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  <section id="empirical-covariance">
<h1>empirical_covariance<a class="headerlink" href="#empirical-covariance" title="Link to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="sklearn.covariance.empirical_covariance">
<span class="sig-prename descclassname"><span class="pre">sklearn.covariance.</span></span><span class="sig-name descname"><span class="pre">empirical_covariance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">assume_centered</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/86d099ec1/sklearn/covariance/_empirical_covariance.py#L60"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.empirical_covariance" title="Link to this definition">#</a></dt>
<dd><p>Compute the Maximum likelihood covariance estimator.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">ndarray of shape (n_samples, n_features)</span></dt><dd><p>Data from which to compute the covariance estimate.</p>
</dd>
<dt><strong>assume_centered</strong><span class="classifier">bool, default=False</span></dt><dd><p>If <code class="docutils literal notranslate"><span class="pre">True</span></code>, data will not be centered before computation.
Useful when working with data whose mean is almost, but not exactly
zero.
If <code class="docutils literal notranslate"><span class="pre">False</span></code>, data will be centered before computation.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>covariance</strong><span class="classifier">ndarray of shape (n_features, n_features)</span></dt><dd><p>Empirical covariance (Maximum Likelihood Estimator).</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.covariance</span><span class="w"> </span><span class="kn">import</span> <span class="n">empirical_covariance</span>
<span class="gp">&gt;&gt;&gt; </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">1</span><span class="p">,</span><span class="mi">1</span><span class="p">],[</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">],[</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span>
<span class="gp">... </span>     <span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">empirical_covariance</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([[0.25, 0.25, 0.25],</span>
<span class="go">       [0.25, 0.25, 0.25],</span>
<span class="go">       [0.25, 0.25, 0.25]])</span>
</pre></div>
</div>
</dd></dl>

<section id="gallery-examples">
<h2>Gallery examples<a class="headerlink" href="#gallery-examples" title="Link to this heading">#</a></h2>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="When working with covariance estimation, the usual approach is to use a maximum likelihood estimator, such as the EmpiricalCovariance. It is unbiased, i.e. it converges to the true (population) covariance when given many observations. However, it can also be beneficial to regularize it, in order to reduce its variance; this, in turn, introduces some bias. This example illustrates the simple regularization used in shrunk_covariance estimators. In particular, it focuses on how to set the amount of regularization, i.e. how to choose the bias-variance trade-off."><img alt="" src="../../_images/sphx_glr_plot_covariance_estimation_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/covariance/plot_covariance_estimation.html#sphx-glr-auto-examples-covariance-plot-covariance-estimation-py"><span class="std std-ref">Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood</span></a></p>
  <div class="sphx-glr-thumbnail-title">Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood</div>
</div></div></section>
</section>


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