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<li><a class="reference internal" href="#">4.4. Imputation of missing values</a><ul>
<li><a class="reference internal" href="#univariate-feature-imputation">4.4.1. Univariate feature imputation</a></li>
<li><a class="reference internal" href="#multivariate-feature-imputation">4.4.2. Multivariate feature imputation</a></li>
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<div class="section" id="imputation-of-missing-values">
<span id="impute"></span><h1>4.4. Imputation of missing values<a class="headerlink" href="#imputation-of-missing-values" title="Permalink to this headline">¶</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.</p>
<div class="section" id="univariate-feature-imputation">
<h2>4.4.1. Univariate feature imputation<a class="headerlink" href="#univariate-feature-imputation" title="Permalink to this headline">¶</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"><span class="pre">SimpleImputer</span></code></a> class provides basic strategies for imputing missing
values, either using the mean, the median or the most frequent value of
the row or 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"><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"><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="k">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="s1">'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(copy=True, missing_values='NaN', strategy='mean', verbose=0)</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"><span class="pre">SimpleImputer</span></code></a> class also supports sparse matrices:</p>
<div class="highlight-default"><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="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="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">0</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(copy=True, missing_values=0, strategy='mean', verbose=0)</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="mi">0</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="mi">0</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="go">[[4. 2. ]</span>
<span class="go"> [6. 3.666...]</span>
<span class="go"> [7. 6. ]]</span>
</pre></div>
</div>
<p>Note that, here, missing values are encoded by 0 and are thus implicitly stored
in the matrix. This format is thus suitable when there are many more missing
values than observed values.</p>
</div>
<div class="section" id="multivariate-feature-imputation">
<span id="mice"></span><h2>4.4.2. Multivariate feature imputation<a class="headerlink" href="#multivariate-feature-imputation" title="Permalink to this headline">¶</a></h2>
<p>A more sophisticated approach is to use the <a class="reference internal" href="generated/sklearn.impute.MICEImputer.html#sklearn.impute.MICEImputer" title="sklearn.impute.MICEImputer"><code class="xref py py-class docutils literal"><span class="pre">MICEImputer</span></code></a> class, which
implements the Multivariate Imputation by Chained Equations technique. MICE
models each feature with missing values as a function of other features, and
uses that estimate for imputation. It does so in a round-robin fashion: at
each step, a feature column is designated as output <cite>y</cite> and the other feature
columns are treated as inputs <cite>X</cite>. A regressor is fit on <cite>(X, y)</cite> for known <cite>y</cite>.
Then, the regressor is used to predict the unknown values of <cite>y</cite>. This is
repeated for each feature, and then is done for a number of imputation rounds.
Here is an example snippet:</p>
<div class="highlight-default"><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="k">import</span> <span class="n">MICEImputer</span>
<span class="gp">>>> </span><span class="n">imp</span> <span class="o">=</span> <span class="n">MICEImputer</span><span class="p">(</span><span class="n">n_imputations</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="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">MICEImputer(imputation_order='ascending', initial_strategy='mean',</span>
<span class="go"> max_value=None, min_value=None, missing_values='NaN', n_burn_in=10,</span>
<span class="go"> n_imputations=10, n_nearest_features=None, predictor=None,</span>
<span class="go"> random_state=0, verbose=False)</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="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. 4.]</span>
<span class="go"> [13. 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"><span class="pre">SimpleImputer</span></code></a> and <a class="reference internal" href="generated/sklearn.impute.MICEImputer.html#sklearn.impute.MICEImputer" title="sklearn.impute.MICEImputer"><code class="xref py py-class docutils literal"><span class="pre">MICEImputer</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/plot_missing_values.html#sphx-glr-auto-examples-plot-missing-values-py"><span class="std std-ref">Imputing missing values before building an estimator</span></a>.</p>
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