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<p>LKJ distribution for lower Cholesky factor of correlation matrices.
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The distribution is controlled by <codeclass="docutils literal notranslate"><spanclass="pre">concentration</span></code> parameter <spanclass="math"><spanclass="katex"><spanclass="katex-mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>η</mi></mrow><annotationencoding="application/x-tex">\eta</annotation></semantics></math></span><spanclass="katex-html" aria-hidden="true"><spanclass="base"><spanclass="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><spanclass="mord mathnormal" style="margin-right:0.03588em;">η</span></span></span></span>
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</span>
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to make the probability of the correlation matrix <spanclass="math"><spanclass="katex"><spanclass="katex-mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi></mrow><annotationencoding="application/x-tex">M</annotation></semantics></math></span><spanclass="katex-html" aria-hidden="true"><spanclass="base"><spanclass="strut" style="height:0.68333em;vertical-align:0em;"></span><spanclass="mord mathnormal" style="margin-right:0.10903em;">M</span></span></span></span>
when <codeclass="docutils literal notranslate"><spanclass="pre">concentration</span><spanclass="pre">==</span><spanclass="pre">1</span></code>, we have a uniform distribution over Cholesky
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factors of correlation matrices. Note that this distribution samples the
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Cholesky factor of correlation matrices and not the correlation matrices
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themselves and thereby differs slightly from the derivations in [1] for
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the <cite>LKJCorr</cite> distribution. For sampling, this uses the Onion method from
<spanclass="gp">>>> </span><spanclass="n">l</span><spanclass="o">.</span><spanclass="n">sample</span><spanclass="p">()</span><spanclass="c1"># l @ l.T is a sample of a correlation 3x3 matrix</span>
<codeclass="sig-name descname">arg_constraints</code><emclass="property"> = {'concentration': GreaterThan(lower_bound=0.0)}</em><aclass="headerlink" href="#torch.distributions.lkj_cholesky.LKJCholesky.arg_constraints" title="Permalink to this definition">¶</a></dt>
<codeclass="sig-name descname">expand</code><spanclass="sig-paren">(</span><emclass="sig-param">batch_shape</em>, <emclass="sig-param">_instance=None</em><spanclass="sig-paren">)</span><aclass="reference internal" href="_modules/torch/distributions/lkj_cholesky.html#LKJCholesky.expand"><spanclass="viewcode-link">[source]</span></a><aclass="headerlink" href="#torch.distributions.lkj_cholesky.LKJCholesky.expand" title="Permalink to this definition">¶</a></dt>
<codeclass="sig-name descname">log_prob</code><spanclass="sig-paren">(</span><emclass="sig-param">value</em><spanclass="sig-paren">)</span><aclass="reference internal" href="_modules/torch/distributions/lkj_cholesky.html#LKJCholesky.log_prob"><spanclass="viewcode-link">[source]</span></a><aclass="headerlink" href="#torch.distributions.lkj_cholesky.LKJCholesky.log_prob" title="Permalink to this definition">¶</a></dt>
<codeclass="sig-name descname">sample</code><spanclass="sig-paren">(</span><emclass="sig-param">sample_shape=torch.Size([])</em><spanclass="sig-paren">)</span><aclass="reference internal" href="_modules/torch/distributions/lkj_cholesky.html#LKJCholesky.sample"><spanclass="viewcode-link">[source]</span></a><aclass="headerlink" href="#torch.distributions.lkj_cholesky.LKJCholesky.sample" title="Permalink to this definition">¶</a></dt>
<codeclass="sig-name descname">support</code><emclass="property"> = CorrCholesky()</em><aclass="headerlink" href="#torch.distributions.lkj_cholesky.LKJCholesky.support" title="Permalink to this definition">¶</a></dt>
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<dd></dd></dl>
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</dd></dl>
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<divclass="section" id="laplace">
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<h2><spanclass="hidden-section">Laplace</span><aclass="headerlink" href="#laplace" title="Permalink to this headline">¶</a></h2>
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