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<li><a class="reference internal" href="#"><code class="docutils literal"><span class="pre">sklearn.covariance</span></code>.graph_lasso</a></li>
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<div class="section" id="sklearn-covariance-graph-lasso">
<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>.graph_lasso<a class="headerlink" href="#sklearn-covariance-graph-lasso" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="sklearn.covariance.graph_lasso">
<code class="descclassname">sklearn.covariance.</code><code class="descname">graph_lasso</code><span class="sig-paren">(</span><em>emp_cov</em>, <em>alpha</em>, <em>cov_init=None</em>, <em>mode='cd'</em>, <em>tol=0.0001</em>, <em>enet_tol=0.0001</em>, <em>max_iter=100</em>, <em>verbose=False</em>, <em>return_costs=False</em>, <em>eps=2.2204460492503131e-16</em>, <em>return_n_iter=False</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/graph_lasso_.py#L81"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.graph_lasso" title="Permalink to this definition">¶</a></dt>
<dd><p>l1-penalized covariance estimator</p>
<p>Read more in the <a class="reference internal" href="../covariance.html#sparse-inverse-covariance"><span>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>emp_cov</strong> : 2D ndarray, shape (n_features, n_features)</p>
<blockquote>
<div><p>Empirical covariance from which to compute the covariance estimate.</p>
</div></blockquote>
<p><strong>alpha</strong> : positive float</p>
<blockquote>
<div><p>The regularization parameter: the higher alpha, the more
regularization, the sparser the inverse covariance.</p>
</div></blockquote>
<p><strong>cov_init</strong> : 2D array (n_features, n_features), optional</p>
<blockquote>
<div><p>The initial guess for the covariance.</p>
</div></blockquote>
<p><strong>mode</strong> : {‘cd’, ‘lars’}</p>
<blockquote>
<div><p>The Lasso solver to use: coordinate descent or LARS. Use LARS for
very sparse underlying graphs, where p > n. Elsewhere prefer cd
which is more numerically stable.</p>
</div></blockquote>
<p><strong>tol</strong> : positive float, optional</p>
<blockquote>
<div><p>The tolerance to declare convergence: if the dual gap goes below
this value, iterations are stopped.</p>
</div></blockquote>
<p><strong>enet_tol</strong> : positive float, optional</p>
<blockquote>
<div><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’.</p>
</div></blockquote>
<p><strong>max_iter</strong> : integer, optional</p>
<blockquote>
<div><p>The maximum number of iterations.</p>
</div></blockquote>
<p><strong>verbose</strong> : boolean, optional</p>
<blockquote>
<div><p>If verbose is True, the objective function and dual gap are
printed at each iteration.</p>
</div></blockquote>
<p><strong>return_costs</strong> : boolean, optional</p>
<blockquote>
<div><p>If return_costs is True, the objective function and dual gap
at each iteration are returned.</p>
</div></blockquote>
<p><strong>eps</strong> : float, optional</p>
<blockquote>
<div><p>The machine-precision regularization in the computation of the
Cholesky diagonal factors. Increase this for very ill-conditioned
systems.</p>
</div></blockquote>
<p><strong>return_n_iter</strong> : bool, optional</p>
<blockquote>
<div><p>Whether or not to return the number of iterations.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>covariance</strong> : 2D ndarray, shape (n_features, n_features)</p>
<blockquote>
<div><p>The estimated covariance matrix.</p>
</div></blockquote>
<p><strong>precision</strong> : 2D ndarray, shape (n_features, n_features)</p>
<blockquote>
<div><p>The estimated (sparse) precision matrix.</p>
</div></blockquote>
<p><strong>costs</strong> : list of (objective, dual_gap) pairs</p>
<blockquote>
<div><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></blockquote>
<p><strong>n_iter</strong> : int</p>
<blockquote class="last">
<div><p>Number of iterations. Returned only if <cite>return_n_iter</cite> is set to True.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><a class="reference internal" href="sklearn.covariance.GraphLasso.html#sklearn.covariance.GraphLasso" title="sklearn.covariance.GraphLasso"><code class="xref py py-obj docutils literal"><span class="pre">GraphLasso</span></code></a>, <a class="reference internal" href="sklearn.covariance.GraphLassoCV.html#sklearn.covariance.GraphLassoCV" title="sklearn.covariance.GraphLassoCV"><code class="xref py py-obj docutils literal"><span class="pre">GraphLassoCV</span></code></a></p>
</div>
<p class="rubric">Notes</p>
<p>The algorithm employed to solve this problem is the GLasso algorithm,
from the Friedman 2008 Biostatistics paper. It is the same algorithm
as in the R <cite>glasso</cite> package.</p>
<p>One possible difference with the <cite>glasso</cite> R package is that the
diagonal coefficients are not penalized.</p>
</dd></dl>
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