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<ul>
<li><a class="reference internal" href="#"><code class="docutils literal"><span class="pre">sklearn.covariance</span></code>.OAS</a><ul>
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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"><code class="xref py py-mod docutils literal"><span class="pre">sklearn.covariance</span></code></a>.OAS<a class="headerlink" href="#sklearn-covariance-oas" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="sklearn.covariance.OAS">
<em class="property">class </em><code class="descclassname">sklearn.covariance.</code><code class="descname">OAS</code><span class="sig-paren">(</span><em>store_precision=True</em>, <em>assume_centered=False</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/shrunk_covariance_.py#L472"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.OAS" title="Permalink to this definition">¶</a></dt>
<dd><p>Oracle Approximating Shrinkage Estimator</p>
<p>Read more in the <a class="reference internal" href="../covariance.html#shrunk-covariance"><span>User Guide</span></a>.</p>
<p>OAS is a particular form of shrinkage described in
“Shrinkage Algorithms for MMSE Covariance Estimation”
Chen et al., IEEE Trans. on Sign. Proc., Volume 58, Issue 10, October 2010.</p>
<p>The formula used here does not correspond to the one given in the
article. It has been taken from the Matlab program available from the
authors’ webpage (<a class="reference external" href="https://tbayes.eecs.umich.edu/yilun/covestimation">https://tbayes.eecs.umich.edu/yilun/covestimation</a>).</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>store_precision</strong> : bool, default=True</p>
<blockquote>
<div><p>Specify if the estimated precision is stored.</p>
</div></blockquote>
<p><strong>assume_centered: bool, default=False</strong> :</p>
<blockquote>
<div><p>If True, data are not centered before computation.
Useful when working with data whose mean is almost, but not exactly
zero.
If False (default), data are centered before computation.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Attributes:</th><td class="field-body"><p class="first"><strong>covariance_</strong> : array-like, shape (n_features, n_features)</p>
<blockquote>
<div><p>Estimated covariance matrix.</p>
</div></blockquote>
<p><strong>precision_</strong> : array-like, shape (n_features, n_features)</p>
<blockquote>
<div><p>Estimated pseudo inverse matrix.
(stored only if store_precision is True)</p>
</div></blockquote>
<p><strong>shrinkage_</strong> : float, 0 <= shrinkage <= 1</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 covariance is:</p>
<div class="highlight-python"><div class="highlight"><pre>(1 - shrinkage)*cov
+ shrinkage*mu*np.identity(n_features)
</pre></div>
</div>
<p>where mu = trace(cov) / n_features
and shrinkage is given by the OAS formula (see References)</p>
<p class="rubric">References</p>
<p>“Shrinkage Algorithms for MMSE Covariance Estimation”
Chen et al., IEEE Trans. on Sign. Proc., Volume 58, Issue 10, October 2010.</p>
<p class="rubric">Methods</p>
<table border="1" class="longtable docutils">
<colgroup>
<col width="10%" />
<col width="90%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.covariance.OAS.error_norm" title="sklearn.covariance.OAS.error_norm"><code class="xref py py-obj docutils literal"><span class="pre">error_norm</span></code></a>(comp_cov[, norm, scaling, squared])</td>
<td>Computes the Mean Squared Error between two covariance estimators.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#sklearn.covariance.OAS.fit" title="sklearn.covariance.OAS.fit"><code class="xref py py-obj docutils literal"><span class="pre">fit</span></code></a>(X[, y])</td>
<td>Fits the Oracle Approximating Shrinkage covariance model according to the given training data and parameters.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.covariance.OAS.get_params" title="sklearn.covariance.OAS.get_params"><code class="xref py py-obj docutils literal"><span class="pre">get_params</span></code></a>([deep])</td>
<td>Get parameters for this estimator.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#sklearn.covariance.OAS.get_precision" title="sklearn.covariance.OAS.get_precision"><code class="xref py py-obj docutils literal"><span class="pre">get_precision</span></code></a>()</td>
<td>Getter for the precision matrix.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.covariance.OAS.mahalanobis" title="sklearn.covariance.OAS.mahalanobis"><code class="xref py py-obj docutils literal"><span class="pre">mahalanobis</span></code></a>(observations)</td>
<td>Computes the squared Mahalanobis distances of given observations.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#sklearn.covariance.OAS.score" title="sklearn.covariance.OAS.score"><code class="xref py py-obj docutils literal"><span class="pre">score</span></code></a>(X_test[, y])</td>
<td>Computes the log-likelihood of a Gaussian data set with <cite>self.covariance_</cite> as an estimator of its covariance matrix.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.covariance.OAS.set_params" title="sklearn.covariance.OAS.set_params"><code class="xref py py-obj docutils literal"><span class="pre">set_params</span></code></a>(**params)</td>
<td>Set the parameters of this estimator.</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="sklearn.covariance.OAS.__init__">
<code class="descname">__init__</code><span class="sig-paren">(</span><em>store_precision=True</em>, <em>assume_centered=False</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/empirical_covariance_.py#L114"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.OAS.__init__" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="sklearn.covariance.OAS.error_norm">
<code class="descname">error_norm</code><span class="sig-paren">(</span><em>comp_cov</em>, <em>norm='frobenius'</em>, <em>scaling=True</em>, <em>squared=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/empirical_covariance_.py#L213"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.OAS.error_norm" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the Mean Squared Error between two covariance estimators.
(In the sense of the Frobenius norm).</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>comp_cov</strong> : array-like, shape = [n_features, n_features]</p>
<blockquote>
<div><p>The covariance to compare with.</p>
</div></blockquote>
<p><strong>norm</strong> : str</p>
<blockquote>
<div><p>The type of norm used to compute the error. Available error types:
- ‘frobenius’ (default): sqrt(tr(A^t.A))
- ‘spectral’: sqrt(max(eigenvalues(A^t.A))
where A is the error <code class="docutils literal"><span class="pre">(comp_cov</span> <span class="pre">-</span> <span class="pre">self.covariance_)</span></code>.</p>
</div></blockquote>
<p><strong>scaling</strong> : bool</p>
<blockquote>
<div><p>If True (default), the squared error norm is divided by n_features.
If False, the squared error norm is not rescaled.</p>
</div></blockquote>
<p><strong>squared</strong> : bool</p>
<blockquote>
<div><p>Whether to compute the squared error norm or the error norm.
If True (default), the squared error norm is returned.
If False, the error norm is returned.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>The Mean Squared Error (in the sense of the Frobenius norm) between</strong> :</p>
<p class="last"><strong>`self` and `comp_cov` covariance estimators.</strong> :</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.OAS.fit">
<code class="descname">fit</code><span class="sig-paren">(</span><em>X</em>, <em>y=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/shrunk_covariance_.py#L526"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.OAS.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fits the Oracle Approximating Shrinkage covariance model
according to the given training data and parameters.</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>Training data, where n_samples is the number of samples
and n_features is the number of features.</p>
</div></blockquote>
<p><strong>y</strong> : not used, present for API consistence purpose.</p>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>self: object</strong> :</p>
<blockquote class="last">
<div><p>Returns self.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.OAS.get_params">
<code class="descname">get_params</code><span class="sig-paren">(</span><em>deep=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/base.py#L199"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.OAS.get_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Get parameters for this estimator.</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>deep: boolean, optional</strong> :</p>
<blockquote>
<div><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>params</strong> : mapping of string to any</p>
<blockquote class="last">
<div><p>Parameter names mapped to their values.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.OAS.get_precision">
<code class="descname">get_precision</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/empirical_covariance_.py#L140"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.OAS.get_precision" title="Permalink to this definition">¶</a></dt>
<dd><p>Getter for the precision matrix.</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">Returns:</th><td class="field-body"><p class="first"><strong>precision_</strong> : array-like,</p>
<blockquote class="last">
<div><p>The precision matrix associated to the current covariance object.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.OAS.mahalanobis">
<code class="descname">mahalanobis</code><span class="sig-paren">(</span><em>observations</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/empirical_covariance_.py#L265"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.OAS.mahalanobis" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the squared Mahalanobis distances of given observations.</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>observations</strong> : array-like, shape = [n_observations, n_features]</p>
<blockquote>
<div><p>The observations, the Mahalanobis distances of the which we
compute. Observations are assumed to be drawn from the same
distribution than the data used in fit.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>mahalanobis_distance</strong> : array, shape = [n_observations,]</p>
<blockquote class="last">
<div><p>Squared Mahalanobis distances of the observations.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.OAS.score">
<code class="descname">score</code><span class="sig-paren">(</span><em>X_test</em>, <em>y=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/empirical_covariance_.py#L184"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.OAS.score" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the log-likelihood of a Gaussian data set with
<cite>self.covariance_</cite> as an estimator of its covariance matrix.</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_test</strong> : array-like, shape = [n_samples, n_features]</p>
<blockquote>
<div><p>Test data of which we compute the likelihood, where n_samples is
the number of samples and n_features is the number of features.
X_test is assumed to be drawn from the same distribution than
the data used in fit (including centering).</p>
</div></blockquote>
<p><strong>y</strong> : not used, present for API consistence purpose.</p>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>res</strong> : float</p>
<blockquote class="last">
<div><p>The likelihood of the data set with <cite>self.covariance_</cite> as an
estimator of its covariance matrix.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.OAS.set_params">
<code class="descname">set_params</code><span class="sig-paren">(</span><em>**params</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/base.py#L236"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.OAS.set_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Set the parameters of this estimator.</p>
<p>The method works on simple estimators as well as on nested objects
(such as pipelines). The former have parameters of the form
<code class="docutils literal"><span class="pre"><component>__<parameter></span></code> so that it’s possible to update each
component of a nested object.</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">Returns:</th><td class="field-body"><strong>self</strong> :</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<div class="section" id="examples-using-sklearn-covariance-oas">
<h2>Examples using <code class="docutils literal"><span class="pre">sklearn.covariance.OAS</span></code><a class="headerlink" href="#examples-using-sklearn-covariance-oas" title="Permalink to this headline">¶</a></h2>
<div class="thumbnailContainer" tooltip="The usual covariance maximum likelihood estimate can be regularized using shrinkage. Ledoit and..."><div class="figure" id="id1">
<a class="reference external image-reference" href="./../../auto_examples/covariance/plot_lw_vs_oas.html"><img alt="../../_images/plot_lw_vs_oas1.png" src="../../_images/plot_lw_vs_oas1.png" /></a>
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/covariance/plot_lw_vs_oas.html#example-covariance-plot-lw-vs-oas-py"><span>Ledoit-Wolf vs OAS estimation</span></a></span></p>
</div>
</div><div class="thumbnailContainer" tooltip="When working with covariance estimation, the usual approach is to use a maximum likelihood esti..."><div class="figure" id="id2">
<a class="reference external image-reference" href="./../../auto_examples/covariance/plot_covariance_estimation.html"><img alt="../../_images/plot_covariance_estimation1.png" src="../../_images/plot_covariance_estimation1.png" /></a>
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/covariance/plot_covariance_estimation.html#example-covariance-plot-covariance-estimation-py"><span>Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood</span></a></span></p>
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