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  <section id="shrunkcovariance">
<h1>ShrunkCovariance<a class="headerlink" href="#shrunkcovariance" title="Link to this heading">#</a></h1>
<dl class="py class">
<dt class="sig sig-object py" id="sklearn.covariance.ShrunkCovariance">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">sklearn.covariance.</span></span><span class="sig-name descname"><span class="pre">ShrunkCovariance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">store_precision</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</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">shrinkage</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.1</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/b54e4deea/sklearn/covariance/_shrunk_covariance.py#L159"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.ShrunkCovariance" title="Link to this definition">#</a></dt>
<dd><p>Covariance estimator with shrinkage.</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">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>store_precision</strong><span class="classifier">bool, default=True</span></dt><dd><p>Specify if the estimated precision is stored.</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 when working with data whose mean is almost, but not exactly
zero.
If False, data will be centered before computation.</p>
</dd>
<dt><strong>shrinkage</strong><span class="classifier">float, default=0.1</span></dt><dd><p>Coefficient in the convex combination used for the computation
of the shrunk estimate. Range is [0, 1].</p>
</dd>
</dl>
</dd>
<dt class="field-even">Attributes<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt><strong>covariance_</strong><span class="classifier">ndarray of shape (n_features, n_features)</span></dt><dd><p>Estimated covariance matrix</p>
</dd>
<dt><strong>location_</strong><span class="classifier">ndarray of shape (n_features,)</span></dt><dd><p>Estimated location, i.e. the estimated mean.</p>
</dd>
<dt><strong>precision_</strong><span class="classifier">ndarray of shape (n_features, n_features)</span></dt><dd><p>Estimated pseudo inverse matrix.
(stored only if store_precision is True)</p>
</dd>
<dt><strong>n_features_in_</strong><span class="classifier">int</span></dt><dd><p>Number of features seen during <a class="reference internal" href="../../glossary.html#term-fit"><span class="xref std std-term">fit</span></a>.</p>
<div class="versionadded">
<p><span class="versionmodified added">Added in version 0.24.</span></p>
</div>
</dd>
<dt><strong>feature_names_in_</strong><span class="classifier">ndarray of shape (<code class="docutils literal notranslate"><span class="pre">n_features_in_</span></code>,)</span></dt><dd><p>Names of features seen during <a class="reference internal" href="../../glossary.html#term-fit"><span class="xref std std-term">fit</span></a>. Defined only when <code class="docutils literal notranslate"><span class="pre">X</span></code>
has feature names that are all strings.</p>
<div class="versionadded">
<p><span class="versionmodified added">Added in version 1.0.</span></p>
</div>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="sklearn.covariance.EllipticEnvelope.html#sklearn.covariance.EllipticEnvelope" title="sklearn.covariance.EllipticEnvelope"><code class="xref py py-obj docutils literal notranslate"><span class="pre">EllipticEnvelope</span></code></a></dt><dd><p>An object for detecting outliers in a Gaussian distributed dataset.</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.EmpiricalCovariance.html#sklearn.covariance.EmpiricalCovariance" title="sklearn.covariance.EmpiricalCovariance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">EmpiricalCovariance</span></code></a></dt><dd><p>Maximum likelihood covariance estimator.</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.GraphicalLasso.html#sklearn.covariance.GraphicalLasso" title="sklearn.covariance.GraphicalLasso"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GraphicalLasso</span></code></a></dt><dd><p>Sparse inverse covariance estimation with an l1-penalized estimator.</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.GraphicalLassoCV.html#sklearn.covariance.GraphicalLassoCV" title="sklearn.covariance.GraphicalLassoCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GraphicalLassoCV</span></code></a></dt><dd><p>Sparse inverse covariance with cross-validated choice of the l1 penalty.</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.LedoitWolf.html#sklearn.covariance.LedoitWolf" title="sklearn.covariance.LedoitWolf"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LedoitWolf</span></code></a></dt><dd><p>LedoitWolf Estimator.</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.MinCovDet.html#sklearn.covariance.MinCovDet" title="sklearn.covariance.MinCovDet"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MinCovDet</span></code></a></dt><dd><p>Minimum Covariance Determinant (robust estimator of covariance).</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.OAS.html#sklearn.covariance.OAS" title="sklearn.covariance.OAS"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OAS</span></code></a></dt><dd><p>Oracle Approximating Shrinkage Estimator.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The regularized covariance is given by:</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">ShrunkCovariance</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.datasets</span><span class="w"> </span><span class="kn">import</span> <span class="n">make_gaussian_quantiles</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">.8</span><span class="p">,</span> <span class="mf">.3</span><span class="p">],</span>
<span class="gp">... </span>                     <span class="p">[</span><span class="mf">.3</span><span class="p">,</span> <span class="mf">.4</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="gp">... </span>                                  <span class="n">cov</span><span class="o">=</span><span class="n">real_cov</span><span class="p">,</span>
<span class="gp">... </span>                                  <span class="n">size</span><span class="o">=</span><span class="mi">500</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">cov</span> <span class="o">=</span> <span class="n">ShrunkCovariance</span><span class="p">()</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="gp">&gt;&gt;&gt; </span><span class="n">cov</span><span class="o">.</span><span class="n">covariance_</span>
<span class="go">array([[0.7387..., 0.2536...],</span>
<span class="go">       [0.2536..., 0.4110...]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">cov</span><span class="o">.</span><span class="n">location_</span>
<span class="go">array([0.0622..., 0.0193...])</span>
</pre></div>
</div>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.ShrunkCovariance.error_norm">
<span class="sig-name descname"><span class="pre">error_norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">comp_cov</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'frobenius'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">scaling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">squared</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/b54e4deea/sklearn/covariance/_empirical_covariance.py#L292"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.ShrunkCovariance.error_norm" title="Link to this definition">#</a></dt>
<dd><p>Compute the Mean Squared Error between two covariance estimators.</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>comp_cov</strong><span class="classifier">array-like of shape (n_features, n_features)</span></dt><dd><p>The covariance to compare with.</p>
</dd>
<dt><strong>norm</strong><span class="classifier">{“frobenius”, “spectral”}, default=”frobenius”</span></dt><dd><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 notranslate"><span class="pre">(comp_cov</span> <span class="pre">-</span> <span class="pre">self.covariance_)</span></code>.</p>
</dd>
<dt><strong>scaling</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True (default), the squared error norm is divided by n_features.
If False, the squared error norm is not rescaled.</p>
</dd>
<dt><strong>squared</strong><span class="classifier">bool, default=True</span></dt><dd><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>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>result</strong><span class="classifier">float</span></dt><dd><p>The Mean Squared Error (in the sense of the Frobenius norm) between
<code class="docutils literal notranslate"><span class="pre">self</span></code> and <code class="docutils literal notranslate"><span class="pre">comp_cov</span></code> covariance estimators.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.ShrunkCovariance.fit">
<span class="sig-name descname"><span class="pre">fit</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="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/b54e4deea/sklearn/covariance/_shrunk_covariance.py#L254"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.ShrunkCovariance.fit" title="Link to this definition">#</a></dt>
<dd><p>Fit the shrunk covariance model to X.</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>Training data, where <code class="docutils literal notranslate"><span class="pre">n_samples</span></code> is the number of samples
and <code class="docutils literal notranslate"><span class="pre">n_features</span></code> is the number of features.</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd><p>Not used, present for API consistency by convention.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">object</span></dt><dd><p>Returns the instance itself.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.ShrunkCovariance.get_metadata_routing">
<span class="sig-name descname"><span class="pre">get_metadata_routing</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/b54e4deea/sklearn/utils/_metadata_requests.py#L1500"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.ShrunkCovariance.get_metadata_routing" title="Link to this definition">#</a></dt>
<dd><p>Get metadata routing of this object.</p>
<p>Please check <a class="reference internal" href="../../metadata_routing.html#metadata-routing"><span class="std std-ref">User Guide</span></a> on how the routing
mechanism works.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>routing</strong><span class="classifier">MetadataRequest</span></dt><dd><p>A <a class="reference internal" href="sklearn.utils.metadata_routing.MetadataRequest.html#sklearn.utils.metadata_routing.MetadataRequest" title="sklearn.utils.metadata_routing.MetadataRequest"><code class="xref py py-class docutils literal notranslate"><span class="pre">MetadataRequest</span></code></a> encapsulating
routing information.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.ShrunkCovariance.get_params">
<span class="sig-name descname"><span class="pre">get_params</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">deep</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/b54e4deea/sklearn/base.py#L231"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.ShrunkCovariance.get_params" title="Link to this definition">#</a></dt>
<dd><p>Get parameters for this 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>deep</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>params</strong><span class="classifier">dict</span></dt><dd><p>Parameter names mapped to their values.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.ShrunkCovariance.get_precision">
<span class="sig-name descname"><span class="pre">get_precision</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/b54e4deea/sklearn/covariance/_empirical_covariance.py#L219"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.ShrunkCovariance.get_precision" title="Link to this definition">#</a></dt>
<dd><p>Getter for the precision matrix.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>precision_</strong><span class="classifier">array-like of shape (n_features, n_features)</span></dt><dd><p>The precision matrix associated to the current covariance object.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.ShrunkCovariance.mahalanobis">
<span class="sig-name descname"><span class="pre">mahalanobis</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/b54e4deea/sklearn/covariance/_empirical_covariance.py#L343"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.ShrunkCovariance.mahalanobis" title="Link to this definition">#</a></dt>
<dd><p>Compute the squared Mahalanobis distances of given observations.</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>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>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>dist</strong><span class="classifier">ndarray of shape (n_samples,)</span></dt><dd><p>Squared Mahalanobis distances of the observations.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.ShrunkCovariance.score">
<span class="sig-name descname"><span class="pre">score</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X_test</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/b54e4deea/sklearn/covariance/_empirical_covariance.py#L261"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.ShrunkCovariance.score" title="Link to this definition">#</a></dt>
<dd><p>Compute the log-likelihood of <code class="docutils literal notranslate"><span class="pre">X_test</span></code> under the estimated Gaussian model.</p>
<p>The Gaussian model is defined by its mean and covariance matrix which are
represented respectively by <code class="docutils literal notranslate"><span class="pre">self.location_</span></code> and <code class="docutils literal notranslate"><span class="pre">self.covariance_</span></code>.</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_test</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><p>Test data of which we compute the likelihood, where <code class="docutils literal notranslate"><span class="pre">n_samples</span></code> is
the number of samples and <code class="docutils literal notranslate"><span class="pre">n_features</span></code> is the number of features.
<code class="docutils literal notranslate"><span class="pre">X_test</span></code> is assumed to be drawn from the same distribution than
the data used in fit (including centering).</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd><p>Not used, present for API consistency by convention.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>res</strong><span class="classifier">float</span></dt><dd><p>The log-likelihood of <code class="docutils literal notranslate"><span class="pre">X_test</span></code> with <code class="docutils literal notranslate"><span class="pre">self.location_</span></code> and <code class="docutils literal notranslate"><span class="pre">self.covariance_</span></code>
as estimators of the Gaussian model mean and covariance matrix respectively.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.ShrunkCovariance.set_params">
<span class="sig-name descname"><span class="pre">set_params</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">params</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/b54e4deea/sklearn/base.py#L255"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.ShrunkCovariance.set_params" title="Link 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 <a class="reference internal" href="sklearn.pipeline.Pipeline.html#sklearn.pipeline.Pipeline" title="sklearn.pipeline.Pipeline"><code class="xref py py-class docutils literal notranslate"><span class="pre">Pipeline</span></code></a>). The latter have
parameters of the form <code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s
possible to update each component of a nested object.</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>**params</strong><span class="classifier">dict</span></dt><dd><p>Estimator parameters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">estimator instance</span></dt><dd><p>Estimator instance.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

</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 class="sphx-glr-thumbcontainer" tooltip="Probabilistic PCA and Factor Analysis are probabilistic models. The consequence is that the likelihood of new data can be used for model selection and covariance estimation. Here we compare PCA and FA with cross-validation on low rank data corrupted with homoscedastic noise (noise variance is the same for each feature) or heteroscedastic noise (noise variance is the different for each feature). In a second step we compare the model likelihood to the likelihoods obtained from shrinkage covariance estimators."><img alt="" src="../../_images/sphx_glr_plot_pca_vs_fa_model_selection_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/decomposition/plot_pca_vs_fa_model_selection.html#sphx-glr-auto-examples-decomposition-plot-pca-vs-fa-model-selection-py"><span class="std std-ref">Model selection with Probabilistic PCA and Factor Analysis (FA)</span></a></p>
  <div class="sphx-glr-thumbnail-title">Model selection with Probabilistic PCA and Factor Analysis (FA)</div>
</div></div></section>
</section>


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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.covariance.ShrunkCovariance"><code class="docutils literal notranslate"><span class="pre">ShrunkCovariance</span></code></a><ul class="nav section-nav flex-column visible">
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.covariance.ShrunkCovariance.error_norm"><code class="docutils literal notranslate"><span class="pre">error_norm</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.covariance.ShrunkCovariance.fit"><code class="docutils literal notranslate"><span class="pre">fit</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.covariance.ShrunkCovariance.get_metadata_routing"><code class="docutils literal notranslate"><span class="pre">get_metadata_routing</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.covariance.ShrunkCovariance.get_params"><code class="docutils literal notranslate"><span class="pre">get_params</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.covariance.ShrunkCovariance.get_precision"><code class="docutils literal notranslate"><span class="pre">get_precision</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.covariance.ShrunkCovariance.mahalanobis"><code class="docutils literal notranslate"><span class="pre">mahalanobis</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.covariance.ShrunkCovariance.score"><code class="docutils literal notranslate"><span class="pre">score</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.covariance.ShrunkCovariance.set_params"><code class="docutils literal notranslate"><span class="pre">set_params</span></code></a></li>
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