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<li><a class="reference internal" href="#">6.4. Imputation of missing values</a><ul>
<li><a class="reference internal" href="#univariate-vs-multivariate-imputation">6.4.1. Univariate vs. Multivariate Imputation</a></li>
<li><a class="reference internal" href="#univariate-feature-imputation">6.4.2. Univariate feature imputation</a></li>
<li><a class="reference internal" href="#multivariate-feature-imputation">6.4.3. Multivariate feature imputation</a><ul>
<li><a class="reference internal" href="#flexibility-of-iterativeimputer">6.4.3.1. Flexibility of IterativeImputer</a></li>
<li><a class="reference internal" href="#multiple-vs-single-imputation">6.4.3.2. Multiple vs. Single Imputation</a></li>
<li><a class="reference internal" href="#references">6.4.3.3. References</a></li>
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<li><a class="reference internal" href="#marking-imputed-values">6.4.6. Marking imputed values</a></li>
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<section id="imputation-of-missing-values">
<span id="impute"></span><h1><span class="section-number">6.4. </span>Imputation of missing values<a class="headerlink" href="#imputation-of-missing-values" title="Link to this heading">¶</a></h1>
<p>For various reasons, many real world datasets contain missing values, often
encoded as blanks, NaNs or other placeholders. Such datasets however are
incompatible with scikit-learn estimators which assume that all values in an
array are numerical, and that all have and hold meaning. A basic strategy to
use incomplete datasets is to discard entire rows and/or columns containing
missing values. However, this comes at the price of losing data which may be
valuable (even though incomplete). A better strategy is to impute the missing
values, i.e., to infer them from the known part of the data. See the
glossary entry on <a class="reference internal" href="../glossary.html#term-imputation"><span class="xref std std-term">imputation</span></a>.</p>
<section id="univariate-vs-multivariate-imputation">
<h2><span class="section-number">6.4.1. </span>Univariate vs. Multivariate Imputation<a class="headerlink" href="#univariate-vs-multivariate-imputation" title="Link to this heading">¶</a></h2>
<p>One type of imputation algorithm is univariate, which imputes values in the
i-th feature dimension using only non-missing values in that feature dimension
(e.g. <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a>). By contrast, multivariate imputation
algorithms use the entire set of available feature dimensions to estimate the
missing values (e.g. <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a>).</p>
</section>
<section id="univariate-feature-imputation">
<span id="single-imputer"></span><h2><span class="section-number">6.4.2. </span>Univariate feature imputation<a class="headerlink" href="#univariate-feature-imputation" title="Link to this heading">¶</a></h2>
<p>The <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a> class provides basic strategies for imputing missing
values. Missing values can be imputed with a provided constant value, or using
the statistics (mean, median or most frequent) of each column in which the
missing values are located. This class also allows for different missing values
encodings.</p>
<p>The following snippet demonstrates how to replace missing values,
encoded as <code class="docutils literal notranslate"><span class="pre">np.nan</span></code>, using the mean value of the columns (axis 0)
that contain the missing values:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.impute</span> <span class="kn">import</span> <span class="n">SimpleImputer</span>
<span class="gp">>>> </span><span class="n">imp</span> <span class="o">=</span> <span class="n">SimpleImputer</span><span class="p">(</span><span class="n">missing_values</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="n">strategy</span><span class="o">=</span><span class="s1">'mean'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">imp</span><span class="o">.</span><span class="n">fit</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">6</span><span class="p">]])</span>
<span class="go">SimpleImputer()</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="p">[[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">6</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">6</span><span class="p">]]</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">imp</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X</span><span class="p">))</span>
<span class="go">[[4. 2. ]</span>
<span class="go"> [6. 3.666...]</span>
<span class="go"> [7. 6. ]]</span>
</pre></div>
</div>
<p>The <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a> class also supports sparse matrices:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">scipy.sparse</span> <span class="k">as</span> <span class="nn">sp</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">csc_matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">8</span><span class="p">,</span> <span class="mi">4</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">imp</span> <span class="o">=</span> <span class="n">SimpleImputer</span><span class="p">(</span><span class="n">missing_values</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">strategy</span><span class="o">=</span><span class="s1">'mean'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">imp</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="go">SimpleImputer(missing_values=-1)</span>
<span class="gp">>>> </span><span class="n">X_test</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">csc_matrix</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">6</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">6</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">imp</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span><span class="o">.</span><span class="n">toarray</span><span class="p">())</span>
<span class="go">[[3. 2.]</span>
<span class="go"> [6. 3.]</span>
<span class="go"> [7. 6.]]</span>
</pre></div>
</div>
<p>Note that this format is not meant to be used to implicitly store missing
values in the matrix because it would densify it at transform time. Missing
values encoded by 0 must be used with dense input.</p>
<p>The <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a> class also supports categorical data represented as
string values or pandas categoricals when using the <code class="docutils literal notranslate"><span class="pre">'most_frequent'</span></code> or
<code class="docutils literal notranslate"><span class="pre">'constant'</span></code> strategy:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></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">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">([[</span><span class="s2">"a"</span><span class="p">,</span> <span class="s2">"x"</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="s2">"a"</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="s2">"b"</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">]],</span> <span class="n">dtype</span><span class="o">=</span><span class="s2">"category"</span><span class="p">)</span>
<span class="gp">...</span>
<span class="gp">>>> </span><span class="n">imp</span> <span class="o">=</span> <span class="n">SimpleImputer</span><span class="p">(</span><span class="n">strategy</span><span class="o">=</span><span class="s2">"most_frequent"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">imp</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">df</span><span class="p">))</span>
<span class="go">[['a' 'x']</span>
<span class="go"> ['a' 'y']</span>
<span class="go"> ['a' 'y']</span>
<span class="go"> ['b' 'y']]</span>
</pre></div>
</div>
<p>For another example on usage, see <a class="reference internal" href="../auto_examples/impute/plot_missing_values.html#sphx-glr-auto-examples-impute-plot-missing-values-py"><span class="std std-ref">Imputing missing values before building an estimator</span></a>.</p>
</section>
<section id="multivariate-feature-imputation">
<span id="iterative-imputer"></span><h2><span class="section-number">6.4.3. </span>Multivariate feature imputation<a class="headerlink" href="#multivariate-feature-imputation" title="Link to this heading">¶</a></h2>
<p>A more sophisticated approach is to use the <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> class,
which models each feature with missing values as a function of other features,
and uses that estimate for imputation. It does so in an iterated round-robin
fashion: at each step, a feature column is designated as output <code class="docutils literal notranslate"><span class="pre">y</span></code> and the
other feature columns are treated as inputs <code class="docutils literal notranslate"><span class="pre">X</span></code>. A regressor is fit on <code class="docutils literal notranslate"><span class="pre">(X,</span>
<span class="pre">y)</span></code> for known <code class="docutils literal notranslate"><span class="pre">y</span></code>. Then, the regressor is used to predict the missing values
of <code class="docutils literal notranslate"><span class="pre">y</span></code>. This is done for each feature in an iterative fashion, and then is
repeated for <code class="docutils literal notranslate"><span class="pre">max_iter</span></code> imputation rounds. The results of the final
imputation round are returned.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This estimator is still <strong>experimental</strong> for now: default parameters or
details of behaviour might change without any deprecation cycle. Resolving
the following issues would help stabilize <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a>:
convergence criteria (<a class="reference external" href="https://github.com/scikit-learn/scikit-learn/issues/14338">#14338</a>), default estimators (<a class="reference external" href="https://github.com/scikit-learn/scikit-learn/issues/13286">#13286</a>),
and use of random state (<a class="reference external" href="https://github.com/scikit-learn/scikit-learn/issues/15611">#15611</a>). To use it, you need to explicitly
import <code class="docutils literal notranslate"><span class="pre">enable_iterative_imputer</span></code>.</p>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.experimental</span> <span class="kn">import</span> <span class="n">enable_iterative_imputer</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.impute</span> <span class="kn">import</span> <span class="n">IterativeImputer</span>
<span class="gp">>>> </span><span class="n">imp</span> <span class="o">=</span> <span class="n">IterativeImputer</span><span class="p">(</span><span class="n">max_iter</span><span class="o">=</span><span class="mi">10</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">imp</span><span class="o">.</span><span class="n">fit</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">]])</span>
<span class="go">IterativeImputer(random_state=0)</span>
<span class="gp">>>> </span><span class="n">X_test</span> <span class="o">=</span> <span class="p">[[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">6</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">6</span><span class="p">]]</span>
<span class="gp">>>> </span><span class="c1"># the model learns that the second feature is double the first</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">imp</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)))</span>
<span class="go">[[ 1. 2.]</span>
<span class="go"> [ 6. 12.]</span>
<span class="go"> [ 3. 6.]]</span>
</pre></div>
</div>
<p>Both <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a> and <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> can be used in a
Pipeline as a way to build a composite estimator that supports imputation.
See <a class="reference internal" href="../auto_examples/impute/plot_missing_values.html#sphx-glr-auto-examples-impute-plot-missing-values-py"><span class="std std-ref">Imputing missing values before building an estimator</span></a>.</p>
<section id="flexibility-of-iterativeimputer">
<h3><span class="section-number">6.4.3.1. </span>Flexibility of IterativeImputer<a class="headerlink" href="#flexibility-of-iterativeimputer" title="Link to this heading">¶</a></h3>
<p>There are many well-established imputation packages in the R data science
ecosystem: Amelia, mi, mice, missForest, etc. missForest is popular, and turns
out to be a particular instance of different sequential imputation algorithms
that can all be implemented with <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> by passing in
different regressors to be used for predicting missing feature values. In the
case of missForest, this regressor is a Random Forest.
See <a class="reference internal" href="../auto_examples/impute/plot_iterative_imputer_variants_comparison.html#sphx-glr-auto-examples-impute-plot-iterative-imputer-variants-comparison-py"><span class="std std-ref">Imputing missing values with variants of IterativeImputer</span></a>.</p>
</section>
<section id="multiple-vs-single-imputation">
<span id="multiple-imputation"></span><h3><span class="section-number">6.4.3.2. </span>Multiple vs. Single Imputation<a class="headerlink" href="#multiple-vs-single-imputation" title="Link to this heading">¶</a></h3>
<p>In the statistics community, it is common practice to perform multiple
imputations, generating, for example, <code class="docutils literal notranslate"><span class="pre">m</span></code> separate imputations for a single
feature matrix. Each of these <code class="docutils literal notranslate"><span class="pre">m</span></code> imputations is then put through the
subsequent analysis pipeline (e.g. feature engineering, clustering, regression,
classification). The <code class="docutils literal notranslate"><span class="pre">m</span></code> final analysis results (e.g. held-out validation
errors) allow the data scientist to obtain understanding of how analytic
results may differ as a consequence of the inherent uncertainty caused by the
missing values. The above practice is called multiple imputation.</p>
<p>Our implementation of <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> was inspired by the R MICE
package (Multivariate Imputation by Chained Equations) <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, but differs from
it by returning a single imputation instead of multiple imputations. However,
<a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> can also be used for multiple imputations by applying
it repeatedly to the same dataset with different random seeds when
<code class="docutils literal notranslate"><span class="pre">sample_posterior=True</span></code>. See <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>, chapter 4 for more discussion on multiple
vs. single imputations.</p>
<p>It is still an open problem as to how useful single vs. multiple imputation is
in the context of prediction and classification when the user is not
interested in measuring uncertainty due to missing values.</p>
<p>Note that a call to the <code class="docutils literal notranslate"><span class="pre">transform</span></code> method of <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> is
not allowed to change the number of samples. Therefore multiple imputations
cannot be achieved by a single call to <code class="docutils literal notranslate"><span class="pre">transform</span></code>.</p>
</section>
<section id="references">
<h3><span class="section-number">6.4.3.3. </span>References<a class="headerlink" href="#references" title="Link to this heading">¶</a></h3>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id3" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
<p><a class="reference external" href="https://www.jstatsoft.org/article/view/v045i03">Stef van Buuren, Karin Groothuis-Oudshoorn (2011). “mice: Multivariate
Imputation by Chained Equations in R”. Journal of Statistical Software 45:
1-67.</a></p>
</aside>
<aside class="footnote brackets" id="id4" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
<p>Roderick J A Little and Donald B Rubin (1986). “Statistical Analysis
with Missing Data”. John Wiley & Sons, Inc., New York, NY, USA.</p>
</aside>
</aside>
</section>
</section>
<section id="nearest-neighbors-imputation">
<span id="knnimpute"></span><h2><span class="section-number">6.4.4. </span>Nearest neighbors imputation<a class="headerlink" href="#nearest-neighbors-imputation" title="Link to this heading">¶</a></h2>
<p>The <a class="reference internal" href="generated/sklearn.impute.KNNImputer.html#sklearn.impute.KNNImputer" title="sklearn.impute.KNNImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">KNNImputer</span></code></a> class provides imputation for filling in missing values
using the k-Nearest Neighbors approach. By default, a euclidean distance metric
that supports missing values,
<a class="reference internal" href="generated/sklearn.metrics.pairwise.nan_euclidean_distances.html#sklearn.metrics.pairwise.nan_euclidean_distances" title="sklearn.metrics.pairwise.nan_euclidean_distances"><code class="xref py py-func docutils literal notranslate"><span class="pre">nan_euclidean_distances</span></code></a>, is used to find the
nearest neighbors. Each missing feature is imputed using values from
<code class="docutils literal notranslate"><span class="pre">n_neighbors</span></code> nearest neighbors that have a value for the feature. The
feature of the neighbors are averaged uniformly or weighted by distance to each
neighbor. If a sample has more than one feature missing, then the neighbors for
that sample can be different depending on the particular feature being imputed.
When the number of available neighbors is less than <code class="docutils literal notranslate"><span class="pre">n_neighbors</span></code> and there are
no defined distances to the training set, the training set average for that
feature is used during imputation. If there is at least one neighbor with a
defined distance, the weighted or unweighted average of the remaining neighbors
will be used during imputation. If a feature is always missing in training, it
is removed during <code class="docutils literal notranslate"><span class="pre">transform</span></code>. For more information on the methodology, see
ref. <a class="reference internal" href="#ol2001" id="id5"><span>[OL2001]</span></a>.</p>
<p>The following snippet demonstrates how to replace missing values,
encoded as <code class="docutils literal notranslate"><span class="pre">np.nan</span></code>, using the mean feature value of the two nearest
neighbors of samples with missing values:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.impute</span> <span class="kn">import</span> <span class="n">KNNImputer</span>
<span class="gp">>>> </span><span class="n">nan</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">nan</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="n">nan</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="p">[</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">7</span><span class="p">]]</span>
<span class="gp">>>> </span><span class="n">imputer</span> <span class="o">=</span> <span class="n">KNNImputer</span><span class="p">(</span><span class="n">n_neighbors</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">weights</span><span class="o">=</span><span class="s2">"uniform"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">imputer</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([[1. , 2. , 4. ],</span>
<span class="go"> [3. , 4. , 3. ],</span>
<span class="go"> [5.5, 6. , 5. ],</span>
<span class="go"> [8. , 8. , 7. ]])</span>
</pre></div>
</div>
<p>For another example on usage, see <a class="reference internal" href="../auto_examples/impute/plot_missing_values.html#sphx-glr-auto-examples-impute-plot-missing-values-py"><span class="std std-ref">Imputing missing values before building an estimator</span></a>.</p>
<aside class="topic">
<p class="topic-title">References</p>
<div role="list" class="citation-list">
<div class="citation" id="ol2001" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id5">OL2001</a><span class="fn-bracket">]</span></span>
<p><a class="reference external" href="https://academic.oup.com/bioinformatics/article/17/6/520/272365">Olga Troyanskaya, Michael Cantor, Gavin Sherlock, Pat Brown,
Trevor Hastie, Robert Tibshirani, David Botstein and Russ B. Altman,
Missing value estimation methods for DNA microarrays, BIOINFORMATICS
Vol. 17 no. 6, 2001 Pages 520-525.</a></p>
</div>
</div>
</aside>
</section>
<section id="keeping-the-number-of-features-constant">
<h2><span class="section-number">6.4.5. </span>Keeping the number of features constant<a class="headerlink" href="#keeping-the-number-of-features-constant" title="Link to this heading">¶</a></h2>
<p>By default, the scikit-learn imputers will drop fully empty features, i.e.
columns containing only missing values. For instance:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">imputer</span> <span class="o">=</span> <span class="n">SimpleImputer</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">imputer</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([[1.],</span>
<span class="go"> [2.],</span>
<span class="go"> [3.]])</span>
</pre></div>
</div>
<p>The first feature in <code class="docutils literal notranslate"><span class="pre">X</span></code> containing only <code class="docutils literal notranslate"><span class="pre">np.nan</span></code> was dropped after the
imputation. While this feature will not help in predictive setting, dropping
the columns will change the shape of <code class="docutils literal notranslate"><span class="pre">X</span></code> which could be problematic when using
imputers in a more complex machine-learning pipeline. The parameter
<code class="docutils literal notranslate"><span class="pre">keep_empty_features</span></code> offers the option to keep the empty features by imputing
with a constant values. In most of the cases, this constant value is zero:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">imputer</span><span class="o">.</span><span class="n">set_params</span><span class="p">(</span><span class="n">keep_empty_features</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="go">SimpleImputer(keep_empty_features=True)</span>
<span class="gp">>>> </span><span class="n">imputer</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([[0., 1.],</span>
<span class="go"> [0., 2.],</span>
<span class="go"> [0., 3.]])</span>
</pre></div>
</div>
</section>
<section id="marking-imputed-values">
<span id="missing-indicator"></span><h2><span class="section-number">6.4.6. </span>Marking imputed values<a class="headerlink" href="#marking-imputed-values" title="Link to this heading">¶</a></h2>
<p>The <a class="reference internal" href="generated/sklearn.impute.MissingIndicator.html#sklearn.impute.MissingIndicator" title="sklearn.impute.MissingIndicator"><code class="xref py py-class docutils literal notranslate"><span class="pre">MissingIndicator</span></code></a> transformer is useful to transform a dataset into
corresponding binary matrix indicating the presence of missing values in the
dataset. This transformation is useful in conjunction with imputation. When
using imputation, preserving the information about which values had been
missing can be informative. Note that both the <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a> and
<a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> have the boolean parameter <code class="docutils literal notranslate"><span class="pre">add_indicator</span></code>
(<code class="docutils literal notranslate"><span class="pre">False</span></code> by default) which when set to <code class="docutils literal notranslate"><span class="pre">True</span></code> provides a convenient way of
stacking the output of the <a class="reference internal" href="generated/sklearn.impute.MissingIndicator.html#sklearn.impute.MissingIndicator" title="sklearn.impute.MissingIndicator"><code class="xref py py-class docutils literal notranslate"><span class="pre">MissingIndicator</span></code></a> transformer with the
output of the imputer.</p>
<p><code class="docutils literal notranslate"><span class="pre">NaN</span></code> is usually used as the placeholder for missing values. However, it
enforces the data type to be float. The parameter <code class="docutils literal notranslate"><span class="pre">missing_values</span></code> allows to
specify other placeholder such as integer. In the following example, we will
use <code class="docutils literal notranslate"><span class="pre">-1</span></code> as missing values:</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.impute</span> <span class="kn">import</span> <span class="n">MissingIndicator</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">8</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">indicator</span> <span class="o">=</span> <span class="n">MissingIndicator</span><span class="p">(</span><span class="n">missing_values</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">mask_missing_values_only</span> <span class="o">=</span> <span class="n">indicator</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">mask_missing_values_only</span>
<span class="go">array([[ True, True, False],</span>
<span class="go"> [False, True, True],</span>
<span class="go"> [False, True, False]])</span>
</pre></div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">features</span></code> parameter is used to choose the features for which the mask is
constructed. By default, it is <code class="docutils literal notranslate"><span class="pre">'missing-only'</span></code> which returns the imputer
mask of the features containing missing values at <code class="docutils literal notranslate"><span class="pre">fit</span></code> time:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">indicator</span><span class="o">.</span><span class="n">features_</span>
<span class="go">array([0, 1, 3])</span>
</pre></div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">features</span></code> parameter can be set to <code class="docutils literal notranslate"><span class="pre">'all'</span></code> to return all features
whether or not they contain missing values:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">indicator</span> <span class="o">=</span> <span class="n">MissingIndicator</span><span class="p">(</span><span class="n">missing_values</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">features</span><span class="o">=</span><span class="s2">"all"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">mask_all</span> <span class="o">=</span> <span class="n">indicator</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">mask_all</span>
<span class="go">array([[ True, True, False, False],</span>
<span class="go"> [False, True, False, True],</span>
<span class="go"> [False, True, False, False]])</span>
<span class="gp">>>> </span><span class="n">indicator</span><span class="o">.</span><span class="n">features_</span>
<span class="go">array([0, 1, 2, 3])</span>
</pre></div>
</div>
<p>When using the <a class="reference internal" href="generated/sklearn.impute.MissingIndicator.html#sklearn.impute.MissingIndicator" title="sklearn.impute.MissingIndicator"><code class="xref py py-class docutils literal notranslate"><span class="pre">MissingIndicator</span></code></a> in 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>, be sure to use the
<a class="reference internal" href="generated/sklearn.pipeline.FeatureUnion.html#sklearn.pipeline.FeatureUnion" title="sklearn.pipeline.FeatureUnion"><code class="xref py py-class docutils literal notranslate"><span class="pre">FeatureUnion</span></code></a> or
<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> to add the indicator features to
the regular features. First we obtain the <code class="docutils literal notranslate"><span class="pre">iris</span></code> dataset, and add some missing
values to it.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_iris</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.impute</span> <span class="kn">import</span> <span class="n">SimpleImputer</span><span class="p">,</span> <span class="n">MissingIndicator</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.pipeline</span> <span class="kn">import</span> <span class="n">FeatureUnion</span><span class="p">,</span> <span class="n">make_pipeline</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.tree</span> <span class="kn">import</span> <span class="n">DecisionTreeClassifier</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">load_iris</span><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">mask</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">bool</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">X</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span>
<span class="gp">>>> </span><span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
</pre></div>
</div>
<p>Now we create a <a class="reference internal" href="generated/sklearn.pipeline.FeatureUnion.html#sklearn.pipeline.FeatureUnion" title="sklearn.pipeline.FeatureUnion"><code class="xref py py-class docutils literal notranslate"><span class="pre">FeatureUnion</span></code></a>. All features will be
imputed using <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a>, in order to enable classifiers to work
with this data. Additionally, it adds the indicator variables from
<a class="reference internal" href="generated/sklearn.impute.MissingIndicator.html#sklearn.impute.MissingIndicator" title="sklearn.impute.MissingIndicator"><code class="xref py py-class docutils literal notranslate"><span class="pre">MissingIndicator</span></code></a>.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">transformer</span> <span class="o">=</span> <span class="n">FeatureUnion</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">transformer_list</span><span class="o">=</span><span class="p">[</span>
<span class="gp">... </span> <span class="p">(</span><span class="s1">'features'</span><span class="p">,</span> <span class="n">SimpleImputer</span><span class="p">(</span><span class="n">strategy</span><span class="o">=</span><span class="s1">'mean'</span><span class="p">)),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s1">'indicators'</span><span class="p">,</span> <span class="n">MissingIndicator</span><span class="p">())])</span>
<span class="gp">>>> </span><span class="n">transformer</span> <span class="o">=</span> <span class="n">transformer</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">results</span> <span class="o">=</span> <span class="n">transformer</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">results</span><span class="o">.</span><span class="n">shape</span>
<span class="go">(100, 8)</span>
</pre></div>
</div>
<p>Of course, we cannot use the transformer to make any predictions. We should
wrap this in 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> with a classifier (e.g., a
<a class="reference internal" href="generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier" title="sklearn.tree.DecisionTreeClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">DecisionTreeClassifier</span></code></a>) to be able to make predictions.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">clf</span> <span class="o">=</span> <span class="n">make_pipeline</span><span class="p">(</span><span class="n">transformer</span><span class="p">,</span> <span class="n">DecisionTreeClassifier</span><span class="p">())</span>
<span class="gp">>>> </span><span class="n">clf</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">results</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">results</span><span class="o">.</span><span class="n">shape</span>
<span class="go">(100,)</span>
</pre></div>
</div>
</section>
<section id="estimators-that-handle-nan-values">
<h2><span class="section-number">6.4.7. </span>Estimators that handle NaN values<a class="headerlink" href="#estimators-that-handle-nan-values" title="Link to this heading">¶</a></h2>
<p>Some estimators are designed to handle NaN values without preprocessing.
Below is the list of these estimators, classified by type
(cluster, regressor, classifier, transform):</p>
<ul>
<li><strong>Estimators that allow NaN values for type </strong><code class="docutils literal notranslate"><span class="pre">cluster</span></code><strong>:
</strong><ul class="simple">
<li><p><a class="reference external" href="./generated/sklearn.cluster.HDBSCAN.html">HDBSCAN</a></p></li>
</ul>
</li>
<li><strong>Estimators that allow NaN values for type </strong><code class="docutils literal notranslate"><span class="pre">regressor</span></code><strong>:
</strong><ul class="simple">
<li><p><a class="reference external" href="./generated/sklearn.ensemble.BaggingRegressor.html">BaggingRegressor</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.tree.DecisionTreeRegressor.html">DecisionTreeRegressor</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.HistGradientBoostingRegressor.html">HistGradientBoostingRegressor</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.RandomForestRegressor.html">RandomForestRegressor</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.StackingRegressor.html">StackingRegressor</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.VotingRegressor.html">VotingRegressor</a></p></li>
</ul>
</li>
<li><strong>Estimators that allow NaN values for type </strong><code class="docutils literal notranslate"><span class="pre">classifier</span></code><strong>:
</strong><ul class="simple">
<li><p><a class="reference external" href="./generated/sklearn.ensemble.BaggingClassifier.html">BaggingClassifier</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.tree.DecisionTreeClassifier.html">DecisionTreeClassifier</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.HistGradientBoostingClassifier.html">HistGradientBoostingClassifier</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.RandomForestClassifier.html">RandomForestClassifier</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.StackingClassifier.html">StackingClassifier</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.VotingClassifier.html">VotingClassifier</a></p></li>
</ul>
</li>
<li><strong>Estimators that allow NaN values for type </strong><code class="docutils literal notranslate"><span class="pre">transformer</span></code><strong>:
</strong><ul class="simple">
<li><p><a class="reference external" href="./generated/sklearn.impute.IterativeImputer.html">IterativeImputer</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.impute.KNNImputer.html">KNNImputer</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.preprocessing.MaxAbsScaler.html">MaxAbsScaler</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.preprocessing.MinMaxScaler.html">MinMaxScaler</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.impute.MissingIndicator.html">MissingIndicator</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.preprocessing.OneHotEncoder.html">OneHotEncoder</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.preprocessing.OrdinalEncoder.html">OrdinalEncoder</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.preprocessing.PowerTransformer.html">PowerTransformer</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.preprocessing.QuantileTransformer.html">QuantileTransformer</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.preprocessing.RobustScaler.html">RobustScaler</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.impute.SimpleImputer.html">SimpleImputer</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.StackingClassifier.html">StackingClassifier</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.StackingRegressor.html">StackingRegressor</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.preprocessing.StandardScaler.html">StandardScaler</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.preprocessing.TargetEncoder.html">TargetEncoder</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.feature_selection.VarianceThreshold.html">VarianceThreshold</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.VotingClassifier.html">VotingClassifier</a></p></li>
<li><p><a class="reference external" href="./generated/sklearn.ensemble.VotingRegressor.html">VotingRegressor</a></p></li>
</ul>
</li>
</ul>
</section>
</section>
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