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<ul>
<li><a class="reference internal" href="#"><code class="docutils literal"><span class="pre">sklearn.covariance</span></code>.LedoitWolf</a><ul>
<li><a class="reference internal" href="#examples-using-sklearn-covariance-ledoitwolf">Examples using <code class="docutils literal"><span class="pre">sklearn.covariance.LedoitWolf</span></code></a></li>
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<div class="section" id="sklearn-covariance-ledoitwolf">
<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>.LedoitWolf<a class="headerlink" href="#sklearn-covariance-ledoitwolf" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="sklearn.covariance.LedoitWolf">
<em class="property">class </em><code class="descclassname">sklearn.covariance.</code><code class="descname">LedoitWolf</code><span class="sig-paren">(</span><em>store_precision=True</em>, <em>assume_centered=False</em>, <em>block_size=1000</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/2d7cd0c/sklearn/covariance/shrunk_covariance_.py#L307"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf" title="Permalink to this definition">¶</a></dt>
<dd><p>LedoitWolf Estimator</p>
<p>Ledoit-Wolf is a particular form of shrinkage, where the shrinkage
coefficient is computed using O. Ledoit and M. Wolf’s formula as
described in “A Well-Conditioned Estimator for Large-Dimensional
Covariance Matrices”, Ledoit and Wolf, Journal of Multivariate
Analysis, Volume 88, Issue 2, February 2004, pages 365-411.</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>
<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</strong> : bool, default=False</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>
<p><strong>block_size</strong> : int, default=1000</p>
<blockquote class="last">
<div><p>Size of the blocks into which the covariance matrix will be split
during its Ledoit-Wolf estimation. This is purely a memory
optimization and does not affect results.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Attributes</p>
<table border="1" class="docutils">
<colgroup>
<col width="11%" />
<col width="89%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><strong>covariance_</strong></td>
<td>(array-like, shape (n_features, n_features)) Estimated covariance matrix</td>
</tr>
<tr class="row-even"><td><strong>precision_</strong></td>
<td>(array-like, shape (n_features, n_features)) Estimated pseudo inverse matrix. (stored only if store_precision is True)</td>
</tr>
<tr class="row-odd"><td><strong>shrinkage_</strong></td>
<td>(float, 0 <= shrinkage <= 1) Coefficient in the convex combination used for the computation of the shrunk estimate.</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>The regularised covariance is:</p>
<p>(1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)</p>
<p>where mu = trace(cov) / n_features
and shrinkage is given by the Ledoit and Wolf formula (see References)</p>
<p class="rubric">References</p>
<p>“A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices”,
Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2,
February 2004, pages 365-411.</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.LedoitWolf.error_norm" title="sklearn.covariance.LedoitWolf.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.LedoitWolf.fit" title="sklearn.covariance.LedoitWolf.fit"><code class="xref py py-obj docutils literal"><span class="pre">fit</span></code></a>(X[, y])</td>
<td>Fits the Ledoit-Wolf shrunk covariance model according to the given training data and parameters.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.covariance.LedoitWolf.get_params" title="sklearn.covariance.LedoitWolf.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.LedoitWolf.get_precision" title="sklearn.covariance.LedoitWolf.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.LedoitWolf.mahalanobis" title="sklearn.covariance.LedoitWolf.mahalanobis"><code class="xref py py-obj docutils literal"><span class="pre">mahalanobis</span></code></a>(X)</td>
<td>Computes the squared Mahalanobis distances of given observations.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#sklearn.covariance.LedoitWolf.score" title="sklearn.covariance.LedoitWolf.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.LedoitWolf.set_params" title="sklearn.covariance.LedoitWolf.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.LedoitWolf.__init__">
<code class="descname">__init__</code><span class="sig-paren">(</span><em>store_precision=True</em>, <em>assume_centered=False</em>, <em>block_size=1000</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/2d7cd0c/sklearn/covariance/shrunk_covariance_.py#L363"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.__init__" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="sklearn.covariance.LedoitWolf.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/2d7cd0c/sklearn/covariance/empirical_covariance_.py#L215"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.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">The Mean Squared Error (in the sense of the Frobenius norm) between</p>
<p class="last"><cite>self</cite> and <cite>comp_cov</cite> covariance estimators.</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.LedoitWolf.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/2d7cd0c/sklearn/covariance/shrunk_covariance_.py#L369"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fits the Ledoit-Wolf shrunk 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></p>
<blockquote>
<div><p>not used, present for API consistence purpose.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last"><strong>self</strong> : object</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.LedoitWolf.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/2d7cd0c/sklearn/base.py#L213"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.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</strong> : boolean, optional</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.LedoitWolf.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/2d7cd0c/sklearn/covariance/empirical_covariance_.py#L141"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.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.LedoitWolf.mahalanobis">
<code class="descname">mahalanobis</code><span class="sig-paren">(</span><em>X</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/2d7cd0c/sklearn/covariance/empirical_covariance_.py#L267"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.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>X</strong> : array-like, shape = [n_samples, 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>dist</strong> : array, shape = [n_samples,]</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.LedoitWolf.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/2d7cd0c/sklearn/covariance/empirical_covariance_.py#L185"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.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></p>
<blockquote>
<div><p>not used, present for API consistence purpose.</p>
</div></blockquote>
</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.LedoitWolf.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/2d7cd0c/sklearn/base.py#L236"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.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 latter 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">self</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<div class="section" id="examples-using-sklearn-covariance-ledoitwolf">
<h2>Examples using <code class="docutils literal"><span class="pre">sklearn.covariance.LedoitWolf</span></code><a class="headerlink" href="#examples-using-sklearn-covariance-ledoitwolf" title="Permalink to this headline">¶</a></h2>
<div class="sphx-glr-thumbcontainer" tooltip="The usual covariance maximum likelihood estimate can be regularized using shrinkage. Ledoit and..."><div class="figure" id="id1">
<img alt="../../_images/sphx_glr_plot_lw_vs_oas_thumb.png" src="../../_images/sphx_glr_plot_lw_vs_oas_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/covariance/plot_lw_vs_oas.html#sphx-glr-auto-examples-covariance-plot-lw-vs-oas-py"><span class="std std-ref">Ledoit-Wolf vs OAS estimation</span></a></span></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="When working with covariance estimation, the usual approach is to use a maximum likelihood esti..."><div class="figure" id="id2">
<img alt="../../_images/sphx_glr_plot_covariance_estimation_thumb.png" src="../../_images/sphx_glr_plot_covariance_estimation_thumb.png" />
<p class="caption"><span class="caption-text"><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></span></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Probabilistic PCA and Factor Analysis are probabilistic models. The consequence is that the lik..."><div class="figure" id="id3">
<img alt="../../_images/sphx_glr_plot_pca_vs_fa_model_selection_thumb.png" src="../../_images/sphx_glr_plot_pca_vs_fa_model_selection_thumb.png" />
<p class="caption"><span class="caption-text"><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></span></p>
</div>
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