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<li><a class="reference internal" href="#">3.2. Tuning the hyper-parameters of an estimator</a><ul>
<li><a class="reference internal" href="#exhaustive-grid-search">3.2.1. Exhaustive Grid Search</a></li>
<li><a class="reference internal" href="#randomized-parameter-optimization">3.2.2. Randomized Parameter Optimization</a></li>
<li><a class="reference internal" href="#searching-for-optimal-parameters-with-successive-halving">3.2.3. Searching for optimal parameters with successive halving</a><ul>
<li><a class="reference internal" href="#choosing-min-resources-and-the-number-of-candidates">3.2.3.1. Choosing <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> and the number of candidates</a></li>
<li><a class="reference internal" href="#amount-of-resource-and-number-of-candidates-at-each-iteration">3.2.3.2. Amount of resource and number of candidates at each iteration</a></li>
<li><a class="reference internal" href="#choosing-a-resource">3.2.3.3. Choosing a resource</a></li>
<li><a class="reference internal" href="#exhausting-the-available-resources">3.2.3.4. Exhausting the available resources</a></li>
<li><a class="reference internal" href="#aggressive-elimination-of-candidates">3.2.3.5. Aggressive elimination of candidates</a></li>
<li><a class="reference internal" href="#analyzing-results-with-the-cv-results-attribute">3.2.3.6. Analyzing results with the <code class="docutils literal notranslate"><span class="pre">cv_results_</span></code> attribute</a></li>
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<li><a class="reference internal" href="#specifying-an-objective-metric">3.2.4.1. Specifying an objective metric</a></li>
<li><a class="reference internal" href="#specifying-multiple-metrics-for-evaluation">3.2.4.2. Specifying multiple metrics for evaluation</a></li>
<li><a class="reference internal" href="#composite-estimators-and-parameter-spaces">3.2.4.3. Composite estimators and parameter spaces</a></li>
<li><a class="reference internal" href="#model-selection-development-and-evaluation">3.2.4.4. Model selection: development and evaluation</a></li>
<li><a class="reference internal" href="#parallelism">3.2.4.5. Parallelism</a></li>
<li><a class="reference internal" href="#robustness-to-failure">3.2.4.6. Robustness to failure</a></li>
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<li><a class="reference internal" href="#alternatives-to-brute-force-parameter-search">3.2.5. Alternatives to brute force parameter search</a><ul>
<li><a class="reference internal" href="#model-specific-cross-validation">3.2.5.1. Model specific cross-validation</a></li>
<li><a class="reference internal" href="#information-criterion">3.2.5.2. Information Criterion</a></li>
<li><a class="reference internal" href="#out-of-bag-estimates">3.2.5.3. Out of Bag Estimates</a></li>
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<section id="tuning-the-hyper-parameters-of-an-estimator">
<span id="grid-search"></span><h1><span class="section-number">3.2. </span>Tuning the hyper-parameters of an estimator<a class="headerlink" href="#tuning-the-hyper-parameters-of-an-estimator" title="Permalink to this heading">¶</a></h1>
<p>Hyper-parameters are parameters that are not directly learnt within estimators.
In scikit-learn they are passed as arguments to the constructor of the
estimator classes. Typical examples include <code class="docutils literal notranslate"><span class="pre">C</span></code>, <code class="docutils literal notranslate"><span class="pre">kernel</span></code> and <code class="docutils literal notranslate"><span class="pre">gamma</span></code>
for Support Vector Classifier, <code class="docutils literal notranslate"><span class="pre">alpha</span></code> for Lasso, etc.</p>
<p>It is possible and recommended to search the hyper-parameter space for the
best <a class="reference internal" href="cross_validation.html#cross-validation"><span class="std std-ref">cross validation</span></a> score.</p>
<p>Any parameter provided when constructing an estimator may be optimized in this
manner. Specifically, to find the names and current values for all parameters
for a given estimator, use:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">estimator</span><span class="o">.</span><span class="n">get_params</span><span class="p">()</span>
</pre></div>
</div>
<p>A search consists of:</p>
<ul class="simple">
<li><p>an estimator (regressor or classifier such as <code class="docutils literal notranslate"><span class="pre">sklearn.svm.SVC()</span></code>);</p></li>
<li><p>a parameter space;</p></li>
<li><p>a method for searching or sampling candidates;</p></li>
<li><p>a cross-validation scheme; and</p></li>
<li><p>a <a class="reference internal" href="#gridsearch-scoring"><span class="std std-ref">score function</span></a>.</p></li>
</ul>
<p>Two generic approaches to parameter search are provided in
scikit-learn: for given values, <a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a> exhaustively considers
all parameter combinations, while <a class="reference internal" href="generated/sklearn.model_selection.RandomizedSearchCV.html#sklearn.model_selection.RandomizedSearchCV" title="sklearn.model_selection.RandomizedSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">RandomizedSearchCV</span></code></a> can sample a
given number of candidates from a parameter space with a specified
distribution. Both these tools have successive halving counterparts
<a class="reference internal" href="generated/sklearn.model_selection.HalvingGridSearchCV.html#sklearn.model_selection.HalvingGridSearchCV" title="sklearn.model_selection.HalvingGridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingGridSearchCV</span></code></a> and <a class="reference internal" href="generated/sklearn.model_selection.HalvingRandomSearchCV.html#sklearn.model_selection.HalvingRandomSearchCV" title="sklearn.model_selection.HalvingRandomSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingRandomSearchCV</span></code></a>, which can be
much faster at finding a good parameter combination.</p>
<p>After describing these tools we detail <a class="reference internal" href="#grid-search-tips"><span class="std std-ref">best practices</span></a> applicable to these approaches. Some models allow for
specialized, efficient parameter search strategies, outlined in
<a class="reference internal" href="#alternative-cv"><span class="std std-ref">Alternatives to brute force parameter search</span></a>.</p>
<p>Note that it is common that a small subset of those parameters can have a large
impact on the predictive or computation performance of the model while others
can be left to their default values. It is recommended to read the docstring of
the estimator class to get a finer understanding of their expected behavior,
possibly by reading the enclosed reference to the literature.</p>
<section id="exhaustive-grid-search">
<h2><span class="section-number">3.2.1. </span>Exhaustive Grid Search<a class="headerlink" href="#exhaustive-grid-search" title="Permalink to this heading">¶</a></h2>
<p>The grid search provided by <a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a> exhaustively generates
candidates from a grid of parameter values specified with the <code class="docutils literal notranslate"><span class="pre">param_grid</span></code>
parameter. For instance, the following <code class="docutils literal notranslate"><span class="pre">param_grid</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">param_grid</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">{</span><span class="s1">'C'</span><span class="p">:</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">1000</span><span class="p">],</span> <span class="s1">'kernel'</span><span class="p">:</span> <span class="p">[</span><span class="s1">'linear'</span><span class="p">]},</span>
<span class="p">{</span><span class="s1">'C'</span><span class="p">:</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">1000</span><span class="p">],</span> <span class="s1">'gamma'</span><span class="p">:</span> <span class="p">[</span><span class="mf">0.001</span><span class="p">,</span> <span class="mf">0.0001</span><span class="p">],</span> <span class="s1">'kernel'</span><span class="p">:</span> <span class="p">[</span><span class="s1">'rbf'</span><span class="p">]},</span>
<span class="p">]</span>
</pre></div>
</div>
<p>specifies that two grids should be explored: one with a linear kernel and
C values in [1, 10, 100, 1000], and the second one with an RBF kernel,
and the cross-product of C values ranging in [1, 10, 100, 1000] and gamma
values in [0.001, 0.0001].</p>
<p>The <a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a> instance implements the usual estimator API: when
“fitting” it on a dataset all the possible combinations of parameter values are
evaluated and the best combination is retained.</p>
<aside class="topic">
<p class="topic-title">Examples:</p>
<ul class="simple">
<li><p>See <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> for an example of
Grid Search computation on the digits dataset.</p></li>
<li><p>See <a class="reference internal" href="../auto_examples/model_selection/plot_grid_search_text_feature_extraction.html#sphx-glr-auto-examples-model-selection-plot-grid-search-text-feature-extraction-py"><span class="std std-ref">Sample pipeline for text feature extraction and evaluation</span></a> for an example
of Grid Search coupling parameters from a text documents feature
extractor (n-gram count vectorizer and TF-IDF transformer) with a
classifier (here a linear SVM trained with SGD with either elastic
net or L2 penalty) using 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> instance.</p></li>
<li><p>See <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>
for an example of Grid Search within a cross validation loop on the iris
dataset. This is the best practice for evaluating the performance of a
model with grid search.</p></li>
<li><p>See <a class="reference internal" href="../auto_examples/model_selection/plot_multi_metric_evaluation.html#sphx-glr-auto-examples-model-selection-plot-multi-metric-evaluation-py"><span class="std std-ref">Demonstration of multi-metric evaluation on cross_val_score and GridSearchCV</span></a>
for an example of <a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a> being used to evaluate multiple
metrics simultaneously.</p></li>
<li><p>See <a class="reference internal" href="../auto_examples/model_selection/plot_grid_search_refit_callable.html#sphx-glr-auto-examples-model-selection-plot-grid-search-refit-callable-py"><span class="std std-ref">Balance model complexity and cross-validated score</span></a>
for an example of using <code class="docutils literal notranslate"><span class="pre">refit=callable</span></code> interface in
<a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a>. The example shows how this interface adds certain
amount of flexibility in identifying the “best” estimator. This interface
can also be used in multiple metrics evaluation.</p></li>
<li><p>See <a class="reference internal" href="../auto_examples/model_selection/plot_grid_search_stats.html#sphx-glr-auto-examples-model-selection-plot-grid-search-stats-py"><span class="std std-ref">Statistical comparison of models using grid search</span></a>
for an example of how to do a statistical comparison on the outputs of
<a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a>.</p></li>
</ul>
</aside>
</section>
<section id="randomized-parameter-optimization">
<span id="randomized-parameter-search"></span><h2><span class="section-number">3.2.2. </span>Randomized Parameter Optimization<a class="headerlink" href="#randomized-parameter-optimization" title="Permalink to this heading">¶</a></h2>
<p>While using a grid of parameter settings is currently the most widely used
method for parameter optimization, other search methods have more
favorable properties.
<a class="reference internal" href="generated/sklearn.model_selection.RandomizedSearchCV.html#sklearn.model_selection.RandomizedSearchCV" title="sklearn.model_selection.RandomizedSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">RandomizedSearchCV</span></code></a> implements a randomized search over parameters,
where each setting is sampled from a distribution over possible parameter values.
This has two main benefits over an exhaustive search:</p>
<ul class="simple">
<li><p>A budget can be chosen independent of the number of parameters and possible values.</p></li>
<li><p>Adding parameters that do not influence the performance does not decrease efficiency.</p></li>
</ul>
<p>Specifying how parameters should be sampled is done using a dictionary, very
similar to specifying parameters for <a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a>. Additionally,
a computation budget, being the number of sampled candidates or sampling
iterations, is specified using the <code class="docutils literal notranslate"><span class="pre">n_iter</span></code> parameter.
For each parameter, either a distribution over possible values or a list of
discrete choices (which will be sampled uniformly) can be specified:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="s1">'C'</span><span class="p">:</span> <span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">expon</span><span class="p">(</span><span class="n">scale</span><span class="o">=</span><span class="mi">100</span><span class="p">),</span> <span class="s1">'gamma'</span><span class="p">:</span> <span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">expon</span><span class="p">(</span><span class="n">scale</span><span class="o">=</span><span class="mf">.1</span><span class="p">),</span>
<span class="s1">'kernel'</span><span class="p">:</span> <span class="p">[</span><span class="s1">'rbf'</span><span class="p">],</span> <span class="s1">'class_weight'</span><span class="p">:[</span><span class="s1">'balanced'</span><span class="p">,</span> <span class="kc">None</span><span class="p">]}</span>
</pre></div>
</div>
<p>This example uses the <code class="docutils literal notranslate"><span class="pre">scipy.stats</span></code> module, which contains many useful
distributions for sampling parameters, such as <code class="docutils literal notranslate"><span class="pre">expon</span></code>, <code class="docutils literal notranslate"><span class="pre">gamma</span></code>,
<code class="docutils literal notranslate"><span class="pre">uniform</span></code>, <code class="docutils literal notranslate"><span class="pre">loguniform</span></code> or <code class="docutils literal notranslate"><span class="pre">randint</span></code>.</p>
<p>In principle, any function can be passed that provides a <code class="docutils literal notranslate"><span class="pre">rvs</span></code> (random
variate sample) method to sample a value. A call to the <code class="docutils literal notranslate"><span class="pre">rvs</span></code> function should
provide independent random samples from possible parameter values on
consecutive calls.</p>
<blockquote>
<div><div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>The distributions in <code class="docutils literal notranslate"><span class="pre">scipy.stats</span></code> prior to version scipy 0.16
do not allow specifying a random state. Instead, they use the global
numpy random state, that can be seeded via <code class="docutils literal notranslate"><span class="pre">np.random.seed</span></code> or set
using <code class="docutils literal notranslate"><span class="pre">np.random.set_state</span></code>. However, beginning scikit-learn 0.18,
the <a class="reference internal" href="classes.html#module-sklearn.model_selection" title="sklearn.model_selection"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.model_selection</span></code></a> module sets the random state provided
by the user if scipy >= 0.16 is also available.</p>
</div>
</div></blockquote>
<p>For continuous parameters, such as <code class="docutils literal notranslate"><span class="pre">C</span></code> above, it is important to specify
a continuous distribution to take full advantage of the randomization. This way,
increasing <code class="docutils literal notranslate"><span class="pre">n_iter</span></code> will always lead to a finer search.</p>
<p>A continuous log-uniform random variable is the continuous version of
a log-spaced parameter. For example to specify the equivalent of <code class="docutils literal notranslate"><span class="pre">C</span></code> from above,
<code class="docutils literal notranslate"><span class="pre">loguniform(1,</span> <span class="pre">100)</span></code> can be used instead of <code class="docutils literal notranslate"><span class="pre">[1,</span> <span class="pre">10,</span> <span class="pre">100]</span></code>.</p>
<p>Mirroring the example above in grid search, we can specify a continuous random
variable that is log-uniformly distributed between <code class="docutils literal notranslate"><span class="pre">1e0</span></code> and <code class="docutils literal notranslate"><span class="pre">1e3</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.utils.fixes</span> <span class="kn">import</span> <span class="n">loguniform</span>
<span class="p">{</span><span class="s1">'C'</span><span class="p">:</span> <span class="n">loguniform</span><span class="p">(</span><span class="mf">1e0</span><span class="p">,</span> <span class="mf">1e3</span><span class="p">),</span>
<span class="s1">'gamma'</span><span class="p">:</span> <span class="n">loguniform</span><span class="p">(</span><span class="mf">1e-4</span><span class="p">,</span> <span class="mf">1e-3</span><span class="p">),</span>
<span class="s1">'kernel'</span><span class="p">:</span> <span class="p">[</span><span class="s1">'rbf'</span><span class="p">],</span>
<span class="s1">'class_weight'</span><span class="p">:[</span><span class="s1">'balanced'</span><span class="p">,</span> <span class="kc">None</span><span class="p">]}</span>
</pre></div>
</div>
<aside class="topic">
<p class="topic-title">Examples:</p>
<ul class="simple">
<li><p><a class="reference internal" href="../auto_examples/model_selection/plot_randomized_search.html#sphx-glr-auto-examples-model-selection-plot-randomized-search-py"><span class="std std-ref">Comparing randomized search and grid search for hyperparameter estimation</span></a> compares the usage and efficiency
of randomized search and grid search.</p></li>
</ul>
</aside>
<aside class="topic">
<p class="topic-title">References:</p>
<ul class="simple">
<li><p>Bergstra, J. and Bengio, Y.,
Random search for hyper-parameter optimization,
The Journal of Machine Learning Research (2012)</p></li>
</ul>
</aside>
</section>
<section id="searching-for-optimal-parameters-with-successive-halving">
<span id="successive-halving-user-guide"></span><h2><span class="section-number">3.2.3. </span>Searching for optimal parameters with successive halving<a class="headerlink" href="#searching-for-optimal-parameters-with-successive-halving" title="Permalink to this heading">¶</a></h2>
<p>Scikit-learn also provides the <a class="reference internal" href="generated/sklearn.model_selection.HalvingGridSearchCV.html#sklearn.model_selection.HalvingGridSearchCV" title="sklearn.model_selection.HalvingGridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingGridSearchCV</span></code></a> and
<a class="reference internal" href="generated/sklearn.model_selection.HalvingRandomSearchCV.html#sklearn.model_selection.HalvingRandomSearchCV" title="sklearn.model_selection.HalvingRandomSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingRandomSearchCV</span></code></a> estimators that can be used to
search a parameter space using successive halving <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>. Successive
halving (SH) is like a tournament among candidate parameter combinations.
SH is an iterative selection process where all candidates (the
parameter combinations) are evaluated with a small amount of resources at
the first iteration. Only some of these candidates are selected for the next
iteration, which will be allocated more resources. For parameter tuning, the
resource is typically the number of training samples, but it can also be an
arbitrary numeric parameter such as <code class="docutils literal notranslate"><span class="pre">n_estimators</span></code> in a random forest.</p>
<p>As illustrated in the figure below, only a subset of candidates
‘survive’ until the last iteration. These are the candidates that have
consistently ranked among the top-scoring candidates across all iterations.
Each iteration is allocated an increasing amount of resources per candidate,
here the number of samples.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/model_selection/plot_successive_halving_iterations.html"><img alt="../_images/sphx_glr_plot_successive_halving_iterations_001.png" src="../_images/sphx_glr_plot_successive_halving_iterations_001.png" /></a>
</figure>
<p>We here briefly describe the main parameters, but each parameter and their
interactions are described in more details in the sections below. The
<code class="docutils literal notranslate"><span class="pre">factor</span></code> (> 1) parameter controls the rate at which the resources grow, and
the rate at which the number of candidates decreases. In each iteration, the
number of resources per candidate is multiplied by <code class="docutils literal notranslate"><span class="pre">factor</span></code> and the number
of candidates is divided by the same factor. Along with <code class="docutils literal notranslate"><span class="pre">resource</span></code> and
<code class="docutils literal notranslate"><span class="pre">min_resources</span></code>, <code class="docutils literal notranslate"><span class="pre">factor</span></code> is the most important parameter to control the
search in our implementation, though a value of 3 usually works well.
<code class="docutils literal notranslate"><span class="pre">factor</span></code> effectively controls the number of iterations in
<a class="reference internal" href="generated/sklearn.model_selection.HalvingGridSearchCV.html#sklearn.model_selection.HalvingGridSearchCV" title="sklearn.model_selection.HalvingGridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingGridSearchCV</span></code></a> and the number of candidates (by default) and
iterations in <a class="reference internal" href="generated/sklearn.model_selection.HalvingRandomSearchCV.html#sklearn.model_selection.HalvingRandomSearchCV" title="sklearn.model_selection.HalvingRandomSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingRandomSearchCV</span></code></a>. <code class="docutils literal notranslate"><span class="pre">aggressive_elimination=True</span></code>
can also be used if the number of available resources is small. More control
is available through tuning the <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> parameter.</p>
<p>These estimators are still <strong>experimental</strong>: their predictions
and their API might change without any deprecation cycle. To use them, you
need to explicitly import <code class="docutils literal notranslate"><span class="pre">enable_halving_search_cv</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="c1"># explicitly require this experimental feature</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.experimental</span> <span class="kn">import</span> <span class="n">enable_halving_search_cv</span> <span class="c1"># noqa</span>
<span class="gp">>>> </span><span class="c1"># now you can import normally from model_selection</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">HalvingGridSearchCV</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">HalvingRandomSearchCV</span>
</pre></div>
</div>
<aside class="topic">
<p class="topic-title">Examples:</p>
<ul class="simple">
<li><p><a class="reference internal" href="../auto_examples/model_selection/plot_successive_halving_heatmap.html#sphx-glr-auto-examples-model-selection-plot-successive-halving-heatmap-py"><span class="std std-ref">Comparison between grid search and successive halving</span></a></p></li>
<li><p><a class="reference internal" href="../auto_examples/model_selection/plot_successive_halving_iterations.html#sphx-glr-auto-examples-model-selection-plot-successive-halving-iterations-py"><span class="std std-ref">Successive Halving Iterations</span></a></p></li>
</ul>
</aside>
<section id="choosing-min-resources-and-the-number-of-candidates">
<h3><span class="section-number">3.2.3.1. </span>Choosing <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> and the number of candidates<a class="headerlink" href="#choosing-min-resources-and-the-number-of-candidates" title="Permalink to this heading">¶</a></h3>
<p>Beside <code class="docutils literal notranslate"><span class="pre">factor</span></code>, the two main parameters that influence the behaviour of a
successive halving search are the <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> parameter, and the
number of candidates (or parameter combinations) that are evaluated.
<code class="docutils literal notranslate"><span class="pre">min_resources</span></code> is the amount of resources allocated at the first
iteration for each candidate. The number of candidates is specified directly
in <a class="reference internal" href="generated/sklearn.model_selection.HalvingRandomSearchCV.html#sklearn.model_selection.HalvingRandomSearchCV" title="sklearn.model_selection.HalvingRandomSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingRandomSearchCV</span></code></a>, and is determined from the <code class="docutils literal notranslate"><span class="pre">param_grid</span></code>
parameter of <a class="reference internal" href="generated/sklearn.model_selection.HalvingGridSearchCV.html#sklearn.model_selection.HalvingGridSearchCV" title="sklearn.model_selection.HalvingGridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingGridSearchCV</span></code></a>.</p>
<p>Consider a case where the resource is the number of samples, and where we
have 1000 samples. In theory, with <code class="docutils literal notranslate"><span class="pre">min_resources=10</span></code> and <code class="docutils literal notranslate"><span class="pre">factor=2</span></code>, we
are able to run <strong>at most</strong> 7 iterations with the following number of
samples: <code class="docutils literal notranslate"><span class="pre">[10,</span> <span class="pre">20,</span> <span class="pre">40,</span> <span class="pre">80,</span> <span class="pre">160,</span> <span class="pre">320,</span> <span class="pre">640]</span></code>.</p>
<p>But depending on the number of candidates, we might run less than 7
iterations: if we start with a <strong>small</strong> number of candidates, the last
iteration might use less than 640 samples, which means not using all the
available resources (samples). For example if we start with 5 candidates, we
only need 2 iterations: 5 candidates for the first iteration, then
<code class="docutils literal notranslate"><span class="pre">5</span> <span class="pre">//</span> <span class="pre">2</span> <span class="pre">=</span> <span class="pre">2</span></code> candidates at the second iteration, after which we know which
candidate performs the best (so we don’t need a third one). We would only be
using at most 20 samples which is a waste since we have 1000 samples at our
disposal. On the other hand, if we start with a <strong>high</strong> number of
candidates, we might end up with a lot of candidates at the last iteration,
which may not always be ideal: it means that many candidates will run with
the full resources, basically reducing the procedure to standard search.</p>
<p>In the case of <a class="reference internal" href="generated/sklearn.model_selection.HalvingRandomSearchCV.html#sklearn.model_selection.HalvingRandomSearchCV" title="sklearn.model_selection.HalvingRandomSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingRandomSearchCV</span></code></a>, the number of candidates is set
by default such that the last iteration uses as much of the available
resources as possible. For <a class="reference internal" href="generated/sklearn.model_selection.HalvingGridSearchCV.html#sklearn.model_selection.HalvingGridSearchCV" title="sklearn.model_selection.HalvingGridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingGridSearchCV</span></code></a>, the number of
candidates is determined by the <code class="docutils literal notranslate"><span class="pre">param_grid</span></code> parameter. Changing the value of
<code class="docutils literal notranslate"><span class="pre">min_resources</span></code> will impact the number of possible iterations, and as a
result will also have an effect on the ideal number of candidates.</p>
<p>Another consideration when choosing <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> is whether or not it
is easy to discriminate between good and bad candidates with a small amount
of resources. For example, if you need a lot of samples to distinguish
between good and bad parameters, a high <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> is recommended. On
the other hand if the distinction is clear even with a small amount of
samples, then a small <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> may be preferable since it would
speed up the computation.</p>
<p>Notice in the example above that the last iteration does not use the maximum
amount of resources available: 1000 samples are available, yet only 640 are
used, at most. By default, both <a class="reference internal" href="generated/sklearn.model_selection.HalvingRandomSearchCV.html#sklearn.model_selection.HalvingRandomSearchCV" title="sklearn.model_selection.HalvingRandomSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingRandomSearchCV</span></code></a> and
<a class="reference internal" href="generated/sklearn.model_selection.HalvingGridSearchCV.html#sklearn.model_selection.HalvingGridSearchCV" title="sklearn.model_selection.HalvingGridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingGridSearchCV</span></code></a> try to use as many resources as possible in the
last iteration, with the constraint that this amount of resources must be a
multiple of both <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> and <code class="docutils literal notranslate"><span class="pre">factor</span></code> (this constraint will be clear
in the next section). <a class="reference internal" href="generated/sklearn.model_selection.HalvingRandomSearchCV.html#sklearn.model_selection.HalvingRandomSearchCV" title="sklearn.model_selection.HalvingRandomSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingRandomSearchCV</span></code></a> achieves this by
sampling the right amount of candidates, while <a class="reference internal" href="generated/sklearn.model_selection.HalvingGridSearchCV.html#sklearn.model_selection.HalvingGridSearchCV" title="sklearn.model_selection.HalvingGridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingGridSearchCV</span></code></a>
achieves this by properly setting <code class="docutils literal notranslate"><span class="pre">min_resources</span></code>. Please see
<a class="reference internal" href="#exhausting-the-resources"><span class="std std-ref">Exhausting the available resources</span></a> for details.</p>
</section>
<section id="amount-of-resource-and-number-of-candidates-at-each-iteration">
<span id="amount-of-resource-and-number-of-candidates"></span><h3><span class="section-number">3.2.3.2. </span>Amount of resource and number of candidates at each iteration<a class="headerlink" href="#amount-of-resource-and-number-of-candidates-at-each-iteration" title="Permalink to this heading">¶</a></h3>
<p>At any iteration <code class="docutils literal notranslate"><span class="pre">i</span></code>, each candidate is allocated a given amount of resources
which we denote <code class="docutils literal notranslate"><span class="pre">n_resources_i</span></code>. This quantity is controlled by the
parameters <code class="docutils literal notranslate"><span class="pre">factor</span></code> and <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> as follows (<code class="docutils literal notranslate"><span class="pre">factor</span></code> is strictly
greater than 1):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n_resources_i</span> <span class="o">=</span> <span class="n">factor</span><span class="o">**</span><span class="n">i</span> <span class="o">*</span> <span class="n">min_resources</span><span class="p">,</span>
</pre></div>
</div>
<p>or equivalently:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n_resources_</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="n">n_resources_i</span> <span class="o">*</span> <span class="n">factor</span>
</pre></div>
</div>
<p>where <code class="docutils literal notranslate"><span class="pre">min_resources</span> <span class="pre">==</span> <span class="pre">n_resources_0</span></code> is the amount of resources used at
the first iteration. <code class="docutils literal notranslate"><span class="pre">factor</span></code> also defines the proportions of candidates
that will be selected for the next iteration:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n_candidates_i</span> <span class="o">=</span> <span class="n">n_candidates</span> <span class="o">//</span> <span class="p">(</span><span class="n">factor</span> <span class="o">**</span> <span class="n">i</span><span class="p">)</span>
</pre></div>
</div>
<p>or equivalently:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n_candidates_0</span> <span class="o">=</span> <span class="n">n_candidates</span>
<span class="n">n_candidates_</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="n">n_candidates_i</span> <span class="o">//</span> <span class="n">factor</span>
</pre></div>
</div>
<p>So in the first iteration, we use <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> resources
<code class="docutils literal notranslate"><span class="pre">n_candidates</span></code> times. In the second iteration, we use <code class="docutils literal notranslate"><span class="pre">min_resources</span> <span class="pre">*</span>
<span class="pre">factor</span></code> resources <code class="docutils literal notranslate"><span class="pre">n_candidates</span> <span class="pre">//</span> <span class="pre">factor</span></code> times. The third again
multiplies the resources per candidate and divides the number of candidates.
This process stops when the maximum amount of resource per candidate is
reached, or when we have identified the best candidate. The best candidate
is identified at the iteration that is evaluating <code class="docutils literal notranslate"><span class="pre">factor</span></code> or less candidates
(see just below for an explanation).</p>
<p>Here is an example with <code class="docutils literal notranslate"><span class="pre">min_resources=3</span></code> and <code class="docutils literal notranslate"><span class="pre">factor=2</span></code>, starting with
70 candidates:</p>
<table class="docutils align-default">
<thead>
<tr class="row-odd"><th class="head"><p><code class="docutils literal notranslate"><span class="pre">n_resources_i</span></code></p></th>
<th class="head"><p><code class="docutils literal notranslate"><span class="pre">n_candidates_i</span></code></p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>3 (=min_resources)</p></td>
<td><p>70 (=n_candidates)</p></td>
</tr>
<tr class="row-odd"><td><p>3 * 2 = 6</p></td>
<td><p>70 // 2 = 35</p></td>
</tr>
<tr class="row-even"><td><p>6 * 2 = 12</p></td>
<td><p>35 // 2 = 17</p></td>
</tr>
<tr class="row-odd"><td><p>12 * 2 = 24</p></td>
<td><p>17 // 2 = 8</p></td>
</tr>
<tr class="row-even"><td><p>24 * 2 = 48</p></td>
<td><p>8 // 2 = 4</p></td>
</tr>
<tr class="row-odd"><td><p>48 * 2 = 96</p></td>
<td><p>4 // 2 = 2</p></td>
</tr>
</tbody>
</table>
<p>We can note that:</p>
<ul class="simple">
<li><p>the process stops at the first iteration which evaluates <code class="docutils literal notranslate"><span class="pre">factor=2</span></code>
candidates: the best candidate is the best out of these 2 candidates. It
is not necessary to run an additional iteration, since it would only
evaluate one candidate (namely the best one, which we have already
identified). For this reason, in general, we want the last iteration to
run at most <code class="docutils literal notranslate"><span class="pre">factor</span></code> candidates. If the last iteration evaluates more
than <code class="docutils literal notranslate"><span class="pre">factor</span></code> candidates, then this last iteration reduces to a regular
search (as in <a class="reference internal" href="generated/sklearn.model_selection.RandomizedSearchCV.html#sklearn.model_selection.RandomizedSearchCV" title="sklearn.model_selection.RandomizedSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">RandomizedSearchCV</span></code></a> or <a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a>).</p></li>
<li><p>each <code class="docutils literal notranslate"><span class="pre">n_resources_i</span></code> is a multiple of both <code class="docutils literal notranslate"><span class="pre">factor</span></code> and
<code class="docutils literal notranslate"><span class="pre">min_resources</span></code> (which is confirmed by its definition above).</p></li>
</ul>
<p>The amount of resources that is used at each iteration can be found in the
<code class="docutils literal notranslate"><span class="pre">n_resources_</span></code> attribute.</p>
</section>
<section id="choosing-a-resource">
<h3><span class="section-number">3.2.3.3. </span>Choosing a resource<a class="headerlink" href="#choosing-a-resource" title="Permalink to this heading">¶</a></h3>
<p>By default, the resource is defined in terms of number of samples. That is,
each iteration will use an increasing amount of samples to train on. You can
however manually specify a parameter to use as the resource with the
<code class="docutils literal notranslate"><span class="pre">resource</span></code> parameter. Here is an example where the resource is defined in
terms of the number of estimators of a random forest:</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.datasets</span> <span class="kn">import</span> <span class="n">make_classification</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">RandomForestClassifier</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.experimental</span> <span class="kn">import</span> <span class="n">enable_halving_search_cv</span> <span class="c1"># noqa</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">HalvingGridSearchCV</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="gp">>>></span>
<span class="gp">>>> </span><span class="n">param_grid</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'max_depth'</span><span class="p">:</span> <span class="p">[</span><span class="mi">3</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="gp">... </span> <span class="s1">'min_samples_split'</span><span class="p">:</span> <span class="p">[</span><span class="mi">2</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="gp">>>> </span><span class="n">base_estimator</span> <span class="o">=</span> <span class="n">RandomForestClassifier</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</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">make_classification</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">1000</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">sh</span> <span class="o">=</span> <span class="n">HalvingGridSearchCV</span><span class="p">(</span><span class="n">base_estimator</span><span class="p">,</span> <span class="n">param_grid</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">factor</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">resource</span><span class="o">=</span><span class="s1">'n_estimators'</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">max_resources</span><span class="o">=</span><span class="mi">30</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sh</span><span class="o">.</span><span class="n">best_estimator_</span>
<span class="go">RandomForestClassifier(max_depth=5, n_estimators=24, random_state=0)</span>
</pre></div>
</div>
<p>Note that it is not possible to budget on a parameter that is part of the
parameter grid.</p>
</section>
<section id="exhausting-the-available-resources">
<span id="exhausting-the-resources"></span><h3><span class="section-number">3.2.3.4. </span>Exhausting the available resources<a class="headerlink" href="#exhausting-the-available-resources" title="Permalink to this heading">¶</a></h3>
<p>As mentioned above, the number of resources that is used at each iteration
depends on the <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> parameter.
If you have a lot of resources available but start with a low number of
resources, some of them might be wasted (i.e. not used):</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.datasets</span> <span class="kn">import</span> <span class="n">make_classification</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <span class="n">SVC</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.experimental</span> <span class="kn">import</span> <span class="n">enable_halving_search_cv</span> <span class="c1"># noqa</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">HalvingGridSearchCV</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="gp">>>> </span><span class="n">param_grid</span><span class="o">=</span> <span class="p">{</span><span class="s1">'kernel'</span><span class="p">:</span> <span class="p">(</span><span class="s1">'linear'</span><span class="p">,</span> <span class="s1">'rbf'</span><span class="p">),</span>
<span class="gp">... </span> <span class="s1">'C'</span><span class="p">:</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">100</span><span class="p">]}</span>
<span class="gp">>>> </span><span class="n">base_estimator</span> <span class="o">=</span> <span class="n">SVC</span><span class="p">(</span><span class="n">gamma</span><span class="o">=</span><span class="s1">'scale'</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="o">=</span> <span class="n">make_classification</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sh</span> <span class="o">=</span> <span class="n">HalvingGridSearchCV</span><span class="p">(</span><span class="n">base_estimator</span><span class="p">,</span> <span class="n">param_grid</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">factor</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">min_resources</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sh</span><span class="o">.</span><span class="n">n_resources_</span>
<span class="go">[20, 40, 80]</span>
</pre></div>
</div>
<p>The search process will only use 80 resources at most, while our maximum
amount of available resources is <code class="docutils literal notranslate"><span class="pre">n_samples=1000</span></code>. Here, we have
<code class="docutils literal notranslate"><span class="pre">min_resources</span> <span class="pre">=</span> <span class="pre">r_0</span> <span class="pre">=</span> <span class="pre">20</span></code>.</p>
<p>For <a class="reference internal" href="generated/sklearn.model_selection.HalvingGridSearchCV.html#sklearn.model_selection.HalvingGridSearchCV" title="sklearn.model_selection.HalvingGridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingGridSearchCV</span></code></a>, by default, the <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> parameter
is set to ‘exhaust’. This means that <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> is automatically set
such that the last iteration can use as many resources as possible, within
the <code class="docutils literal notranslate"><span class="pre">max_resources</span></code> limit:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">sh</span> <span class="o">=</span> <span class="n">HalvingGridSearchCV</span><span class="p">(</span><span class="n">base_estimator</span><span class="p">,</span> <span class="n">param_grid</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">factor</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">min_resources</span><span class="o">=</span><span class="s1">'exhaust'</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sh</span><span class="o">.</span><span class="n">n_resources_</span>
<span class="go">[250, 500, 1000]</span>
</pre></div>
</div>
<p><code class="docutils literal notranslate"><span class="pre">min_resources</span></code> was here automatically set to 250, which results in the last
iteration using all the resources. The exact value that is used depends on
the number of candidate parameter, on <code class="docutils literal notranslate"><span class="pre">max_resources</span></code> and on <code class="docutils literal notranslate"><span class="pre">factor</span></code>.</p>
<p>For <a class="reference internal" href="generated/sklearn.model_selection.HalvingRandomSearchCV.html#sklearn.model_selection.HalvingRandomSearchCV" title="sklearn.model_selection.HalvingRandomSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingRandomSearchCV</span></code></a>, exhausting the resources can be done in 2
ways:</p>
<ul class="simple">
<li><p>by setting <code class="docutils literal notranslate"><span class="pre">min_resources='exhaust'</span></code>, just like for
<a class="reference internal" href="generated/sklearn.model_selection.HalvingGridSearchCV.html#sklearn.model_selection.HalvingGridSearchCV" title="sklearn.model_selection.HalvingGridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingGridSearchCV</span></code></a>;</p></li>
<li><p>by setting <code class="docutils literal notranslate"><span class="pre">n_candidates='exhaust'</span></code>.</p></li>
</ul>
<p>Both options are mutually exclusive: using <code class="docutils literal notranslate"><span class="pre">min_resources='exhaust'</span></code> requires
knowing the number of candidates, and symmetrically <code class="docutils literal notranslate"><span class="pre">n_candidates='exhaust'</span></code>
requires knowing <code class="docutils literal notranslate"><span class="pre">min_resources</span></code>.</p>
<p>In general, exhausting the total number of resources leads to a better final
candidate parameter, and is slightly more time-intensive.</p>
</section>
<section id="aggressive-elimination-of-candidates">
<span id="aggressive-elimination"></span><h3><span class="section-number">3.2.3.5. </span>Aggressive elimination of candidates<a class="headerlink" href="#aggressive-elimination-of-candidates" title="Permalink to this heading">¶</a></h3>
<p>Ideally, we want the last iteration to evaluate <code class="docutils literal notranslate"><span class="pre">factor</span></code> candidates (see
<a class="reference internal" href="#amount-of-resource-and-number-of-candidates"><span class="std std-ref">Amount of resource and number of candidates at each iteration</span></a>). We then just have to
pick the best one. When the number of available resources is small with
respect to the number of candidates, the last iteration may have to evaluate
more than <code class="docutils literal notranslate"><span class="pre">factor</span></code> candidates:</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.datasets</span> <span class="kn">import</span> <span class="n">make_classification</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <span class="n">SVC</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.experimental</span> <span class="kn">import</span> <span class="n">enable_halving_search_cv</span> <span class="c1"># noqa</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">HalvingGridSearchCV</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="gp">>>></span>
<span class="gp">>>></span>
<span class="gp">>>> </span><span class="n">param_grid</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'kernel'</span><span class="p">:</span> <span class="p">(</span><span class="s1">'linear'</span><span class="p">,</span> <span class="s1">'rbf'</span><span class="p">),</span>
<span class="gp">... </span> <span class="s1">'C'</span><span class="p">:</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">100</span><span class="p">]}</span>
<span class="gp">>>> </span><span class="n">base_estimator</span> <span class="o">=</span> <span class="n">SVC</span><span class="p">(</span><span class="n">gamma</span><span class="o">=</span><span class="s1">'scale'</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="o">=</span> <span class="n">make_classification</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sh</span> <span class="o">=</span> <span class="n">HalvingGridSearchCV</span><span class="p">(</span><span class="n">base_estimator</span><span class="p">,</span> <span class="n">param_grid</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">factor</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">max_resources</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">aggressive_elimination</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sh</span><span class="o">.</span><span class="n">n_resources_</span>
<span class="go">[20, 40]</span>
<span class="gp">>>> </span><span class="n">sh</span><span class="o">.</span><span class="n">n_candidates_</span>
<span class="go">[6, 3]</span>
</pre></div>
</div>
<p>Since we cannot use more than <code class="docutils literal notranslate"><span class="pre">max_resources=40</span></code> resources, the process
has to stop at the second iteration which evaluates more than <code class="docutils literal notranslate"><span class="pre">factor=2</span></code>
candidates.</p>
<p>Using the <code class="docutils literal notranslate"><span class="pre">aggressive_elimination</span></code> parameter, you can force the search
process to end up with less than <code class="docutils literal notranslate"><span class="pre">factor</span></code> candidates at the last
iteration. To do this, the process will eliminate as many candidates as
necessary using <code class="docutils literal notranslate"><span class="pre">min_resources</span></code> resources:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">sh</span> <span class="o">=</span> <span class="n">HalvingGridSearchCV</span><span class="p">(</span><span class="n">base_estimator</span><span class="p">,</span> <span class="n">param_grid</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">factor</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">max_resources</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">aggressive_elimination</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="gp">... </span> <span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sh</span><span class="o">.</span><span class="n">n_resources_</span>
<span class="go">[20, 20, 40]</span>
<span class="gp">>>> </span><span class="n">sh</span><span class="o">.</span><span class="n">n_candidates_</span>
<span class="go">[6, 3, 2]</span>
</pre></div>
</div>
<p>Notice that we end with 2 candidates at the last iteration since we have
eliminated enough candidates during the first iterations, using <code class="docutils literal notranslate"><span class="pre">n_resources</span> <span class="pre">=</span>
<span class="pre">min_resources</span> <span class="pre">=</span> <span class="pre">20</span></code>.</p>
</section>
<section id="analyzing-results-with-the-cv-results-attribute">
<span id="successive-halving-cv-results"></span><h3><span class="section-number">3.2.3.6. </span>Analyzing results with the <code class="docutils literal notranslate"><span class="pre">cv_results_</span></code> attribute<a class="headerlink" href="#analyzing-results-with-the-cv-results-attribute" title="Permalink to this heading">¶</a></h3>
<p>The <code class="docutils literal notranslate"><span class="pre">cv_results_</span></code> attribute contains useful information for analyzing the
results of a search. It can be converted to a pandas dataframe with <code class="docutils literal notranslate"><span class="pre">df</span> <span class="pre">=</span>
<span class="pre">pd.DataFrame(est.cv_results_)</span></code>. The <code class="docutils literal notranslate"><span class="pre">cv_results_</span></code> attribute of
<a class="reference internal" href="generated/sklearn.model_selection.HalvingGridSearchCV.html#sklearn.model_selection.HalvingGridSearchCV" title="sklearn.model_selection.HalvingGridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingGridSearchCV</span></code></a> and <a class="reference internal" href="generated/sklearn.model_selection.HalvingRandomSearchCV.html#sklearn.model_selection.HalvingRandomSearchCV" title="sklearn.model_selection.HalvingRandomSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingRandomSearchCV</span></code></a> is similar
to that of <a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a> and <a class="reference internal" href="generated/sklearn.model_selection.RandomizedSearchCV.html#sklearn.model_selection.RandomizedSearchCV" title="sklearn.model_selection.RandomizedSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">RandomizedSearchCV</span></code></a>, with
additional information related to the successive halving process.</p>
<p>Here is an example with some of the columns of a (truncated) dataframe:</p>
<table class="docutils align-default">
<thead>
<tr class="row-odd"><th class="head"></th>
<th class="head"><p>iter</p></th>
<th class="head"><p>n_resources</p></th>
<th class="head"><p>mean_test_score</p></th>
<th class="head"><p>params</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>0</p></td>
<td><p>0</p></td>
<td><p>125</p></td>
<td><p>0.983667</p></td>
<td><p>{‘criterion’: ‘log_loss’, ‘max_depth’: None, ‘max_features’: 9, ‘min_samples_split’: 5}</p></td>
</tr>
<tr class="row-odd"><td><p>1</p></td>
<td><p>0</p></td>
<td><p>125</p></td>
<td><p>0.983667</p></td>
<td><p>{‘criterion’: ‘gini’, ‘max_depth’: None, ‘max_features’: 8, ‘min_samples_split’: 7}</p></td>
</tr>
<tr class="row-even"><td><p>2</p></td>
<td><p>0</p></td>
<td><p>125</p></td>
<td><p>0.983667</p></td>
<td><p>{‘criterion’: ‘gini’, ‘max_depth’: None, ‘max_features’: 10, ‘min_samples_split’: 10}</p></td>
</tr>
<tr class="row-odd"><td><p>3</p></td>
<td><p>0</p></td>
<td><p>125</p></td>
<td><p>0.983667</p></td>
<td><p>{‘criterion’: ‘log_loss’, ‘max_depth’: None, ‘max_features’: 6, ‘min_samples_split’: 6}</p></td>
</tr>
<tr class="row-even"><td><p>…</p></td>
<td><p>…</p></td>
<td><p>…</p></td>
<td><p>…</p></td>
<td><p>…</p></td>
</tr>
<tr class="row-odd"><td><p>15</p></td>
<td><p>2</p></td>
<td><p>500</p></td>
<td><p>0.951958</p></td>
<td><p>{‘criterion’: ‘log_loss’, ‘max_depth’: None, ‘max_features’: 9, ‘min_samples_split’: 10}</p></td>
</tr>
<tr class="row-even"><td><p>16</p></td>
<td><p>2</p></td>
<td><p>500</p></td>
<td><p>0.947958</p></td>
<td><p>{‘criterion’: ‘gini’, ‘max_depth’: None, ‘max_features’: 10, ‘min_samples_split’: 10}</p></td>
</tr>
<tr class="row-odd"><td><p>17</p></td>
<td><p>2</p></td>
<td><p>500</p></td>
<td><p>0.951958</p></td>
<td><p>{‘criterion’: ‘gini’, ‘max_depth’: None, ‘max_features’: 10, ‘min_samples_split’: 4}</p></td>
</tr>
<tr class="row-even"><td><p>18</p></td>
<td><p>3</p></td>
<td><p>1000</p></td>
<td><p>0.961009</p></td>
<td><p>{‘criterion’: ‘log_loss’, ‘max_depth’: None, ‘max_features’: 9, ‘min_samples_split’: 10}</p></td>
</tr>
<tr class="row-odd"><td><p>19</p></td>
<td><p>3</p></td>
<td><p>1000</p></td>
<td><p>0.955989</p></td>
<td><p>{‘criterion’: ‘gini’, ‘max_depth’: None, ‘max_features’: 10, ‘min_samples_split’: 4}</p></td>
</tr>
</tbody>
</table>
<p>Each row corresponds to a given parameter combination (a candidate) and a given
iteration. The iteration is given by the <code class="docutils literal notranslate"><span class="pre">iter</span></code> column. The <code class="docutils literal notranslate"><span class="pre">n_resources</span></code>
column tells you how many resources were used.</p>
<p>In the example above, the best parameter combination is <code class="docutils literal notranslate"><span class="pre">{'criterion':</span>
<span class="pre">'log_loss',</span> <span class="pre">'max_depth':</span> <span class="pre">None,</span> <span class="pre">'max_features':</span> <span class="pre">9,</span> <span class="pre">'min_samples_split':</span> <span class="pre">10}</span></code>
since it has reached the last iteration (3) with the highest score:
0.96.</p>
<aside class="topic">
<p class="topic-title">References:</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id3" role="note">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
<p>K. Jamieson, A. Talwalkar,
<a class="reference external" href="http://proceedings.mlr.press/v51/jamieson16.html">Non-stochastic Best Arm Identification and Hyperparameter
Optimization</a>, in
proc. of Machine Learning Research, 2016.</p>
</aside>
<aside class="footnote brackets" id="id4" role="note">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
<p>L. Li, K. Jamieson, G. DeSalvo, A. Rostamizadeh, A. Talwalkar,
<a class="reference external" href="https://arxiv.org/abs/1603.06560">Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization</a>, in Machine Learning Research 18, 2018.</p>
</aside>
</aside>
</aside>
</section>
</section>
<section id="tips-for-parameter-search">
<span id="grid-search-tips"></span><h2><span class="section-number">3.2.4. </span>Tips for parameter search<a class="headerlink" href="#tips-for-parameter-search" title="Permalink to this heading">¶</a></h2>
<section id="specifying-an-objective-metric">
<span id="gridsearch-scoring"></span><h3><span class="section-number">3.2.4.1. </span>Specifying an objective metric<a class="headerlink" href="#specifying-an-objective-metric" title="Permalink to this heading">¶</a></h3>
<p>By default, parameter search uses the <code class="docutils literal notranslate"><span class="pre">score</span></code> function of the estimator
to evaluate a parameter setting. These are the
<a class="reference internal" href="generated/sklearn.metrics.accuracy_score.html#sklearn.metrics.accuracy_score" title="sklearn.metrics.accuracy_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">sklearn.metrics.accuracy_score</span></code></a> for classification and
<a class="reference internal" href="generated/sklearn.metrics.r2_score.html#sklearn.metrics.r2_score" title="sklearn.metrics.r2_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">sklearn.metrics.r2_score</span></code></a> for regression. For some applications,
other scoring functions are better suited (for example in unbalanced
classification, the accuracy score is often uninformative). An alternative
scoring function can be specified via the <code class="docutils literal notranslate"><span class="pre">scoring</span></code> parameter of most
parameter search tools. 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 more details.</p>
</section>
<section id="specifying-multiple-metrics-for-evaluation">
<span id="multimetric-grid-search"></span><h3><span class="section-number">3.2.4.2. </span>Specifying multiple metrics for evaluation<a class="headerlink" href="#specifying-multiple-metrics-for-evaluation" title="Permalink to this heading">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a> and <a class="reference internal" href="generated/sklearn.model_selection.RandomizedSearchCV.html#sklearn.model_selection.RandomizedSearchCV" title="sklearn.model_selection.RandomizedSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">RandomizedSearchCV</span></code></a> allow specifying
multiple metrics for the <code class="docutils literal notranslate"><span class="pre">scoring</span></code> parameter.</p>
<p>Multimetric scoring can either be specified as a list of strings of predefined
scores names or a dict mapping the scorer name to the scorer function and/or
the predefined scorer name(s). See <a class="reference internal" href="model_evaluation.html#multimetric-scoring"><span class="std std-ref">Using multiple metric evaluation</span></a> for more details.</p>
<p>When specifying multiple metrics, the <code class="docutils literal notranslate"><span class="pre">refit</span></code> parameter must be set to the
metric (string) for which the <code class="docutils literal notranslate"><span class="pre">best_params_</span></code> will be found and used to build
the <code class="docutils literal notranslate"><span class="pre">best_estimator_</span></code> on the whole dataset. If the search should not be
refit, set <code class="docutils literal notranslate"><span class="pre">refit=False</span></code>. Leaving refit to the default value <code class="docutils literal notranslate"><span class="pre">None</span></code> will
result in an error when using multiple metrics.</p>
<p>See <a class="reference internal" href="../auto_examples/model_selection/plot_multi_metric_evaluation.html#sphx-glr-auto-examples-model-selection-plot-multi-metric-evaluation-py"><span class="std std-ref">Demonstration of multi-metric evaluation on cross_val_score and GridSearchCV</span></a>
for an example usage.</p>
<p><a class="reference internal" href="generated/sklearn.model_selection.HalvingRandomSearchCV.html#sklearn.model_selection.HalvingRandomSearchCV" title="sklearn.model_selection.HalvingRandomSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingRandomSearchCV</span></code></a> and <a class="reference internal" href="generated/sklearn.model_selection.HalvingGridSearchCV.html#sklearn.model_selection.HalvingGridSearchCV" title="sklearn.model_selection.HalvingGridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">HalvingGridSearchCV</span></code></a> do not support
multimetric scoring.</p>
</section>
<section id="composite-estimators-and-parameter-spaces">
<span id="composite-grid-search"></span><h3><span class="section-number">3.2.4.3. </span>Composite estimators and parameter spaces<a class="headerlink" href="#composite-estimators-and-parameter-spaces" title="Permalink to this heading">¶</a></h3>
<p><a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a> and <a class="reference internal" href="generated/sklearn.model_selection.RandomizedSearchCV.html#sklearn.model_selection.RandomizedSearchCV" title="sklearn.model_selection.RandomizedSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">RandomizedSearchCV</span></code></a> allow searching over
parameters of composite or nested estimators such as
<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>,
<a class="reference internal" href="generated/sklearn.compose.ColumnTransformer.html#sklearn.compose.ColumnTransformer" title="sklearn.compose.ColumnTransformer"><code class="xref py py-class docutils literal notranslate"><span class="pre">ColumnTransformer</span></code></a>,
<a class="reference internal" href="generated/sklearn.ensemble.VotingClassifier.html#sklearn.ensemble.VotingClassifier" title="sklearn.ensemble.VotingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">VotingClassifier</span></code></a> or
<a class="reference internal" href="generated/sklearn.calibration.CalibratedClassifierCV.html#sklearn.calibration.CalibratedClassifierCV" title="sklearn.calibration.CalibratedClassifierCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">CalibratedClassifierCV</span></code></a> using a dedicated
<code class="docutils literal notranslate"><span class="pre"><estimator>__<parameter></span></code> syntax:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">GridSearchCV</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.calibration</span> <span class="kn">import</span> <span class="n">CalibratedClassifierCV</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">RandomForestClassifier</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_moons</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">make_moons</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">calibrated_forest</span> <span class="o">=</span> <span class="n">CalibratedClassifierCV</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">estimator</span><span class="o">=</span><span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">10</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">param_grid</span> <span class="o">=</span> <span class="p">{</span>
<span class="gp">... </span> <span class="s1">'estimator__max_depth'</span><span class="p">:</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">8</span><span class="p">]}</span>
<span class="gp">>>> </span><span class="n">search</span> <span class="o">=</span> <span class="n">GridSearchCV</span><span class="p">(</span><span class="n">calibrated_forest</span><span class="p">,</span> <span class="n">param_grid</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">search</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="go">GridSearchCV(cv=5,</span>
<span class="go"> estimator=CalibratedClassifierCV(...),</span>
<span class="go"> param_grid={'estimator__max_depth': [2, 4, 6, 8]})</span>
</pre></div>
</div>
<p>Here, <code class="docutils literal notranslate"><span class="pre"><estimator></span></code> is the parameter name of the nested estimator,
in this case <code class="docutils literal notranslate"><span class="pre">estimator</span></code>.
If the meta-estimator is constructed as a collection of estimators as in
<code class="docutils literal notranslate"><span class="pre">pipeline.Pipeline</span></code>, then <code class="docutils literal notranslate"><span class="pre"><estimator></span></code> refers to the name of the estimator,
see <a class="reference internal" href="compose.html#pipeline-nested-parameters"><span class="std std-ref">Nested parameters</span></a>. In practice, there can be several
levels of nesting:</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">Pipeline</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.feature_selection</span> <span class="kn">import</span> <span class="n">SelectKBest</span>
<span class="gp">>>> </span><span class="n">pipe</span> <span class="o">=</span> <span class="n">Pipeline</span><span class="p">([</span>
<span class="gp">... </span> <span class="p">(</span><span class="s1">'select'</span><span class="p">,</span> <span class="n">SelectKBest</span><span class="p">()),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s1">'model'</span><span class="p">,</span> <span class="n">calibrated_forest</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">param_grid</span> <span class="o">=</span> <span class="p">{</span>
<span class="gp">... </span> <span class="s1">'select__k'</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="gp">... </span> <span class="s1">'model__estimator__max_depth'</span><span class="p">:</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">8</span><span class="p">]}</span>
<span class="gp">>>> </span><span class="n">search</span> <span class="o">=</span> <span class="n">GridSearchCV</span><span class="p">(</span><span class="n">pipe</span><span class="p">,</span> <span class="n">param_grid</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="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
</pre></div>
</div>
<p>Please refer to <a class="reference internal" href="compose.html#pipeline"><span class="std std-ref">Pipeline: chaining estimators</span></a> for performing parameter searches over
pipelines.</p>
</section>
<section id="model-selection-development-and-evaluation">
<h3><span class="section-number">3.2.4.4. </span>Model selection: development and evaluation<a class="headerlink" href="#model-selection-development-and-evaluation" title="Permalink to this heading">¶</a></h3>
<p>Model selection by evaluating various parameter settings can be seen as a way
to use the labeled data to “train” the parameters of the grid.</p>
<p>When evaluating the resulting model it is important to do it on
held-out samples that were not seen during the grid search process:
it is recommended to split the data into a <strong>development set</strong> (to
be fed to the <a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">GridSearchCV</span></code></a> instance) and an <strong>evaluation set</strong>
to compute performance metrics.</p>
<p>This can be done by using 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>
utility function.</p>
</section>
<section id="parallelism">
<h3><span class="section-number">3.2.4.5. </span>Parallelism<a class="headerlink" href="#parallelism" title="Permalink to this heading">¶</a></h3>
<p>The parameter search tools evaluate each parameter combination on each data
fold independently. Computations can be run in parallel by using the keyword
<code class="docutils literal notranslate"><span class="pre">n_jobs=-1</span></code>. See function signature for more details, and also the Glossary
entry for <a class="reference internal" href="../glossary.html#term-n_jobs"><span class="xref std std-term">n_jobs</span></a>.</p>
</section>
<section id="robustness-to-failure">
<h3><span class="section-number">3.2.4.6. </span>Robustness to failure<a class="headerlink" href="#robustness-to-failure" title="Permalink to this heading">¶</a></h3>
<p>Some parameter settings may result in a failure to <code class="docutils literal notranslate"><span class="pre">fit</span></code> one or more folds
of the data. By default, this will cause the entire search to fail, even if
some parameter settings could be fully evaluated. Setting <code class="docutils literal notranslate"><span class="pre">error_score=0</span></code>
(or <code class="docutils literal notranslate"><span class="pre">=np.nan</span></code>) will make the procedure robust to such failure, issuing a
warning and setting the score for that fold to 0 (or <code class="docutils literal notranslate"><span class="pre">nan</span></code>), but completing
the search.</p>
</section>
</section>
<section id="alternatives-to-brute-force-parameter-search">
<span id="alternative-cv"></span><h2><span class="section-number">3.2.5. </span>Alternatives to brute force parameter search<a class="headerlink" href="#alternatives-to-brute-force-parameter-search" title="Permalink to this heading">¶</a></h2>
<section id="model-specific-cross-validation">
<h3><span class="section-number">3.2.5.1. </span>Model specific cross-validation<a class="headerlink" href="#model-specific-cross-validation" title="Permalink to this heading">¶</a></h3>
<p>Some models can fit data for a range of values of some parameter almost
as efficiently as fitting the estimator for a single value of the
parameter. This feature can be leveraged to perform a more efficient
cross-validation used for model selection of this parameter.</p>
<p>The most common parameter amenable to this strategy is the parameter
encoding the strength of the regularizer. In this case we say that we
compute the <strong>regularization path</strong> of the estimator.</p>
<p>Here is the list of such models:</p>
<table class="autosummary longtable docutils align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/sklearn.linear_model.ElasticNetCV.html#sklearn.linear_model.ElasticNetCV" title="sklearn.linear_model.ElasticNetCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linear_model.ElasticNetCV</span></code></a>(*[, l1_ratio, ...])</p></td>
<td><p>Elastic Net model with iterative fitting along a regularization path.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/sklearn.linear_model.LarsCV.html#sklearn.linear_model.LarsCV" title="sklearn.linear_model.LarsCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linear_model.LarsCV</span></code></a>(*[, fit_intercept, ...])</p></td>
<td><p>Cross-validated Least Angle Regression model.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/sklearn.linear_model.LassoCV.html#sklearn.linear_model.LassoCV" title="sklearn.linear_model.LassoCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linear_model.LassoCV</span></code></a>(*[, eps, n_alphas, ...])</p></td>
<td><p>Lasso linear model with iterative fitting along a regularization path.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/sklearn.linear_model.LassoLarsCV.html#sklearn.linear_model.LassoLarsCV" title="sklearn.linear_model.LassoLarsCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linear_model.LassoLarsCV</span></code></a>(*[, fit_intercept, ...])</p></td>
<td><p>Cross-validated Lasso, using the LARS algorithm.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/sklearn.linear_model.LogisticRegressionCV.html#sklearn.linear_model.LogisticRegressionCV" title="sklearn.linear_model.LogisticRegressionCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linear_model.LogisticRegressionCV</span></code></a>(*[, Cs, ...])</p></td>
<td><p>Logistic Regression CV (aka logit, MaxEnt) classifier.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/sklearn.linear_model.MultiTaskElasticNetCV.html#sklearn.linear_model.MultiTaskElasticNetCV" title="sklearn.linear_model.MultiTaskElasticNetCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linear_model.MultiTaskElasticNetCV</span></code></a>(*[, ...])</p></td>
<td><p>Multi-task L1/L2 ElasticNet with built-in cross-validation.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/sklearn.linear_model.MultiTaskLassoCV.html#sklearn.linear_model.MultiTaskLassoCV" title="sklearn.linear_model.MultiTaskLassoCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linear_model.MultiTaskLassoCV</span></code></a>(*[, eps, ...])</p></td>
<td><p>Multi-task Lasso model trained with L1/L2 mixed-norm as regularizer.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/sklearn.linear_model.OrthogonalMatchingPursuitCV.html#sklearn.linear_model.OrthogonalMatchingPursuitCV" title="sklearn.linear_model.OrthogonalMatchingPursuitCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linear_model.OrthogonalMatchingPursuitCV</span></code></a>(*)</p></td>
<td><p>Cross-validated Orthogonal Matching Pursuit model (OMP).</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/sklearn.linear_model.RidgeCV.html#sklearn.linear_model.RidgeCV" title="sklearn.linear_model.RidgeCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linear_model.RidgeCV</span></code></a>([alphas, ...])</p></td>
<td><p>Ridge regression with built-in cross-validation.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/sklearn.linear_model.RidgeClassifierCV.html#sklearn.linear_model.RidgeClassifierCV" title="sklearn.linear_model.RidgeClassifierCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linear_model.RidgeClassifierCV</span></code></a>([alphas, ...])</p></td>
<td><p>Ridge classifier with built-in cross-validation.</p></td>
</tr>
</tbody>
</table>
</section>
<section id="information-criterion">
<h3><span class="section-number">3.2.5.2. </span>Information Criterion<a class="headerlink" href="#information-criterion" title="Permalink to this heading">¶</a></h3>
<p>Some models can offer an information-theoretic closed-form formula of the
optimal estimate of the regularization parameter by computing a single
regularization path (instead of several when using cross-validation).</p>
<p>Here is the list of models benefiting from the Akaike Information
Criterion (AIC) or the Bayesian Information Criterion (BIC) for automated
model selection:</p>
<table class="autosummary longtable docutils align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/sklearn.linear_model.LassoLarsIC.html#sklearn.linear_model.LassoLarsIC" title="sklearn.linear_model.LassoLarsIC"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linear_model.LassoLarsIC</span></code></a>([criterion, ...])</p></td>
<td><p>Lasso model fit with Lars using BIC or AIC for model selection.</p></td>
</tr>
</tbody>
</table>
</section>
<section id="out-of-bag-estimates">
<span id="out-of-bag"></span><h3><span class="section-number">3.2.5.3. </span>Out of Bag Estimates<a class="headerlink" href="#out-of-bag-estimates" title="Permalink to this heading">¶</a></h3>
<p>When using ensemble methods base upon bagging, i.e. generating new
training sets using sampling with replacement, part of the training set
remains unused. For each classifier in the ensemble, a different part
of the training set is left out.</p>
<p>This left out portion can be used to estimate the generalization error
without having to rely on a separate validation set. This estimate
comes “for free” as no additional data is needed and can be used for
model selection.</p>
<p>This is currently implemented in the following classes:</p>
<table class="autosummary longtable docutils align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="sklearn.ensemble.RandomForestClassifier"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ensemble.RandomForestClassifier</span></code></a>([...])</p></td>
<td><p>A random forest classifier.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/sklearn.ensemble.RandomForestRegressor.html#sklearn.ensemble.RandomForestRegressor" title="sklearn.ensemble.RandomForestRegressor"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ensemble.RandomForestRegressor</span></code></a>([...])</p></td>
<td><p>A random forest regressor.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/sklearn.ensemble.ExtraTreesClassifier.html#sklearn.ensemble.ExtraTreesClassifier" title="sklearn.ensemble.ExtraTreesClassifier"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ensemble.ExtraTreesClassifier</span></code></a>([...])</p></td>
<td><p>An extra-trees classifier.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/sklearn.ensemble.ExtraTreesRegressor.html#sklearn.ensemble.ExtraTreesRegressor" title="sklearn.ensemble.ExtraTreesRegressor"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ensemble.ExtraTreesRegressor</span></code></a>([n_estimators, ...])</p></td>
<td><p>An extra-trees regressor.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="sklearn.ensemble.GradientBoostingClassifier"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ensemble.GradientBoostingClassifier</span></code></a>(*[, ...])</p></td>
<td><p>Gradient Boosting for classification.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingRegressor.html#sklearn.ensemble.GradientBoostingRegressor" title="sklearn.ensemble.GradientBoostingRegressor"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ensemble.GradientBoostingRegressor</span></code></a>(*[, ...])</p></td>
<td><p>Gradient Boosting for regression.</p></td>
</tr>
</tbody>
</table>
</section>
</section>
</section>
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