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<ul>
<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="#obtaining-predictions-by-cross-validation">3.1.1.1. Obtaining predictions by cross-validation</a></li>
</ul>
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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="#k-fold">3.1.2.1. K-fold</a></li>
<li><a class="reference internal" href="#stratified-k-fold">3.1.2.2. Stratified k-fold</a></li>
<li><a class="reference internal" href="#label-k-fold">3.1.2.3. Label k-fold</a></li>
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<li><a class="reference internal" href="#leave-p-label-out">3.1.2.7. Leave-P-Label-Out</a></li>
<li><a class="reference internal" href="#random-permutations-cross-validation-a-k-a-shuffle-split">3.1.2.8. Random permutations cross-validation a.k.a. Shuffle & Split</a></li>
<li><a class="reference internal" href="#label-shuffle-split">3.1.2.9. Label-Shuffle-Split</a></li>
<li><a class="reference internal" href="#predefined-fold-splits-validation-sets">3.1.2.10. Predefined Fold-Splits / Validation-Sets</a></li>
<li><a class="reference internal" href="#see-also">3.1.2.11. See also</a></li>
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<div class="section" id="cross-validation-evaluating-estimator-performance">
<span id="cross-validation"></span><h1>3.1. Cross-validation: evaluating estimator performance<a class="headerlink" href="#cross-validation-evaluating-estimator-performance" title="Permalink to this headline">¶</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"><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.</p>
<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.cross_validation.train_test_split.html#sklearn.cross_validation.train_test_split" title="sklearn.cross_validation.train_test_split"><code class="xref py py-func docutils literal"><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-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">cross_validation</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">iris</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="gp">>>> </span><span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</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-python"><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">cross_validation</span><span class="o">.</span><span class="n">train_test_split</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span><span class="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"><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="http://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>A model is trained using <img class="math" src="../_images/math/aff99fd5805e4be25fcb57c9a2667f8337206a66.png" alt="k-1"/> of the folds as training data;</li>
<li>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).</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 it is the case when fixing an arbitrary test set),
which is a major advantage in problem such as inverse inference
where the number of samples is very small.</p>
<div class="section" id="computing-cross-validated-metrics">
<h2>3.1.1. Computing cross-validated metrics<a class="headerlink" href="#computing-cross-validated-metrics" title="Permalink to this headline">¶</a></h2>
<p>The simplest way to use cross-validation is to call the
<a class="reference internal" href="generated/sklearn.cross_validation.cross_val_score.html#sklearn.cross_validation.cross_val_score" title="sklearn.cross_validation.cross_val_score"><code class="xref py py-func docutils literal"><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-python"><div class="highlight"><pre><span></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="gp">>>> </span><span class="n">scores</span> <span class="o">=</span> <span class="n">cross_validation</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">iris</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span><span class="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="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 95% confidence interval of the score estimate are hence
given by:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">print</span><span class="p">(</span><span class="s2">"Accuracy: </span><span class="si">%0.2f</span><span class="s2"> (+/- </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="o">*</span> <span class="mi">2</span><span class="p">))</span>
<span class="go">Accuracy: 0.98 (+/- 0.03)</span>
</pre></div>
</div>
<p>By default, the score computed at each CV iteration is the <code class="docutils literal"><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-python"><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_validation</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">iris</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span><span class="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">scoring</span><span class="o">=</span><span class="s1">'f1_weighted'</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>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"><span class="pre">cv</span></code> argument is an integer, <a class="reference internal" href="generated/sklearn.cross_validation.cross_val_score.html#sklearn.cross_validation.cross_val_score" title="sklearn.cross_validation.cross_val_score"><code class="xref py py-func docutils literal"><span class="pre">cross_val_score</span></code></a> uses the
<a class="reference internal" href="generated/sklearn.cross_validation.KFold.html#sklearn.cross_validation.KFold" title="sklearn.cross_validation.KFold"><code class="xref py py-class docutils literal"><span class="pre">KFold</span></code></a> or <a class="reference internal" href="generated/sklearn.cross_validation.StratifiedKFold.html#sklearn.cross_validation.StratifiedKFold" title="sklearn.cross_validation.StratifiedKFold"><code class="xref py py-class docutils literal"><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"><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-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">n_samples</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</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">cross_validation</span><span class="o">.</span><span class="n">ShuffleSplit</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">n_iter</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
<span class="gp">... </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_validation</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">iris</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="n">cv</span><span class="p">)</span>
<span class="gp">... </span>
<span class="go">array([ 0.97..., 0.97..., 1. ])</span>
</pre></div>
</div>
<div class="topic">
<p class="topic-title first">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>data transformations</span></a> similarly should
be learnt from a training set and applied to held-out data for prediction:</p>
<div class="highlight-python"><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">cross_validation</span><span class="o">.</span><span class="n">train_test_split</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span><span class="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"><span class="pre">Pipeline</span></code></a> makes it easier to compose
estimators, providing this behavior under cross-validation:</p>
<div class="highlight-python"><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_validation</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">iris</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="n">cv</span><span class="p">)</span>
<span class="gp">... </span>
<span class="go">array([ 0.97..., 0.93..., 0.95...])</span>
</pre></div>
</div>
<p>See <a class="reference internal" href="pipeline.html#combining-estimators"><span>Pipeline and FeatureUnion: combining estimators</span></a>.</p>
</div>
<div class="section" id="obtaining-predictions-by-cross-validation">
<h3>3.1.1.1. Obtaining predictions by cross-validation<a class="headerlink" href="#obtaining-predictions-by-cross-validation" title="Permalink to this headline">¶</a></h3>
<p>The function <a class="reference internal" href="generated/sklearn.cross_validation.cross_val_predict.html#sklearn.cross_validation.cross_val_predict" title="sklearn.cross_validation.cross_val_predict"><code class="xref py py-func docutils literal"><span class="pre">cross_val_predict</span></code></a> has a similar interface to
<a class="reference internal" href="generated/sklearn.cross_validation.cross_val_score.html#sklearn.cross_validation.cross_val_score" title="sklearn.cross_validation.cross_val_score"><code class="xref py py-func docutils literal"><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>
<p>These prediction can then be used to evaluate the classifier:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">predicted</span> <span class="o">=</span> <span class="n">cross_validation</span><span class="o">.</span><span class="n">cross_val_predict</span><span class="p">(</span><span class="n">clf</span><span class="p">,</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">metrics</span><span class="o">.</span><span class="n">accuracy_score</span><span class="p">(</span><span class="n">iris</span><span class="o">.</span><span class="n">target</span><span class="p">,</span> <span class="n">predicted</span><span class="p">)</span>
<span class="go">0.966...</span>
</pre></div>
</div>
<p>Note that the result of this computation may be slightly different from those
obtained using <a class="reference internal" href="generated/sklearn.cross_validation.cross_val_score.html#sklearn.cross_validation.cross_val_score" title="sklearn.cross_validation.cross_val_score"><code class="xref py py-func docutils literal"><span class="pre">cross_val_score</span></code></a> as the elements are grouped in different
ways.</p>
<p>The available cross validation iterators are introduced in the following
section.</p>
<div class="topic">
<p class="topic-title first">Examples</p>
<ul class="simple">
<li><a class="reference internal" href="../auto_examples/model_selection/plot_roc_crossval.html#example-model-selection-plot-roc-crossval-py"><span>Receiver Operating Characteristic (ROC) with cross validation</span></a>,</li>
<li><a class="reference internal" href="../auto_examples/feature_selection/plot_rfe_with_cross_validation.html#example-feature-selection-plot-rfe-with-cross-validation-py"><span>Recursive feature elimination with cross-validation</span></a>,</li>
<li><a class="reference internal" href="../auto_examples/model_selection/grid_search_digits.html#example-model-selection-grid-search-digits-py"><span>Parameter estimation using grid search with cross-validation</span></a>,</li>
<li><a class="reference internal" href="../auto_examples/model_selection/grid_search_text_feature_extraction.html#example-model-selection-grid-search-text-feature-extraction-py"><span>Sample pipeline for text feature extraction and evaluation</span></a>,</li>
<li><a class="reference internal" href="../auto_examples/plot_cv_predict.html#example-plot-cv-predict-py"><span>Plotting Cross-Validated Predictions</span></a>,</li>
</ul>
</div>
</div>
</div>
<div class="section" id="cross-validation-iterators">
<h2>3.1.2. Cross validation iterators<a class="headerlink" href="#cross-validation-iterators" title="Permalink to this headline">¶</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>
<div class="section" id="k-fold">
<h3>3.1.2.1. K-fold<a class="headerlink" href="#k-fold" title="Permalink to this headline">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.cross_validation.KFold.html#sklearn.cross_validation.KFold" title="sklearn.cross_validation.KFold"><code class="xref py py-class docutils literal"><span class="pre">KFold</span></code></a> divides all the samples in <img class="math" src="../_images/math/e9203da50e1059455123460d4e716c9c7f440cc3.png" alt="k"/> groups of samples,
called folds (if <img class="math" src="../_images/math/48b80c2fee19e41a529e3220199a5562ea29e35d.png" alt="k = n"/>, this is equivalent to the <em>Leave One
Out</em> strategy), of equal sizes (if possible). The prediction function is
learned using <img class="math" src="../_images/math/23ca2c534b3fe41683cbc51a0948ba22563356d1.png" alt="k - 1"/> 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-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">KFold</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="mi">4</span><span class="p">,</span> <span class="n">n_folds</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="p">:</span>
<span class="gp">... </span> <span class="k">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>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-python"><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>
</div>
<div class="section" id="stratified-k-fold">
<h3>3.1.2.2. Stratified k-fold<a class="headerlink" href="#stratified-k-fold" title="Permalink to this headline">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.cross_validation.StratifiedKFold.html#sklearn.cross_validation.StratifiedKFold" title="sklearn.cross_validation.StratifiedKFold"><code class="xref py py-class docutils literal"><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>Example of stratified 3-fold cross-validation on a dataset with 10 samples from
two slightly unbalanced classes:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">StratifiedKFold</span>
<span class="gp">>>> </span><span class="n">labels</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</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">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">1</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">labels</span><span class="p">,</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="p">:</span>
<span class="gp">... </span> <span class="k">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 6 7 8 9] [0 1 4 5]</span>
<span class="go">[0 1 3 4 5 8 9] [2 6 7]</span>
<span class="go">[0 1 2 4 5 6 7] [3 8 9]</span>
</pre></div>
</div>
</div>
<div class="section" id="label-k-fold">
<h3>3.1.2.3. Label k-fold<a class="headerlink" href="#label-k-fold" title="Permalink to this headline">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.cross_validation.LabelKFold.html#sklearn.cross_validation.LabelKFold" title="sklearn.cross_validation.LabelKFold"><code class="xref py py-class docutils literal"><span class="pre">LabelKFold</span></code></a> is a variation of <em>k-fold</em> which ensures that the same
label is not in both testing and training sets. This is necessary for example
if you obtained data from different subjects and you want to avoid over-fitting
(i.e., learning person specific features) by testing and training on different
subjects.</p>
<p>Imagine you have three subjects, each with an associated number from 1 to 3:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">LabelKFold</span>
<span class="gp">>>> </span><span class="n">labels</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">lkf</span> <span class="o">=</span> <span class="n">LabelKFold</span><span class="p">(</span><span class="n">labels</span><span class="p">,</span> <span class="n">n_folds</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">lkf</span><span class="p">:</span>
<span class="gp">... </span> <span class="k">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.</p>
</div>
<div class="section" id="leave-one-out-loo">
<h3>3.1.2.4. Leave-One-Out - LOO<a class="headerlink" href="#leave-one-out-loo" title="Permalink to this headline">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.cross_validation.LeaveOneOut.html#sklearn.cross_validation.LeaveOneOut" title="sklearn.cross_validation.LeaveOneOut"><code class="xref py py-class docutils literal"><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 <img class="math" src="../_images/math/413f8a8e40062a9090d9d50b88bc7b551b314c26.png" alt="n"/> samples, we have <img class="math" src="../_images/math/413f8a8e40062a9090d9d50b88bc7b551b314c26.png" alt="n"/> different
training sets and <img class="math" src="../_images/math/413f8a8e40062a9090d9d50b88bc7b551b314c26.png" alt="n"/> 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-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">LeaveOneOut</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="mi">4</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="p">:</span>
<span class="gp">... </span> <span class="k">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 <img class="math" src="../_images/math/e9203da50e1059455123460d4e716c9c7f440cc3.png" alt="k"/>-fold cross validation, one builds <img class="math" src="../_images/math/413f8a8e40062a9090d9d50b88bc7b551b314c26.png" alt="n"/> models
from <img class="math" src="../_images/math/413f8a8e40062a9090d9d50b88bc7b551b314c26.png" alt="n"/> samples instead of <img class="math" src="../_images/math/e9203da50e1059455123460d4e716c9c7f440cc3.png" alt="k"/> models, where <img class="math" src="../_images/math/1f8d6a1c6e2d5114c2d22fd2592a116661811378.png" alt="n > k"/>.
Moreover, each is trained on <img class="math" src="../_images/math/baa709da88ecdd56290056e3c38fabe588997875.png" alt="n - 1"/> samples rather than
<img class="math" src="../_images/math/7b9f3442b3a233a596cbd4f46f76e7ce4f1ca6fb.png" alt="(k-1)n / k"/>. In both ways, assuming <img class="math" src="../_images/math/e9203da50e1059455123460d4e716c9c7f440cc3.png" alt="k"/> is not too large
and <img class="math" src="../_images/math/9409722cc2a6a7d686d6cd7011aabf9fea6197df.png" alt="k < n"/>, LOO is more computationally expensive than <img class="math" src="../_images/math/e9203da50e1059455123460d4e716c9c7f440cc3.png" alt="k"/>-fold
cross validation.</p>
<p>In terms of accuracy, LOO often results in high variance as an estimator for the
test error. Intuitively, since <img class="math" src="../_images/math/baa709da88ecdd56290056e3c38fabe588997875.png" alt="n - 1"/> of
the <img class="math" src="../_images/math/413f8a8e40062a9090d9d50b88bc7b551b314c26.png" alt="n"/> 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>
<div class="topic">
<p class="topic-title first">References:</p>
<ul class="simple">
<li><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></li>
<li>T. Hastie, R. Tibshirani, J. Friedman, <a class="reference external" href="http://www-stat.stanford.edu/~tibs/ElemStatLearn">The Elements of Statistical Learning</a>, Springer 2009</li>
<li>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</li>
<li>R. Kohavi, <a class="reference external" href="http://www.cs.iastate.edu/~jtian/cs573/Papers/Kohavi-IJCAI-95.pdf">A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection</a>, Intl. Jnt. Conf. AI</li>
<li>R. Bharat Rao, G. Fung, R. Rosales, <a class="reference external" href="http://www.siam.org/proceedings/datamining/2008/dm08_54_Rao.pdf">On the Dangers of Cross-Validation. An Experimental Evaluation</a>, SIAM 2008</li>
<li>G. James, D. Witten, T. Hastie, R Tibshirani, <a class="reference external" href="http://www-bcf.usc.edu/~gareth/ISL">An Introduction to
Statistical Learning</a>, Springer 2013</li>
</ul>
</div>
</div>
<div class="section" id="leave-p-out-lpo">
<h3>3.1.2.5. Leave-P-Out - LPO<a class="headerlink" href="#leave-p-out-lpo" title="Permalink to this headline">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.cross_validation.LeavePOut.html#sklearn.cross_validation.LeavePOut" title="sklearn.cross_validation.LeavePOut"><code class="xref py py-class docutils literal"><span class="pre">LeavePOut</span></code></a> is very similar to <a class="reference internal" href="generated/sklearn.cross_validation.LeaveOneOut.html#sklearn.cross_validation.LeaveOneOut" title="sklearn.cross_validation.LeaveOneOut"><code class="xref py py-class docutils literal"><span class="pre">LeaveOneOut</span></code></a> as it creates all
the possible training/test sets by removing <img class="math" src="../_images/math/3eca8557203e86160952e1c0f735f7417f3285b1.png" alt="p"/> samples from the complete
set. For <img class="math" src="../_images/math/413f8a8e40062a9090d9d50b88bc7b551b314c26.png" alt="n"/> samples, this produces <img class="math" src="../_images/math/d72a9aef7b3237cc3733eef2e7aef97a156230e8.png" alt="{n \choose p}"/> train-test
pairs. Unlike <a class="reference internal" href="generated/sklearn.cross_validation.LeaveOneOut.html#sklearn.cross_validation.LeaveOneOut" title="sklearn.cross_validation.LeaveOneOut"><code class="xref py py-class docutils literal"><span class="pre">LeaveOneOut</span></code></a> and <a class="reference internal" href="generated/sklearn.cross_validation.KFold.html#sklearn.cross_validation.KFold" title="sklearn.cross_validation.KFold"><code class="xref py py-class docutils literal"><span class="pre">KFold</span></code></a>, the test sets will
overlap for <img class="math" src="../_images/math/db30f65159c0f4b2e3ec318ed09839aa42bf261a.png" alt="p > 1"/>.</p>
<p>Example of Leave-2-Out on a dataset with 4 samples:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">LeavePOut</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="mi">4</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="p">:</span>
<span class="gp">... </span> <span class="k">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>
</div>
<div class="section" id="leave-one-label-out-lolo">
<h3>3.1.2.6. Leave-One-Label-Out - LOLO<a class="headerlink" href="#leave-one-label-out-lolo" title="Permalink to this headline">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.cross_validation.LeaveOneLabelOut.html#sklearn.cross_validation.LeaveOneLabelOut" title="sklearn.cross_validation.LeaveOneLabelOut"><code class="xref py py-class docutils literal"><span class="pre">LeaveOneLabelOut</span></code></a> (LOLO) is a cross-validation scheme which holds out
the samples according to a third-party provided array of integer labels. This
label 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 label.</p>
<p>For example, in the cases of multiple experiments, <em>LOLO</em> 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-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">LeaveOneLabelOut</span>
<span class="gp">>>> </span><span class="n">labels</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="gp">>>> </span><span class="n">lolo</span> <span class="o">=</span> <span class="n">LeaveOneLabelOut</span><span class="p">(</span><span class="n">labels</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">lolo</span><span class="p">:</span>
<span class="gp">... </span> <span class="k">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>Another common application is to use time information: for instance the
labels could be the year of collection of the samples and thus allow
for cross-validation against time-based splits.</p>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p class="last">Contrary to <a class="reference internal" href="generated/sklearn.cross_validation.StratifiedKFold.html#sklearn.cross_validation.StratifiedKFold" title="sklearn.cross_validation.StratifiedKFold"><code class="xref py py-class docutils literal"><span class="pre">StratifiedKFold</span></code></a>, <strong>the ``labels`` of
:class:`LeaveOneLabelOut` should not encode the target class to predict</strong>:
the goal of <a class="reference internal" href="generated/sklearn.cross_validation.StratifiedKFold.html#sklearn.cross_validation.StratifiedKFold" title="sklearn.cross_validation.StratifiedKFold"><code class="xref py py-class docutils literal"><span class="pre">StratifiedKFold</span></code></a> is to rebalance dataset classes across
the train / test split to ensure that the train and test folds have
approximately the same percentage of samples of each class while
<a class="reference internal" href="generated/sklearn.cross_validation.LeaveOneLabelOut.html#sklearn.cross_validation.LeaveOneLabelOut" title="sklearn.cross_validation.LeaveOneLabelOut"><code class="xref py py-class docutils literal"><span class="pre">LeaveOneLabelOut</span></code></a> will do the opposite by ensuring that the samples
of the train and test fold will not share the same label value.</p>
</div>
</div>
<div class="section" id="leave-p-label-out">
<h3>3.1.2.7. Leave-P-Label-Out<a class="headerlink" href="#leave-p-label-out" title="Permalink to this headline">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.cross_validation.LeavePLabelOut.html#sklearn.cross_validation.LeavePLabelOut" title="sklearn.cross_validation.LeavePLabelOut"><code class="xref py py-class docutils literal"><span class="pre">LeavePLabelOut</span></code></a> is similar as <em>Leave-One-Label-Out</em>, but removes
samples related to <img class="math" src="../_images/math/f48b617185733d8dd6712643f1ab17c736661a06.png" alt="P"/> labels for each training/test set.</p>
<p>Example of Leave-2-Label Out:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">LeavePLabelOut</span>
<span class="gp">>>> </span><span class="n">labels</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">lplo</span> <span class="o">=</span> <span class="n">LeavePLabelOut</span><span class="p">(</span><span class="n">labels</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">lplo</span><span class="p">:</span>
<span class="gp">... </span> <span class="k">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>
</div>
<div class="section" id="random-permutations-cross-validation-a-k-a-shuffle-split">
<span id="shufflesplit"></span><h3>3.1.2.8. 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 headline">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.cross_validation.ShuffleSplit.html#sklearn.cross_validation.ShuffleSplit" title="sklearn.cross_validation.ShuffleSplit"><code class="xref py py-class docutils literal"><span class="pre">ShuffleSplit</span></code></a></p>
<p>The <a class="reference internal" href="generated/sklearn.cross_validation.ShuffleSplit.html#sklearn.cross_validation.ShuffleSplit" title="sklearn.cross_validation.ShuffleSplit"><code class="xref py py-class docutils literal"><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"><span class="pre">random_state</span></code> pseudo random number
generator.</p>
<p>Here is a usage example:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">ss</span> <span class="o">=</span> <span class="n">cross_validation</span><span class="o">.</span><span class="n">ShuffleSplit</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="n">n_iter</span><span class="o">=</span><span class="mi">3</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="gp">... </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="p">:</span>
<span class="gp">... </span> <span class="k">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="gp">...</span>
<span class="go">[1 3 4] [2 0]</span>
<span class="go">[1 4 3] [0 2]</span>
<span class="go">[4 0 2] [1 3]</span>
</pre></div>
</div>
<p><a class="reference internal" href="generated/sklearn.cross_validation.ShuffleSplit.html#sklearn.cross_validation.ShuffleSplit" title="sklearn.cross_validation.ShuffleSplit"><code class="xref py py-class docutils literal"><span class="pre">ShuffleSplit</span></code></a> is thus a good alternative to <a class="reference internal" href="generated/sklearn.cross_validation.KFold.html#sklearn.cross_validation.KFold" title="sklearn.cross_validation.KFold"><code class="xref py py-class docutils literal"><span class="pre">KFold</span></code></a> cross
validation that allows a finer control on the number of iterations and
the proportion of samples in on each side of the train / test split.</p>
</div>
<div class="section" id="label-shuffle-split">
<h3>3.1.2.9. Label-Shuffle-Split<a class="headerlink" href="#label-shuffle-split" title="Permalink to this headline">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.cross_validation.LabelShuffleSplit.html#sklearn.cross_validation.LabelShuffleSplit" title="sklearn.cross_validation.LabelShuffleSplit"><code class="xref py py-class docutils literal"><span class="pre">LabelShuffleSplit</span></code></a></p>
<p>The <a class="reference internal" href="generated/sklearn.cross_validation.LabelShuffleSplit.html#sklearn.cross_validation.LabelShuffleSplit" title="sklearn.cross_validation.LabelShuffleSplit"><code class="xref py py-class docutils literal"><span class="pre">LabelShuffleSplit</span></code></a> iterator behaves as a combination of
<a class="reference internal" href="generated/sklearn.cross_validation.ShuffleSplit.html#sklearn.cross_validation.ShuffleSplit" title="sklearn.cross_validation.ShuffleSplit"><code class="xref py py-class docutils literal"><span class="pre">ShuffleSplit</span></code></a> and <code class="xref py py-class docutils literal"><span class="pre">LeavePLabelsOut</span></code>, and generates a
sequence of randomized partitions in which a subset of labels are held
out for each split.</p>
<p>Here is a usage example:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">LabelShuffleSplit</span>
<span class="gp">>>> </span><span class="n">labels</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">slo</span> <span class="o">=</span> <span class="n">LabelShuffleSplit</span><span class="p">(</span><span class="n">labels</span><span class="p">,</span> <span class="n">n_iter</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="gp">... </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">slo</span><span class="p">:</span>
<span class="gp">... </span> <span class="k">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>This class is useful when the behavior of <code class="xref py py-class docutils literal"><span class="pre">LeavePLabelsOut</span></code> is
desired, but the number of labels is large enough that generating all
possible partitions with <img class="math" src="../_images/math/f48b617185733d8dd6712643f1ab17c736661a06.png" alt="P"/> labels withheld would be prohibitively
expensive. In such a scenario, <a class="reference internal" href="generated/sklearn.cross_validation.LabelShuffleSplit.html#sklearn.cross_validation.LabelShuffleSplit" title="sklearn.cross_validation.LabelShuffleSplit"><code class="xref py py-class docutils literal"><span class="pre">LabelShuffleSplit</span></code></a> provides
a random sample (with replacement) of the train / test splits
generated by <code class="xref py py-class docutils literal"><span class="pre">LeavePLabelsOut</span></code>.</p>
</div>
<div class="section" id="predefined-fold-splits-validation-sets">
<h3>3.1.2.10. Predefined Fold-Splits / Validation-Sets<a class="headerlink" href="#predefined-fold-splits-validation-sets" title="Permalink to this headline">¶</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.cross_validation.PredefinedSplit.html#sklearn.cross_validation.PredefinedSplit" title="sklearn.cross_validation.PredefinedSplit"><code class="xref py py-class docutils literal"><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"><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>
</div>
<div class="section" id="see-also">
<h3>3.1.2.11. See also<a class="headerlink" href="#see-also" title="Permalink to this headline">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.cross_validation.StratifiedShuffleSplit.html#sklearn.cross_validation.StratifiedShuffleSplit" title="sklearn.cross_validation.StratifiedShuffleSplit"><code class="xref py py-class docutils literal"><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>
</div>
</div>
<div class="section" id="a-note-on-shuffling">
<h2>3.1.3. A note on shuffling<a class="headerlink" href="#a-note-on-shuffling" title="Permalink to this headline">¶</a></h2>
<p>If the data ordering is not arbitrary (e.g. samples with the same label are
contiguous), shuffling it first may be essential to get a meaningful cross-
validation result. However, the opposite may be true if the samples are not
independently and identically distributed. For example, if samples correspond
to news articles, and are ordered by their time of publication, then shuffling
the data will likely lead to a model that is overfit and an inflated validation
score: it will be tested on samples that are artificially similar (close in
time) to training samples.</p>
<p>Some cross validation iterators, such as <a class="reference internal" href="generated/sklearn.cross_validation.KFold.html#sklearn.cross_validation.KFold" title="sklearn.cross_validation.KFold"><code class="xref py py-class docutils literal"><span class="pre">KFold</span></code></a>, have an inbuilt option
to shuffle the data indices before splitting them. Note that:</p>
<ul class="simple">
<li>This consumes less memory than shuffling the data directly.</li>
<li>By default no shuffling occurs, including for the (stratified) K fold cross-
validation performed by specifying <code class="docutils literal"><span class="pre">cv=some_integer</span></code> to
<a class="reference internal" href="generated/sklearn.cross_validation.cross_val_score.html#sklearn.cross_validation.cross_val_score" title="sklearn.cross_validation.cross_val_score"><code class="xref py py-func docutils literal"><span class="pre">cross_val_score</span></code></a>, grid search, etc. Keep in mind that
<a class="reference internal" href="generated/sklearn.cross_validation.train_test_split.html#sklearn.cross_validation.train_test_split" title="sklearn.cross_validation.train_test_split"><code class="xref py py-func docutils literal"><span class="pre">train_test_split</span></code></a> still returns a random split.</li>
<li>The <code class="docutils literal"><span class="pre">random_state</span></code> parameter defaults to <code class="docutils literal"><span class="pre">None</span></code>, meaning that the
shuffling will be different every time <code class="docutils literal"><span class="pre">KFold(...,</span> <span class="pre">shuffle=True)</span></code> is
iterated. However, <code class="docutils literal"><span class="pre">GridSearchCV</span></code> will use the same shuffling for each set
of parameters validated by a single call to its <code class="docutils literal"><span class="pre">fit</span></code> method.</li>
<li>To ensure results are repeatable (<em>on the same platform</em>), use a fixed value
for <code class="docutils literal"><span class="pre">random_state</span></code>.</li>
</ul>
</div>
<div class="section" id="cross-validation-and-model-selection">
<h2>3.1.4. Cross validation and model selection<a class="headerlink" href="#cross-validation-and-model-selection" title="Permalink to this headline">¶</a></h2>
<p>Cross validation iterators can also be used to directly perform model
selection using Grid Search for the optimal hyperparameters of the
model. This is the topic if the next section: <a class="reference internal" href="grid_search.html#grid-search"><span>Grid Search: Searching for estimator parameters</span></a>.</p>
</div>
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