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  <section id="ledoit-wolf">
<h1>ledoit_wolf<a class="headerlink" href="#ledoit-wolf" title="Link to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="sklearn.covariance.ledoit_wolf">
<span class="sig-prename descclassname"><span class="pre">sklearn.covariance.</span></span><span class="sig-name descname"><span class="pre">ledoit_wolf</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>, <em class="sig-param"><span class="n"><span class="pre">block_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/86d099ec1/sklearn/covariance/_shrunk_covariance.py#L403"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.ledoit_wolf" title="Link to this definition">#</a></dt>
<dd><p>Estimate the shrunk Ledoit-Wolf covariance matrix.</p>
<p>Read more in the <a class="reference internal" href="../covariance.html#shrunk-covariance"><span class="std std-ref">User Guide</span></a>.</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">array-like 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 True, data will not be centered before computation.
Useful to work with data whose mean is significantly equal to
zero but is not exactly zero.
If False, data will be centered before computation.</p>
</dd>
<dt><strong>block_size</strong><span class="classifier">int, default=1000</span></dt><dd><p>Size of blocks into which the covariance matrix will be split.
This is purely a memory optimization and does not affect results.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>shrunk_cov</strong><span class="classifier">ndarray of shape (n_features, n_features)</span></dt><dd><p>Shrunk covariance.</p>
</dd>
<dt><strong>shrinkage</strong><span class="classifier">float</span></dt><dd><p>Coefficient in the convex combination used for the computation
of the shrunk estimate.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The regularized (shrunk) covariance is:</p>
<p>(1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)</p>
<p>where mu = trace(cov) / n_features</p>
<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">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</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="p">,</span> <span class="n">ledoit_wolf</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">real_cov</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">.4</span><span class="p">,</span> <span class="mf">.2</span><span class="p">],</span> <span class="p">[</span><span class="mf">.2</span><span class="p">,</span> <span class="mf">.8</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">rng</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">RandomState</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">multivariate_normal</span><span class="p">(</span><span class="n">mean</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">cov</span><span class="o">=</span><span class="n">real_cov</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">50</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">covariance</span><span class="p">,</span> <span class="n">shrinkage</span> <span class="o">=</span> <span class="n">ledoit_wolf</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">covariance</span>
<span class="go">array([[0.44..., 0.16...],</span>
<span class="go">       [0.16..., 0.80...]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">shrinkage</span>
<span class="go">np.float64(0.23...)</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="Using the GraphicalLasso estimator to learn a covariance and sparse precision from a small number of samples."><img alt="" src="../../_images/sphx_glr_plot_sparse_cov_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/covariance/plot_sparse_cov.html#sphx-glr-auto-examples-covariance-plot-sparse-cov-py"><span class="std std-ref">Sparse inverse covariance estimation</span></a></p>
  <div class="sphx-glr-thumbnail-title">Sparse inverse covariance estimation</div>
</div></div></section>
</section>


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