">sgkf</span> <span class="o">=</span> <span class="n">StratifiedGroupKFold</span><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="mi">3</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">sgkf</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">groups</span><span class="o">=</span><span class="n">groups</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>
<span class="go">[ 0 2 3 4 5 6 7 10 11 15 16 17] [ 1 8 9 12 13 14]</span>
<span class="go">[ 0 1 4 5 6 7 8 9 11 12 13 14] [ 2 3 10 15 16 17]</span>
<span class="go">[ 1 2 3 8 9 10 12 13 14 15 16 17] [ 0 4 5 6 7 11]</span>
</pre></div>
</div>
<p>Implementation notes:</p>
<ul>
<li><p>With the current implementation full shuffle is not possible in most
scenarios. When shuffle=True, the following happens:</p>
<ol class="arabic simple">
<li><p>All groups are shuffled.</p></li>
<li><p>Groups are sorted by standard deviation of classes using stable sort.</p></li>
<li><p>Sorted groups are iterated over and assigned to folds.</p></li>
</ol>
<p>That means that only groups with the same standard deviation of class
distribution will be shuffled, which might be useful when each group has only
a single class.</p>
</li>
<li><p>The algorithm greedily assigns each group to one of n_splits test sets,
choosing the test set that minimises the variance in class distribution
across test sets. Group assignment proceeds from groups with highest to
lowest variance in class frequency, i.e. large groups peaked on one or few
classes are assigned first.</p></li>
<li><p>This split is suboptimal in a sense that it might produce imbalanced splits
even if perfect stratification is possible. If you have relatively close
distribution of classes in each group, using <a class="reference internal" href="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> is better.</p></li>
</ul>
<p>Here is a visualization of cross-validation behavior for uneven groups:</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/model_selection/plot_cv_indices.html"><img alt="../_images/sphx_glr_plot_cv_indices_005.png" src="../_images/sphx_glr_plot_cv_indices_005.png" style="width: 450.0px; height: 225.0px;" /></a>
</figure>
</section>
<section id="leave-one-group-out">
<span id="id7"></span><h4><span class="section-number">3.1.2.3.3. </span>Leave One Group Out<a class="headerlink" href="#leave-one-group-out" title="Permalink to this heading">¶</a></h4>
<p><a class="reference internal" href="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> is a cross-validation scheme which holds out
the samples according to a third-party provided array of integer groups. This
group information can be used to encode arbitrary domain specific pre-defined
cross-validation folds.</p>
<p>Each training set is thus constituted by all the samples except the ones
related to a specific group. This is basically the same as
<a class="reference internal" href="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> with <code class="docutils literal notranslate"><span class="pre">n_groups=1</span></code>.</p>
<p>For example, in the cases of multiple experiments, <a class="reference internal" href="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>
can be used to create a cross-validation based on the different experiments:
we create a training set using the samples of all the experiments except one:</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">LeaveOneGroupOut</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">60</span><span class="p">,</span> <span class="mi">70</span><span class="p">,</span> <span class="mi">80</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">groups</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">logo</span> <span class="o">=</span> <span class="n">LeaveOneGroupOut</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">logo</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">groups</span><span class="o">=</span><span class="n">groups</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>
<span class="go">[2 3 4 5 6] [0 1]</span>
<span class="go">[0 1 4 5 6] [2 3]</span>
<span class="go">[0 1 2 3] [4 5 6]</span>
</pre></div>
</div>
<p>Another common application is to use time information: for instance the
groups could be the year of collection of the samples and thus allow
for cross-validation against time-based splits.</p>
</section>
<section id="leave-p-groups-out">
<span id="id8"></span><h4><span class="section-number">3.1.2.3.4. </span>Leave P Groups Out<a class="headerlink" href="#leave-p-groups-out" title="Permalink to this heading">¶</a></h4>
<p><a class="reference internal" href="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> is similar as <a class="reference internal" href="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>, but removes
samples related to <span class="math notranslate nohighlight">\(P\)</span> groups for each training/test set. All possible
combinations of <span class="math notranslate nohighlight">\(P\)</span> groups are left out, meaning test sets will overlap
for <span class="math notranslate nohighlight">\(P>1\)</span>.</p>
<p>Example of Leave-2-Group Out:</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">LeavePGroupsOut</span>
<span class="gp">>>> </span><span class="n">X</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="mi">6</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">groups</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">lpgo</span> <span class="o">=</span> <span class="n">LeavePGroupsOut</span><span class="p">(</span><span class="n">n_groups</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">lpgo</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">groups</span><span class="o">=</span><span class="n">groups</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>
<span class="go">[4 5] [0 1 2 3]</span>
<span class="go">[2 3] [0 1 4 5]</span>
<span class="go">[0 1] [2 3 4 5]</span>
</pre></div>
</div>
</section>
<section id="group-shuffle-split">
<span id="id9"></span><h4><span class="section-number">3.1.2.3.5. </span>Group Shuffle Split<a class="headerlink" href="#group-shuffle-split" title="Permalink to this heading">¶</a></h4>
<p>The <a class="reference internal" href="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> iterator behaves as a combination of
<a class="reference internal" href="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> and <a class="reference internal" href="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>, and generates a
sequence of randomized partitions in which a subset of groups are held
out for each split. Each train/test split is performed independently meaning
there is no guaranteed relationship between successive test sets.</p>
<p>Here is a usage example:</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">GroupShuffleSplit</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">2.2</span><span class="p">,</span> <span class="mf">2.4</span><span class="p">,</span> <span class="mf">2.3</span><span class="p">,</span> <span class="mf">4.55</span><span class="p">,</span> <span class="mf">5.8</span><span class="p">,</span> <span class="mf">0.001</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">y</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">"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">"a"</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">groups</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">gss</span> <span class="o">=</span> <span class="n">GroupShuffleSplit</span><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</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">gss</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">groups</span><span class="o">=</span><span class="n">groups</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>
<span class="gp">...</span>
<span class="go">[0 1 2 3] [4 5 6 7]</span>
<span class="go">[2 3 6 7] [0 1 4 5]</span>
<span class="go">[2 3 4 5] [0 1 6 7]</span>
<span class="go">[4 5 6 7] [0 1 2 3]</span>
</pre></div>
</div>
<p>Here is a visualization of the cross-validation behavior.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/model_selection/plot_cv_indices.html"><img alt="../_images/sphx_glr_plot_cv_indices_011.png" src="../_images/sphx_glr_plot_cv_indices_011.png" style="width: 450.0px; height: 225.0px;" /></a>
</figure>
<p>This class is useful when the behavior of <a class="reference internal" href="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> is
desired, but the number of groups is large enough that generating all
possible partitions with <span class="math notranslate nohighlight">\(P\)</span> groups withheld would be prohibitively
expensive. In such a scenario, <a class="reference internal" href="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> provides
a random sample (with replacement) of the train / test splits
generated by <a class="reference internal" href="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>.</p>
</section>
</section>
<section id="predefined-fold-splits-validation-sets">
<span id="predefined-split"></span><h3><span class="section-number">3.1.2.4. </span>Predefined Fold-Splits / Validation-Sets<a class="headerlink" href="#predefined-fold-splits-validation-sets" title="Permalink to this heading">¶</a></h3>
<p>For some datasets, a pre-defined split of the data into training- and
validation fold or into several cross-validation folds already
exists. Using <a class="reference internal" href="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> it is possible to use these folds
e.g. when searching for hyperparameters.</p>
<p>For example, when using a validation set, set the <code class="docutils literal notranslate"><span class="pre">test_fold</span></code> to 0 for all
samples that are part of the validation set, and to -1 for all other samples.</p>
</section>
<section id="using-cross-validation-iterators-to-split-train-and-test">
<h3><span class="section-number">3.1.2.5. </span>Using cross-validation iterators to split train and test<a class="headerlink" href="#using-cross-validation-iterators-to-split-train-and-test" title="Permalink to this heading">¶</a></h3>
<p>The above group cross-validation functions may also be useful for splitting a
dataset into training and testing subsets. Note that the convenience
function <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> is a wrapper around <a class="reference internal" href="generated/sklearn.model_selection.ShuffleSplit.html#sklearn.model_selection.ShuffleSplit" title="sklearn.model_selection.ShuffleSplit"><code class="xref py py-func docutils literal notranslate"><span class="pre">ShuffleSplit</span></code></a>
and thus only allows for stratified splitting (using the class labels)
and cannot account for groups.</p>
<p>To perform the train and test split, use the indices for the train and test
subsets yielded by the generator output by the <code class="docutils literal notranslate"><span class="pre">split()</span></code> method of the
cross-validation splitter. For example:</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.model_selection</span> <span class="kn">import</span> <span class="n">GroupShuffleSplit</span>
<span class="gp">>>> </span><span class="n">X</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="mf">0.1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">2.2</span><span class="p">,</span> <span class="mf">2.4</span><span class="p">,</span> <span class="mf">2.3</span><span class="p">,</span> <span class="mf">4.55</span><span class="p">,</span> <span class="mf">5.8</span><span class="p">,</span> <span class="mf">0.001</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">y</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="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">"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">"a"</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">groups</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="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">train_indx</span><span class="p">,</span> <span class="n">test_indx</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">GroupShuffleSplit</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">7</span><span class="p">)</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">groups</span><span class="p">)</span>
<span class="gp">... </span><span class="p">)</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="gp">... </span> <span class="n">X</span><span class="p">[</span><span class="n">train_indx</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="n">test_indx</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">train_indx</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">test_indx</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">X_test</span><span class="o">.</span><span class="n">shape</span>
<span class="go">((6,), (2,))</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">groups</span><span class="p">[</span><span class="n">train_indx</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">groups</span><span class="p">[</span><span class="n">test_indx</span><span class="p">])</span>
<span class="go">(array([1, 2, 4]), array([3]))</span>
</pre></div>
</div>
</section>
<section id="cross-validation-of-time-series-data">
<span id="timeseries-cv"></span><h3><span class="section-number">3.1.2.6. </span>Cross validation of time series data<a class="headerlink" href="#cross-validation-of-time-series-data" title="Permalink to this heading">¶</a></h3>
<p>Time series data is characterized by the correlation between observations
that are near in time (<em>autocorrelation</em>). However, classical
cross-validation techniques such as <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> and
<a class="reference internal" href="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> assume the samples are independent and
identically distributed, and would result in unreasonable correlation
between training and testing instances (yielding poor estimates of
generalization error) on time series data. Therefore, it is very important
to evaluate our model for time series data on the “future” observations
least like those that are used to train the model. To achieve this, one
solution is provided by <a class="reference internal" href="generated/sklearn.model_selection.TimeSeriesSplit.html#sklearn.model_selection.TimeSeriesSplit" title="sklearn.model_selection.TimeSeriesSplit"><code class="xref py py-class docutils literal notranslate"><span class="pre">TimeSeriesSplit</span></code></a>.</p>
<section id="time-series-split">
<span id="id10"></span><h4><span class="section-number">3.1.2.6.1. </span>Time Series Split<a class="headerlink" href="#time-series-split" title="Permalink to this heading">¶</a></h4>
<p><a class="reference internal" href="generated/sklearn.model_selection.TimeSeriesSplit.html#sklearn.model_selection.TimeSeriesSplit" title="sklearn.model_selection.TimeSeriesSplit"><code class="xref py py-class docutils literal notranslate"><span class="pre">TimeSeriesSplit</span></code></a> is a variation of <em>k-fold</em> which
returns first <span class="math notranslate nohighlight">\(k\)</span> folds as train set and the <span class="math notranslate nohighlight">\((k+1)\)</span> th
fold as test set. Note that unlike standard cross-validation methods,
successive training sets are supersets of those that come before them.
Also, it adds all surplus data to the first training partition, which
is always used to train the model.</p>
<p>This class can be used to cross-validate time series data samples
that are observed at fixed time intervals.</p>
<p>Example of 3-split time series cross-validation on a dataset with 6 samples:</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">TimeSeriesSplit</span>
<span class="gp">>>> </span><span class="n">X</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="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">y</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="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">tscv</span> <span class="o">=</span> <span class="n">TimeSeriesSplit</span><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">tscv</span><span class="p">)</span>
<span class="go">TimeSeriesSplit(gap=0, max_train_size=None, n_splits=3, test_size=None)</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">tscv</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>
<span class="go">[0 1 2] [3]</span>
<span class="go">[0 1 2 3] [4]</span>
<span class="go">[0 1 2 3 4] [5]</span>
</pre></div>
</div>
<p>Here is a visualization of the cross-validation behavior.</p>
<figure class="align-center">