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<ul>
<li><a class="reference internal" href="#"><tt class="docutils literal"><span class="pre">sklearn.covariance</span></tt>.oas</a></li>
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<div class="section" id="sklearn-covariance-oas">
<h1><a class="reference internal" href="../classes.html#module-sklearn.covariance" title="sklearn.covariance"><tt class="xref py py-mod docutils literal"><span class="pre">sklearn.covariance</span></tt></a>.oas<a class="headerlink" href="#sklearn-covariance-oas" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="sklearn.covariance.oas">
<tt class="descclassname">sklearn.covariance.</tt><tt class="descname">oas</tt><big>(</big><em>X</em>, <em>assume_centered=False</em><big>)</big><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/a95203b/sklearn/covariance/shrunk_covariance_.py#L394"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.oas" title="Permalink to this definition">¶</a></dt>
<dd><p>Estimate covariance with the Oracle Approximating Shrinkage algorithm.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>X</strong> : array-like, shape (n_samples, n_features)</p>
<blockquote>
<div><p>Data from which to compute the covariance estimate.</p>
</div></blockquote>
<p><strong>assume_centered</strong> : boolean</p>
<blockquote>
<div><p>If True, data are not centered before computation.
Useful to work with data whose mean is significantly equal to
zero but is not exactly zero.
If False, data are centered before computation.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>shrunk_cov</strong> : array-like, shape (n_features, n_features)</p>
<blockquote>
<div><p>Shrunk covariance.</p>
</div></blockquote>
<p><strong>shrinkage</strong> : float</p>
<blockquote class="last">
<div><p>Coefficient in the convex combination used for the computation
of the shrunk estimate.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>The regularised (shrunk) covariance is:</p>
<dl class="docutils">
<dt>(1 - shrinkage)*cov</dt>
<dd><ul class="first last simple">
<li>shrinkage * mu * np.identity(n_features)</li>
</ul>
</dd>
</dl>
<p>where mu = trace(cov) / n_features</p>
<p>The formula we used to implement the OAS
does not correspond to the one given in the article. It has been taken
from the MATLAB program available from the author’s webpage
(<a class="reference external" href="https://tbayes.eecs.umich.edu/yilun/covestimation">https://tbayes.eecs.umich.edu/yilun/covestimation</a>).</p>
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