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<ul>
<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.covariance</span></code>.GraphicalLassoCV</a><ul>
<li><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV"><code class="docutils literal notranslate"><span class="pre">GraphicalLassoCV</span></code></a><ul>
<li><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.error_norm"><code class="docutils literal notranslate"><span class="pre">GraphicalLassoCV.error_norm</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.fit"><code class="docutils literal notranslate"><span class="pre">GraphicalLassoCV.fit</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.get_metadata_routing"><code class="docutils literal notranslate"><span class="pre">GraphicalLassoCV.get_metadata_routing</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.get_params"><code class="docutils literal notranslate"><span class="pre">GraphicalLassoCV.get_params</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.get_precision"><code class="docutils literal notranslate"><span class="pre">GraphicalLassoCV.get_precision</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.mahalanobis"><code class="docutils literal notranslate"><span class="pre">GraphicalLassoCV.mahalanobis</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.score"><code class="docutils literal notranslate"><span class="pre">GraphicalLassoCV.score</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.set_params"><code class="docutils literal notranslate"><span class="pre">GraphicalLassoCV.set_params</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.set_score_request"><code class="docutils literal notranslate"><span class="pre">GraphicalLassoCV.set_score_request</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#examples-using-sklearn-covariance-graphicallassocv">Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.covariance.GraphicalLassoCV</span></code></a></li>
</ul>
</li>
</ul>
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<section id="sklearn-covariance-graphicallassocv">
<h1><a class="reference internal" href="../classes.html#module-sklearn.covariance" title="sklearn.covariance"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.covariance</span></code></a>.GraphicalLassoCV<a class="headerlink" href="#sklearn-covariance-graphicallassocv" title="Permalink to this heading">¶</a></h1>
<dl class="py class">
<dt class="sig sig-object py" id="sklearn.covariance.GraphicalLassoCV">
<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">GraphicalLassoCV</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">alphas</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">4</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_refinements</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">4</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cv</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0001</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enet_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0001</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_iter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'cd'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_jobs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">verbose</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">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2.220446049250313e-16</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><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/702316c27/sklearn/covariance/_graph_lasso.py#L708"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.GraphicalLassoCV" title="Permalink to this definition">¶</a></dt>
<dd><p>Sparse inverse covariance w/ cross-validated choice of the l1 penalty.</p>
<p>See glossary entry for <a class="reference internal" href="../../glossary.html#term-cross-validation-estimator"><span class="xref std std-term">cross-validation estimator</span></a>.</p>
<p>Read more in the <a class="reference internal" href="../covariance.html#sparse-inverse-covariance"><span class="std std-ref">User Guide</span></a>.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version v0.20: </span>GraphLassoCV has been renamed to GraphicalLassoCV</p>
</div>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl>
<dt><strong>alphas</strong><span class="classifier">int or array-like of shape (n_alphas,), dtype=float, default=4</span></dt><dd><p>If an integer is given, it fixes the number of points on the
grids of alpha to be used. If a list is given, it gives the
grid to be used. See the notes in the class docstring for
more details. Range is [1, inf) for an integer.
Range is (0, inf] for an array-like of floats.</p>
</dd>
<dt><strong>n_refinements</strong><span class="classifier">int, default=4</span></dt><dd><p>The number of times the grid is refined. Not used if explicit
values of alphas are passed. Range is [1, inf).</p>
</dd>
<dt><strong>cv</strong><span class="classifier">int, cross-validation generator or iterable, default=None</span></dt><dd><p>Determines the cross-validation splitting strategy.
Possible inputs for cv are:</p>
<ul class="simple">
<li><p>None, to use the default 5-fold cross-validation,</p></li>
<li><p>integer, to specify the number of folds.</p></li>
<li><p><a class="reference internal" href="../../glossary.html#term-CV-splitter"><span class="xref std std-term">CV splitter</span></a>,</p></li>
<li><p>An iterable yielding (train, test) splits as arrays of indices.</p></li>
</ul>
<p>For integer/None inputs <a class="reference internal" href="sklearn.model_selection.KFold.html#sklearn.model_selection.KFold" title="sklearn.model_selection.KFold"><code class="xref py py-class docutils literal notranslate"><span class="pre">KFold</span></code></a> is used.</p>
<p>Refer <a class="reference internal" href="../cross_validation.html#cross-validation"><span class="std std-ref">User Guide</span></a> for the various
cross-validation strategies that can be used here.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 0.20: </span><code class="docutils literal notranslate"><span class="pre">cv</span></code> default value if None changed from 3-fold to 5-fold.</p>
</div>
</dd>
<dt><strong>tol</strong><span class="classifier">float, default=1e-4</span></dt><dd><p>The tolerance to declare convergence: if the dual gap goes below
this value, iterations are stopped. Range is (0, inf].</p>
</dd>
<dt><strong>enet_tol</strong><span class="classifier">float, default=1e-4</span></dt><dd><p>The tolerance for the elastic net solver used to calculate the descent
direction. This parameter controls the accuracy of the search direction
for a given column update, not of the overall parameter estimate. Only
used for mode=’cd’. Range is (0, inf].</p>
</dd>
<dt><strong>max_iter</strong><span class="classifier">int, default=100</span></dt><dd><p>Maximum number of iterations.</p>
</dd>
<dt><strong>mode</strong><span class="classifier">{‘cd’, ‘lars’}, default=’cd’</span></dt><dd><p>The Lasso solver to use: coordinate descent or LARS. Use LARS for
very sparse underlying graphs, where number of features is greater
than number of samples. Elsewhere prefer cd which is more numerically
stable.</p>
</dd>
<dt><strong>n_jobs</strong><span class="classifier">int, default=None</span></dt><dd><p>Number of jobs to run in parallel.
<code class="docutils literal notranslate"><span class="pre">None</span></code> means 1 unless in a <a class="reference external" href="https://joblib.readthedocs.io/en/latest/generated/joblib.parallel_backend.html#joblib.parallel_backend" title="(in joblib v1.3.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">joblib.parallel_backend</span></code></a> context.
<code class="docutils literal notranslate"><span class="pre">-1</span></code> means using all processors. See <a class="reference internal" href="../../glossary.html#term-n_jobs"><span class="xref std std-term">Glossary</span></a>
for more details.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version v0.20: </span><code class="docutils literal notranslate"><span class="pre">n_jobs</span></code> default changed from 1 to None</p>
</div>
</dd>
<dt><strong>verbose</strong><span class="classifier">bool, default=False</span></dt><dd><p>If verbose is True, the objective function and duality gap are
printed at each iteration.</p>
</dd>
<dt><strong>eps</strong><span class="classifier">float, default=eps</span></dt><dd><p>The machine-precision regularization in the computation of the
Cholesky diagonal factors. Increase this for very ill-conditioned
systems. Default is <code class="docutils literal notranslate"><span class="pre">np.finfo(np.float64).eps</span></code>.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.3.</span></p>
</div>
</dd>
<dt><strong>assume_centered</strong><span class="classifier">bool, default=False</span></dt><dd><p>If True, data are not centered before computation.
Useful when working with data whose mean is almost, but not exactly
zero.
If False, data are centered before computation.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Attributes<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<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>covariance_</strong><span class="classifier">ndarray of shape (n_features, n_features)</span></dt><dd><p>Estimated covariance matrix.</p>
</dd>
<dt><strong>precision_</strong><span class="classifier">ndarray of shape (n_features, n_features)</span></dt><dd><p>Estimated precision matrix (inverse covariance).</p>
</dd>
<dt><strong>costs_</strong><span class="classifier">list of (objective, dual_gap) pairs</span></dt><dd><p>The list of values of the objective function and the dual gap at
each iteration. Returned only if return_costs is True.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.3.</span></p>
</div>
</dd>
<dt><strong>alpha_</strong><span class="classifier">float</span></dt><dd><p>Penalization parameter selected.</p>
</dd>
<dt><strong>cv_results_</strong><span class="classifier">dict of ndarrays</span></dt><dd><p>A dict with keys:</p>
<dl>
<dt>alphas<span class="classifier">ndarray of shape (n_alphas,)</span></dt><dd><p>All penalization parameters explored.</p>
</dd>
<dt>split(k)_test_score<span class="classifier">ndarray of shape (n_alphas,)</span></dt><dd><p>Log-likelihood score on left-out data across (k)th fold.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.0.</span></p>
</div>
</dd>
<dt>mean_test_score<span class="classifier">ndarray of shape (n_alphas,)</span></dt><dd><p>Mean of scores over the folds.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.0.</span></p>
</div>
</dd>
<dt>std_test_score<span class="classifier">ndarray of shape (n_alphas,)</span></dt><dd><p>Standard deviation of scores over the folds.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.0.</span></p>
</div>
</dd>
</dl>
</dd>
<dt><strong>n_iter_</strong><span class="classifier">int</span></dt><dd><p>Number of iterations run for the optimal alpha.</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">New 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">New 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.graphical_lasso.html#sklearn.covariance.graphical_lasso" title="sklearn.covariance.graphical_lasso"><code class="xref py py-obj docutils literal notranslate"><span class="pre">graphical_lasso</span></code></a></dt><dd><p>L1-penalized 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>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The search for the optimal penalization parameter (<code class="docutils literal notranslate"><span class="pre">alpha</span></code>) is done on an
iteratively refined grid: first the cross-validated scores on a grid are
computed, then a new refined grid is centered around the maximum, and so
on.</p>
<p>One of the challenges which is faced here is that the solvers can
fail to converge to a well-conditioned estimate. The corresponding
values of <code class="docutils literal notranslate"><span class="pre">alpha</span></code> then come out as missing values, but the optimum may
be close to these missing values.</p>
<p>In <code class="docutils literal notranslate"><span class="pre">fit</span></code>, once the best parameter <code class="docutils literal notranslate"><span class="pre">alpha</span></code> is found through
cross-validation, the model is fit again using the entire training set.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.covariance</span> <span class="kn">import</span> <span class="n">GraphicalLassoCV</span>
<span class="gp">>>> </span><span class="n">true_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">0.8</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">X</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">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="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">true_cov</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">size</span><span class="o">=</span><span class="mi">200</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">cov</span> <span class="o">=</span> <span class="n">GraphicalLassoCV</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">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">around</span><span class="p">(</span><span class="n">cov</span><span class="o">.</span><span class="n">covariance_</span><span class="p">,</span> <span class="n">decimals</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="go">array([[0.816, 0.051, 0.22 , 0.017],</span>
<span class="go"> [0.051, 0.364, 0.018, 0.036],</span>
<span class="go"> [0.22 , 0.018, 0.322, 0.094],</span>
<span class="go"> [0.017, 0.036, 0.094, 0.69 ]])</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">around</span><span class="p">(</span><span class="n">cov</span><span class="o">.</span><span class="n">location_</span><span class="p">,</span> <span class="n">decimals</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="go">array([0.073, 0.04 , 0.038, 0.143])</span>
</pre></div>
</div>
<p class="rubric">Methods</p>
<table class="autosummary longtable docutils align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.error_norm" title="sklearn.covariance.GraphicalLassoCV.error_norm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">error_norm</span></code></a>(comp_cov[, norm, scaling, squared])</p></td>
<td><p>Compute the Mean Squared Error between two covariance estimators.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.fit" title="sklearn.covariance.GraphicalLassoCV.fit"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code></a>(X[, y])</p></td>
<td><p>Fit the GraphicalLasso covariance model to X.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.get_metadata_routing" title="sklearn.covariance.GraphicalLassoCV.get_metadata_routing"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_metadata_routing</span></code></a>()</p></td>
<td><p>Get metadata routing of this object.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.get_params" title="sklearn.covariance.GraphicalLassoCV.get_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code></a>([deep])</p></td>
<td><p>Get parameters for this estimator.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.get_precision" title="sklearn.covariance.GraphicalLassoCV.get_precision"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_precision</span></code></a>()</p></td>
<td><p>Getter for the precision matrix.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.mahalanobis" title="sklearn.covariance.GraphicalLassoCV.mahalanobis"><code class="xref py py-obj docutils literal notranslate"><span class="pre">mahalanobis</span></code></a>(X)</p></td>
<td><p>Compute the squared Mahalanobis distances of given observations.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.score" title="sklearn.covariance.GraphicalLassoCV.score"><code class="xref py py-obj docutils literal notranslate"><span class="pre">score</span></code></a>(X_test[, y])</p></td>
<td><p>Compute the log-likelihood of <code class="docutils literal notranslate"><span class="pre">X_test</span></code> under the estimated Gaussian model.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.set_params" title="sklearn.covariance.GraphicalLassoCV.set_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code></a>(**params)</p></td>
<td><p>Set the parameters of this estimator.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV.set_score_request" title="sklearn.covariance.GraphicalLassoCV.set_score_request"><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_score_request</span></code></a>(*[, X_test])</p></td>
<td><p>Request metadata passed to the <code class="docutils literal notranslate"><span class="pre">score</span></code> method.</p></td>
</tr>
</tbody>
</table>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.GraphicalLassoCV.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/702316c27/sklearn/covariance/_empirical_covariance.py#L289"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.GraphicalLassoCV.error_norm" title="Permalink 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.GraphicalLassoCV.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/702316c27/sklearn/covariance/_graph_lasso.py#L928"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.GraphicalLassoCV.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit the GraphicalLasso 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>Data from which to compute the covariance estimate.</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.GraphicalLassoCV.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/702316c27/sklearn/utils/_metadata_requests.py#L1287"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.GraphicalLassoCV.get_metadata_routing" title="Permalink 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.GraphicalLassoCV.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/702316c27/sklearn/base.py#L178"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.GraphicalLassoCV.get_params" title="Permalink 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.GraphicalLassoCV.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/702316c27/sklearn/covariance/_empirical_covariance.py#L216"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.GraphicalLassoCV.get_precision" title="Permalink 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.GraphicalLassoCV.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/702316c27/sklearn/covariance/_empirical_covariance.py#L340"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.GraphicalLassoCV.mahalanobis" title="Permalink 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.GraphicalLassoCV.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/702316c27/sklearn/covariance/_empirical_covariance.py#L258"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.GraphicalLassoCV.score" title="Permalink 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.GraphicalLassoCV.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/702316c27/sklearn/base.py#L202"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.GraphicalLassoCV.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 <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"><component>__<parameter></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>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.GraphicalLassoCV.set_score_request">
<span class="sig-name descname"><span class="pre">set_score_request</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">X_test</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><span class="pre">Union</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><span class="pre">bool</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><span class="pre">None</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><span class="pre">str</span></a><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'$UNCHANGED$'</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><a class="reference internal" href="#sklearn.covariance.GraphicalLassoCV" title="sklearn.covariance._graph_lasso.GraphicalLassoCV"><span class="pre">GraphicalLassoCV</span></a></span></span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/702316c27/sklearn/utils/_metadata_requests.py#L1077"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.GraphicalLassoCV.set_score_request" title="Permalink to this definition">¶</a></dt>
<dd><p>Request metadata passed to the <code class="docutils literal notranslate"><span class="pre">score</span></code> method.</p>
<p>Note that this method is only relevant if
<code class="docutils literal notranslate"><span class="pre">enable_metadata_routing=True</span></code> (see <a class="reference internal" href="sklearn.set_config.html#sklearn.set_config" title="sklearn.set_config"><code class="xref py py-func docutils literal notranslate"><span class="pre">sklearn.set_config</span></code></a>).
Please see <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>
<p>The options for each parameter are:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">True</span></code>: metadata is requested, and passed to <code class="docutils literal notranslate"><span class="pre">score</span></code> if provided. The request is ignored if metadata is not provided.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">False</span></code>: metadata is not requested and the meta-estimator will not pass it to <code class="docutils literal notranslate"><span class="pre">score</span></code>.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">None</span></code>: metadata is not requested, and the meta-estimator will raise an error if the user provides it.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">str</span></code>: metadata should be passed to the meta-estimator with this given alias instead of the original name.</p></li>
</ul>
<p>The default (<code class="docutils literal notranslate"><span class="pre">sklearn.utils.metadata_routing.UNCHANGED</span></code>) retains the
existing request. This allows you to change the request for some
parameters and not others.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.3.</span></p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This method is only relevant if this estimator is used as a
sub-estimator of a meta-estimator, e.g. used inside a
<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>. Otherwise it has no effect.</p>
</div>
<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">str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED</span></dt><dd><p>Metadata routing for <code class="docutils literal notranslate"><span class="pre">X_test</span></code> parameter in <code class="docutils literal notranslate"><span class="pre">score</span></code>.</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>The updated object.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
</dd></dl>
<section id="examples-using-sklearn-covariance-graphicallassocv">
<h2>Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.covariance.GraphicalLassoCV</span></code><a class="headerlink" href="#examples-using-sklearn-covariance-graphicallassocv" title="Permalink 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 numb..."><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 class="sphx-glr-thumbcontainer" tooltip="This example employs several unsupervised learning techniques to extract the stock market struc..."><img alt="" src="../../_images/sphx_glr_plot_stock_market_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/applications/plot_stock_market.html#sphx-glr-auto-examples-applications-plot-stock-market-py"><span class="std std-ref">Visualizing the stock market structure</span></a></p>
<div class="sphx-glr-thumbnail-title">Visualizing the stock market structure</div>
</div></div><div class="clearer"></div></section>
</section>
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