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<!DOCTYPE html>
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POT Python Optimal Transport
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<li class="toctree-l1"><a class="reference internal" href="../index.html">POT: Python Optimal Transport</a></li>
<li class="toctree-l1"><a class="reference internal" href="../auto_examples/plot_quickstart_guide.html">Quickstart Guide</a></li>
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<li class="toctree-l1 current"><a class="reference internal" href="../all.html">API and modules</a><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="ot.backend.html">ot.backend</a></li>
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<li class="toctree-l2 current"><a class="current reference internal" href="#">ot.da</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#functions">Functions</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#ot.da.distribution_estimation_uniform"><code class="docutils literal notranslate"><span class="pre">distribution_estimation_uniform()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#ot.da.emd_laplace"><code class="docutils literal notranslate"><span class="pre">emd_laplace()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#ot.da.sinkhorn_l1l2_gl"><code class="docutils literal notranslate"><span class="pre">sinkhorn_l1l2_gl()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#ot.da.sinkhorn_lpl1_mm"><code class="docutils literal notranslate"><span class="pre">sinkhorn_lpl1_mm()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#classes">Classes</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#ot.da.BaseTransport"><code class="docutils literal notranslate"><span class="pre">BaseTransport</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-da-basetransport">Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.BaseTransport</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-da-emdlaplacetransport">Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.EMDLaplaceTransport</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-da-emdtransport">Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.EMDTransport</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-da-jcpottransport">Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.JCPOTTransport</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-da-lineargwtransport">Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.LinearGWTransport</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-da-lineartransport">Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.LinearTransport</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-da-mappingtransport">Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.MappingTransport</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-da-sinkhornl1l2transport">Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.SinkhornL1l2Transport</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-da-sinkhornlpl1transport">Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.SinkhornLpl1Transport</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-da-sinkhorntransport">Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.SinkhornTransport</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id0"><code class="docutils literal notranslate"><span class="pre">BaseTransport</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id38"><code class="docutils literal notranslate"><span class="pre">BaseTransport.fit()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id39"><code class="docutils literal notranslate"><span class="pre">BaseTransport.fit_transform()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id40"><code class="docutils literal notranslate"><span class="pre">BaseTransport.inverse_transform()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id41"><code class="docutils literal notranslate"><span class="pre">BaseTransport.inverse_transform_labels()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id42"><code class="docutils literal notranslate"><span class="pre">BaseTransport.transform()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id43"><code class="docutils literal notranslate"><span class="pre">BaseTransport.transform_labels()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id46"><code class="docutils literal notranslate"><span class="pre">EMDLaplaceTransport</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id47"><code class="docutils literal notranslate"><span class="pre">EMDLaplaceTransport.coupling_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id52"><code class="docutils literal notranslate"><span class="pre">EMDLaplaceTransport.fit()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id53"><code class="docutils literal notranslate"><span class="pre">EMDTransport</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id54"><code class="docutils literal notranslate"><span class="pre">EMDTransport.coupling_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id58"><code class="docutils literal notranslate"><span class="pre">EMDTransport.fit()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id59"><code class="docutils literal notranslate"><span class="pre">JCPOTTransport</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id60"><code class="docutils literal notranslate"><span class="pre">JCPOTTransport.coupling_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id61"><code class="docutils literal notranslate"><span class="pre">JCPOTTransport.proportions_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id62"><code class="docutils literal notranslate"><span class="pre">JCPOTTransport.log_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id66"><code class="docutils literal notranslate"><span class="pre">JCPOTTransport.fit()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id67"><code class="docutils literal notranslate"><span class="pre">JCPOTTransport.inverse_transform_labels()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id68"><code class="docutils literal notranslate"><span class="pre">JCPOTTransport.transform()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id69"><code class="docutils literal notranslate"><span class="pre">JCPOTTransport.transform_labels()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id72"><code class="docutils literal notranslate"><span class="pre">LinearGWTransport</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id75"><code class="docutils literal notranslate"><span class="pre">LinearGWTransport.fit()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id76"><code class="docutils literal notranslate"><span class="pre">LinearTransport</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id80"><code class="docutils literal notranslate"><span class="pre">LinearTransport.fit()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id81"><code class="docutils literal notranslate"><span class="pre">LinearTransport.inverse_transform()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id82"><code class="docutils literal notranslate"><span class="pre">LinearTransport.transform()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id83"><code class="docutils literal notranslate"><span class="pre">MappingTransport</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id84"><code class="docutils literal notranslate"><span class="pre">MappingTransport.coupling_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id85"><code class="docutils literal notranslate"><span class="pre">MappingTransport.mapping_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id86"><code class="docutils literal notranslate"><span class="pre">MappingTransport.log_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id88"><code class="docutils literal notranslate"><span class="pre">MappingTransport.fit()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id89"><code class="docutils literal notranslate"><span class="pre">MappingTransport.transform()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id90"><code class="docutils literal notranslate"><span class="pre">NearestBrenierPotential</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id93"><code class="docutils literal notranslate"><span class="pre">NearestBrenierPotential.fit()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id95"><code class="docutils literal notranslate"><span class="pre">NearestBrenierPotential.transform()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id98"><code class="docutils literal notranslate"><span class="pre">SinkhornL1l2Transport</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id99"><code class="docutils literal notranslate"><span class="pre">SinkhornL1l2Transport.coupling_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id100"><code class="docutils literal notranslate"><span class="pre">SinkhornL1l2Transport.log_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id105"><code class="docutils literal notranslate"><span class="pre">SinkhornL1l2Transport.fit()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id106"><code class="docutils literal notranslate"><span class="pre">SinkhornLpl1Transport</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id107"><code class="docutils literal notranslate"><span class="pre">SinkhornLpl1Transport.coupling_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id112"><code class="docutils literal notranslate"><span class="pre">SinkhornLpl1Transport.fit()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id113"><code class="docutils literal notranslate"><span class="pre">SinkhornTransport</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id114"><code class="docutils literal notranslate"><span class="pre">SinkhornTransport.coupling_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id115"><code class="docutils literal notranslate"><span class="pre">SinkhornTransport.log_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id122"><code class="docutils literal notranslate"><span class="pre">SinkhornTransport.fit()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id123"><code class="docutils literal notranslate"><span class="pre">SinkhornTransport.inverse_transform()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id124"><code class="docutils literal notranslate"><span class="pre">SinkhornTransport.transform()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id125"><code class="docutils literal notranslate"><span class="pre">UnbalancedSinkhornTransport</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id126"><code class="docutils literal notranslate"><span class="pre">UnbalancedSinkhornTransport.coupling_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id127"><code class="docutils literal notranslate"><span class="pre">UnbalancedSinkhornTransport.log_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id131"><code class="docutils literal notranslate"><span class="pre">UnbalancedSinkhornTransport.fit()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id132"><code class="docutils literal notranslate"><span class="pre">distribution_estimation_uniform()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id133"><code class="docutils literal notranslate"><span class="pre">emd_laplace()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id137"><code class="docutils literal notranslate"><span class="pre">sinkhorn_l1l2_gl()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id141"><code class="docutils literal notranslate"><span class="pre">sinkhorn_lpl1_mm()</span></code></a></li>
</ul>
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<section id="module-ot.da">
<span id="ot-da"></span><h1>ot.da<a class="headerlink" href="#module-ot.da" title="Link to this heading"></a></h1>
<p>Domain adaptation with optimal transport</p>
<section id="functions">
<h2>Functions<a class="headerlink" href="#functions" title="Link to this heading"></a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="ot.da.distribution_estimation_uniform">
<span class="sig-prename descclassname"><span class="pre">ot.da.</span></span><span class="sig-name descname"><span class="pre">distribution_estimation_uniform</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 internal" href="../_modules/ot/da.html#distribution_estimation_uniform"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.distribution_estimation_uniform" title="Link to this definition"></a></dt>
<dd><p>estimates a uniform distribution from an array of samples <span class="math notranslate nohighlight">\(\mathbf{X}\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>X</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – The array of samples</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>mu</strong> – The uniform distribution estimated from <span class="math notranslate nohighlight">\(\mathbf{X}\)</span></p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (n_samples,)</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.da.emd_laplace">
<span class="sig-prename descclassname"><span class="pre">ot.da.</span></span><span class="sig-name descname"><span class="pre">emd_laplace</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">xs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">xt</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'knn'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sim_param</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">reg</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'pos'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.5</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">numItermax</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">stopThr</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-09</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">numInnerItermax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100000</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stopInnerThr</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-09</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log</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">verbose</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 internal" href="../_modules/ot/da.html#emd_laplace"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.emd_laplace" title="Link to this definition"></a></dt>
<dd><p>Solve the optimal transport problem (OT) with Laplacian regularization</p>
<div class="math notranslate nohighlight">
\[ \begin{align}\begin{aligned}\gamma = \mathop{\arg \min}_\gamma \quad \langle \gamma, \mathbf{M} \rangle_F +
\eta \cdot \Omega_\alpha(\gamma)\\s.t. \ \gamma \mathbf{1} = \mathbf{a}\\ \gamma^T \mathbf{1} = \mathbf{b}\\ \gamma \geq 0\end{aligned}\end{align} \]</div>
<p>where:</p>
<ul class="simple">
<li><p><span class="math notranslate nohighlight">\(\mathbf{a}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{b}\)</span> are source and target weights (sum to 1)</p></li>
<li><p><span class="math notranslate nohighlight">\(\mathbf{x_s}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{x_t}\)</span> are source and target samples</p></li>
<li><p><span class="math notranslate nohighlight">\(\mathbf{M}\)</span> is the (<cite>ns</cite>, <cite>nt</cite>) metric cost matrix</p></li>
<li><p><span class="math notranslate nohighlight">\(\Omega_\alpha\)</span> is the Laplacian regularization term</p></li>
</ul>
<div class="math notranslate nohighlight">
\[\Omega_\alpha = \frac{1 - \alpha}{n_s^2} \sum_{i,j}
\mathbf{S^s}_{i,j} \|T(\mathbf{x}^s_i) - T(\mathbf{x}^s_j) \|^2 +
\frac{\alpha}{n_t^2} \sum_{i,j}
\mathbf{S^t}_{i,j} \|T(\mathbf{x}^t_i) - T(\mathbf{x}^t_j) \|^2\]</div>
<p>with <span class="math notranslate nohighlight">\(\mathbf{S^s}_{i,j}, \mathbf{S^t}_{i,j}\)</span> denoting source and target similarity
matrices and <span class="math notranslate nohighlight">\(T(\cdot)\)</span> being a barycentric mapping.</p>
<p>The algorithm used for solving the problem is the conditional gradient algorithm as proposed in
<span class="xref std std-ref">[5]</span>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>a</strong> (<em>array-like</em><em> (</em><em>ns</em><em>,</em><em>)</em>) – samples weights in the source domain</p></li>
<li><p><strong>b</strong> (<em>array-like</em><em> (</em><em>nt</em><em>,</em><em>)</em>) – samples weights in the target domain</p></li>
<li><p><strong>xs</strong> (<em>array-like</em><em> (</em><em>ns</em><em>,</em><em>d</em><em>)</em>) – samples in the source domain</p></li>
<li><p><strong>xt</strong> (<em>array-like</em><em> (</em><em>nt</em><em>,</em><em>d</em><em>)</em>) – samples in the target domain</p></li>
<li><p><strong>M</strong> (<em>array-like</em><em> (</em><em>ns</em><em>,</em><em>nt</em><em>)</em>) – loss matrix</p></li>
<li><p><strong>sim</strong> (<em>string</em><em>, </em><em>optional</em>) – Type of similarity (‘knn’ or ‘gauss’) used to construct the Laplacian.</p></li>
<li><p><strong>sim_param</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em>) – Parameter (number of the nearest neighbors for sim=’knn’
or bandwidth for sim=’gauss’) used to compute the Laplacian.</p></li>
<li><p><strong>reg</strong> (<em>string</em>) – Type of Laplacian regularization</p></li>
<li><p><strong>eta</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a>) – Regularization term for Laplacian regularization</p></li>
<li><p><strong>alpha</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a>) – Regularization term for source domain’s importance in regularization</p></li>
<li><p><strong>numItermax</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em>) – Max number of iterations</p></li>
<li><p><strong>stopThr</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em>) – Stop threshold on error (inner emd solver) (>0)</p></li>
<li><p><strong>numInnerItermax</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em>) – Max number of iterations (inner CG solver)</p></li>
<li><p><strong>stopInnerThr</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em>) – Stop threshold on error (inner CG solver) (>0)</p></li>
<li><p><strong>verbose</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#bool" title="(in Python v3.15)"><em>bool</em></a><em>, </em><em>optional</em>) – Print information along iterations</p></li>
<li><p><strong>log</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#bool" title="(in Python v3.15)"><em>bool</em></a><em>, </em><em>optional</em>) – record log if True</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>gamma</strong> (<em>(ns, nt) array-like</em>) – Optimal transportation matrix for the given parameters</p></li>
<li><p><strong>log</strong> (<em>dict</em>) – log dictionary return only if log==True in parameters</p></li>
</ul>
</p>
</dd>
</dl>
<p class="rubric" id="references-emd-laplace">References</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id1" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>5<span class="fn-bracket">]</span></span>
<p>N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy,
“Optimal Transport for Domain Adaptation,” in IEEE
Transactions on Pattern Analysis and Machine Intelligence,
vol.PP, no.99, pp.1-1</p>
</aside>
<aside class="footnote brackets" id="id2" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>30<span class="fn-bracket">]</span></span>
<p>R. Flamary, N. Courty, D. Tuia, A. Rakotomamonjy,
“Optimal transport with Laplacian regularization: Applications to domain adaptation and shape matching,”
in NIPS Workshop on Optimal Transport and Machine Learning OTML, 2014.</p>
</aside>
</aside>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="ot.lp.html#ot.lp.emd" title="ot.lp.emd"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ot.lp.emd</span></code></a></dt><dd><p>Unregularized OT</p>
</dd>
<dt><a class="reference internal" href="ot.optim.html#id0" title="ot.optim.cg"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ot.optim.cg</span></code></a></dt><dd><p>General regularized OT</p>
</dd>
</dl>
</div>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.da.sinkhorn_l1l2_gl">
<span class="sig-prename descclassname"><span class="pre">ot.da.</span></span><span class="sig-name descname"><span class="pre">sinkhorn_l1l2_gl</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">labels_a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">reg</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">numItermax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">numInnerItermax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stopInnerThr</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-09</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">1e-12</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">log</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 internal" href="../_modules/ot/da.html#sinkhorn_l1l2_gl"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.sinkhorn_l1l2_gl" title="Link to this definition"></a></dt>
<dd><p>Solve the entropic regularization optimal transport problem with group
lasso regularization</p>
<p>The function solves the following optimization problem:</p>
<div class="math notranslate nohighlight">
\[ \begin{align}\begin{aligned}\gamma = \mathop{\arg \min}_\gamma \quad \langle \gamma, \mathbf{M} \rangle_F +
\mathrm{reg} \cdot \Omega_e(\gamma) + \eta \ \Omega_g(\gamma)\\s.t. \ \gamma \mathbf{1} = \mathbf{a}\\ \gamma^T \mathbf{1} = \mathbf{b}\\ \gamma \geq 0\end{aligned}\end{align} \]</div>
<p>where :</p>
<ul class="simple">
<li><p><span class="math notranslate nohighlight">\(\mathbf{M}\)</span> is the (<cite>ns</cite>, <cite>nt</cite>) metric cost matrix</p></li>
<li><p><span class="math notranslate nohighlight">\(\Omega_e\)</span> is the entropic regularization term
<span class="math notranslate nohighlight">\(\Omega_e(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})\)</span></p></li>
<li><p><span class="math notranslate nohighlight">\(\Omega_g\)</span> is the group lasso regularization term
<span class="math notranslate nohighlight">\(\Omega_g(\gamma)=\sum_{i,c} \|\gamma_{i,\mathcal{I}_c}\|^2\)</span>
where <span class="math notranslate nohighlight">\(\mathcal{I}_c\)</span> are the index of samples from class
<cite>c</cite> in the source domain.</p></li>
<li><p><span class="math notranslate nohighlight">\(\mathbf{a}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{b}\)</span> are source and target weights (sum to 1)</p></li>
</ul>
<p>The algorithm used for solving the problem is the generalized conditional
gradient as proposed in <span class="xref std std-ref">[5, 7]</span>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>a</strong> (<em>array-like</em><em> (</em><em>ns</em><em>,</em><em>)</em>) – samples weights in the source domain</p></li>
<li><p><strong>labels_a</strong> (<em>array-like</em><em> (</em><em>ns</em><em>,</em><em>)</em>) – labels of samples in the source domain</p></li>
<li><p><strong>b</strong> (<em>array-like</em><em> (</em><em>nt</em><em>,</em><em>)</em>) – samples in the target domain</p></li>
<li><p><strong>M</strong> (<em>array-like</em><em> (</em><em>ns</em><em>,</em><em>nt</em><em>)</em>) – loss matrix</p></li>
<li><p><strong>reg</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a>) – Regularization term for entropic regularization >0</p></li>
<li><p><strong>eta</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em>) – Regularization term for group lasso regularization >0</p></li>
<li><p><strong>numItermax</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em>) – Max number of iterations</p></li>
<li><p><strong>numInnerItermax</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em>) – Max number of iterations (inner sinkhorn solver)</p></li>
<li><p><strong>stopInnerThr</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em>) – Stop threshold on error (inner sinkhorn solver) (>0)</p></li>
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=1e-12</em><em>)</em>) – Small value to avoid division by zero</p></li>
<li><p><strong>verbose</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#bool" title="(in Python v3.15)"><em>bool</em></a><em>, </em><em>optional</em>) – Print information along iterations</p></li>
<li><p><strong>log</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#bool" title="(in Python v3.15)"><em>bool</em></a><em>, </em><em>optional</em>) – record log if True</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>gamma</strong> (<em>(ns, nt) array-like</em>) – Optimal transportation matrix for the given parameters</p></li>
<li><p><strong>log</strong> (<em>dict</em>) – log dictionary return only if log==True in parameters</p></li>
</ul>
</p>
</dd>
</dl>
<p class="rubric" id="references-sinkhorn-l1l2-gl">References</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id3" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>5<span class="fn-bracket">]</span></span>
<p>N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy,
“Optimal Transport for Domain Adaptation,” in IEEE Transactions
on Pattern Analysis and Machine Intelligence , vol.PP, no.99, pp.1-1</p>
</aside>
<aside class="footnote brackets" id="id4" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>7<span class="fn-bracket">]</span></span>
<p>Rakotomamonjy, A., Flamary, R., & Courty, N. (2015).
Generalized conditional gradient: analysis of convergence and
applications. arXiv preprint arXiv:1510.06567.</p>
</aside>
</aside>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="ot.optim.html#id22" title="ot.optim.gcg"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ot.optim.gcg</span></code></a></dt><dd><p>Generalized conditional gradient for OT problems</p>
</dd>
</dl>
</div>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.da.sinkhorn_lpl1_mm">
<span class="sig-prename descclassname"><span class="pre">ot.da.</span></span><span class="sig-name descname"><span class="pre">sinkhorn_lpl1_mm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">labels_a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">reg</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">numItermax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">numInnerItermax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stopInnerThr</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-09</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">log</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 internal" href="../_modules/ot/da.html#sinkhorn_lpl1_mm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.sinkhorn_lpl1_mm" title="Link to this definition"></a></dt>
<dd><p>Solve the entropic regularization optimal transport problem with non-convex
group lasso regularization</p>
<p>The function solves the following optimization problem:</p>
<div class="math notranslate nohighlight">
\[ \begin{align}\begin{aligned}\gamma = \mathop{\arg \min}_\gamma \quad \langle \gamma, \mathbf{M} \rangle_F +
\mathrm{reg} \cdot \Omega_e(\gamma) + \eta \ \Omega_g(\gamma)\\s.t. \ \gamma \mathbf{1} = \mathbf{a}\\ \gamma^T \mathbf{1} = \mathbf{b}\\ \gamma \geq 0\end{aligned}\end{align} \]</div>
<p>where :</p>
<ul class="simple">
<li><p><span class="math notranslate nohighlight">\(\mathbf{M}\)</span> is the (<cite>ns</cite>, <cite>nt</cite>) metric cost matrix</p></li>
<li><p><span class="math notranslate nohighlight">\(\Omega_e\)</span> is the entropic regularization term <span class="math notranslate nohighlight">\(\Omega_e
(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})\)</span></p></li>
<li><p><span class="math notranslate nohighlight">\(\Omega_g\)</span> is the group lasso regularization term
<span class="math notranslate nohighlight">\(\Omega_g(\gamma)=\sum_{i,c} \|\gamma_{i,\mathcal{I}_c}\|^{1/2}_1\)</span>
where <span class="math notranslate nohighlight">\(\mathcal{I}_c\)</span> are the index of samples from class <cite>c</cite>
in the source domain.</p></li>
<li><p><span class="math notranslate nohighlight">\(\mathbf{a}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{b}\)</span> are source and target weights (sum to 1)</p></li>
</ul>
<p>The algorithm used for solving the problem is the generalized conditional
gradient as proposed in <a class="reference internal" href="../all.html#references-sinkhorn-lpl1-mm"><span class="std std-ref">[5, 7]</span></a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>a</strong> (<em>array-like</em><em> (</em><em>ns</em><em>,</em><em>)</em>) – samples weights in the source domain</p></li>
<li><p><strong>labels_a</strong> (<em>array-like</em><em> (</em><em>ns</em><em>,</em><em>)</em>) – labels of samples in the source domain</p></li>
<li><p><strong>b</strong> (<em>array-like</em><em> (</em><em>nt</em><em>,</em><em>)</em>) – samples weights in the target domain</p></li>
<li><p><strong>M</strong> (<em>array-like</em><em> (</em><em>ns</em><em>,</em><em>nt</em><em>)</em>) – loss matrix</p></li>
<li><p><strong>reg</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a>) – Regularization term for entropic regularization >0</p></li>
<li><p><strong>eta</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em>) – Regularization term for group lasso regularization >0</p></li>
<li><p><strong>numItermax</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em>) – Max number of iterations</p></li>
<li><p><strong>numInnerItermax</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em>) – Max number of iterations (inner sinkhorn solver)</p></li>
<li><p><strong>stopInnerThr</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em>) – Stop threshold on error (inner sinkhorn solver) (>0)</p></li>
<li><p><strong>verbose</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#bool" title="(in Python v3.15)"><em>bool</em></a><em>, </em><em>optional</em>) – Print information along iterations</p></li>
<li><p><strong>log</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#bool" title="(in Python v3.15)"><em>bool</em></a><em>, </em><em>optional</em>) – record log if True</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>gamma</strong> (<em>(ns, nt) array-like</em>) – Optimal transportation matrix for the given parameters</p></li>
<li><p><strong>log</strong> (<em>dict</em>) – log dictionary return only if log==True in parameters</p></li>
</ul>
</p>
</dd>
</dl>
<p class="rubric" id="references-sinkhorn-lpl1-mm">References</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id5" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>5<span class="fn-bracket">]</span></span>
<p>N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy,
“Optimal Transport for Domain Adaptation,” in IEEE
Transactions on Pattern Analysis and Machine Intelligence ,
vol.PP, no.99, pp.1-1</p>
</aside>
<aside class="footnote brackets" id="id6" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>7<span class="fn-bracket">]</span></span>
<p>Rakotomamonjy, A., Flamary, R., & Courty, N. (2015).
Generalized conditional gradient: analysis of convergence
and applications. arXiv preprint arXiv:1510.06567.</p>
</aside>
</aside>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="ot.lp.html#ot.lp.emd" title="ot.lp.emd"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ot.lp.emd</span></code></a></dt><dd><p>Unregularized OT</p>
</dd>
<dt><a class="reference internal" href="ot.bregman.html#ot.bregman.sinkhorn" title="ot.bregman.sinkhorn"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ot.bregman.sinkhorn</span></code></a></dt><dd><p>Entropic regularized OT</p>
</dd>
<dt><a class="reference internal" href="ot.optim.html#id0" title="ot.optim.cg"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ot.optim.cg</span></code></a></dt><dd><p>General regularized OT</p>
</dd>
</dl>
</div>
</dd></dl>
<div class="sphx-glr-clear"></div></section>
<section id="classes">
<h2>Classes<a class="headerlink" href="#classes" title="Link to this heading"></a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="ot.da.BaseTransport">
<span class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></span><span class="sig-prename descclassname"><span class="pre">ot.da.</span></span><span class="sig-name descname"><span class="pre">BaseTransport</span></span><a class="reference internal" href="../_modules/ot/da.html#BaseTransport"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.BaseTransport" title="Link to this definition"></a></dt>
<dd><p>Base class for OTDA objects</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>All estimators should specify all the parameters that can be set
at the class level in their <code class="docutils literal notranslate"><span class="pre">__init__</span></code> as explicit keyword
arguments (no <code class="docutils literal notranslate"><span class="pre">*args</span></code> or <code class="docutils literal notranslate"><span class="pre">**kwargs</span></code>).</p>
</div>
<p>The fit method should:</p>
<ul class="simple">
<li><p>estimate a cost matrix and store it in a <cite>cost_</cite> attribute</p></li>
<li><p>estimate a coupling matrix and store it in a <cite>coupling_</cite> attribute</p></li>
<li><p>estimate distributions from source and target data and store them in
<cite>mu_s</cite> and <cite>mu_t</cite> attributes</p></li>
<li><p>store <cite>Xs</cite> and <cite>Xt</cite> in attributes to be used later on in <cite>transform</cite> and
<cite>inverse_transform</cite> methods</p></li>
</ul>
<p><cite>transform</cite> method should always get as input a <cite>Xs</cite> parameter</p>
<p><cite>inverse_transform</cite> method should always get as input a <cite>Xt</cite> parameter</p>
<p><cite>transform_labels</cite> method should always get as input a <cite>ys</cite> parameter</p>
<p><cite>inverse_transform_labels</cite> method should always get as input a <cite>yt</cite> parameter</p>
<dl class="py method">
<dt class="sig sig-object py" id="ot.da.BaseTransport.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">Xs</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">ys</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">Xt</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">yt</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 internal" href="../_modules/ot/da.html#BaseTransport.fit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.BaseTransport.fit" title="Link to this definition"></a></dt>
<dd><p>Build a coupling matrix from source and target sets of samples
<span class="math notranslate nohighlight">\((\mathbf{X_s}, \mathbf{y_s})\)</span> and <span class="math notranslate nohighlight">\((\mathbf{X_t}, \mathbf{y_t})\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>Xs</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>, </em><em>n_features</em><em>)</em>) – The training input samples.</p></li>
<li><p><strong>ys</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>,</em><em>)</em>) – The training class labels</p></li>
<li><p><strong>Xt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>, </em><em>n_features</em><em>)</em>) – The training input samples.</p></li>
<li><p><strong>yt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>,</em><em>)</em>) – <p>The class labels. If some target samples are unlabelled, fill the
<span class="math notranslate nohighlight">\(\mathbf{y_t}\)</span>’s elements with -1.</p>
<p>Warning: Note that, due to this convention -1 cannot be used as a
class label</p>
</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>self</strong> – Returns self.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#object" title="(in Python v3.15)">object</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="ot.da.BaseTransport.fit_transform">
<span class="sig-name descname"><span class="pre">fit_transform</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Xs</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">ys</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">Xt</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">yt</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 internal" href="../_modules/ot/da.html#BaseTransport.fit_transform"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.BaseTransport.fit_transform" title="Link to this definition"></a></dt>
<dd><p>Build a coupling matrix from source and target sets of samples
<span class="math notranslate nohighlight">\((\mathbf{X_s}, \mathbf{y_s})\)</span> and <span class="math notranslate nohighlight">\((\mathbf{X_t}, \mathbf{y_t})\)</span>
and transports source samples <span class="math notranslate nohighlight">\(\mathbf{X_s}\)</span> onto target ones <span class="math notranslate nohighlight">\(\mathbf{X_t}\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>Xs</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>, </em><em>n_features</em><em>)</em>) – The training input samples.</p></li>
<li><p><strong>ys</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>,</em><em>)</em>) – The class labels for training samples</p></li>
<li><p><strong>Xt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>, </em><em>n_features</em><em>)</em>) – The training input samples.</p></li>
<li><p><strong>yt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>,</em><em>)</em>) – <p>The class labels. If some target samples are unlabelled, fill the
<span class="math notranslate nohighlight">\(\mathbf{y_t}\)</span>’s elements with -1.</p>
<p>Warning: Note that, due to this convention -1 cannot be used as a
class label</p>
</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>transp_Xs</strong> – The source samples samples.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (n_source_samples, n_features)</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="ot.da.BaseTransport.inverse_transform">
<span class="sig-name descname"><span class="pre">inverse_transform</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Xs</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">ys</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">Xt</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">yt</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">batch_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">128</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/da.html#BaseTransport.inverse_transform"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.BaseTransport.inverse_transform" title="Link to this definition"></a></dt>
<dd><p>Transports target samples <span class="math notranslate nohighlight">\(\mathbf{X_t}\)</span> onto source samples <span class="math notranslate nohighlight">\(\mathbf{X_s}\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>Xs</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>, </em><em>n_features</em><em>)</em>) – The source input samples.</p></li>
<li><p><strong>ys</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>,</em><em>)</em>) – The source class labels</p></li>
<li><p><strong>Xt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>, </em><em>n_features</em><em>)</em>) – The target input samples.</p></li>
<li><p><strong>yt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>,</em><em>)</em>) – <p>The target class labels. If some target samples are unlabelled, fill the
<span class="math notranslate nohighlight">\(\mathbf{y_t}\)</span>’s elements with -1.</p>
<p>Warning: Note that, due to this convention -1 cannot be used as a
class label</p>
</p></li>
<li><p><strong>batch_size</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em><em> (</em><em>default=128</em><em>)</em>) – The batch size for out of sample inverse transform</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>transp_Xt</strong> – The transported target samples.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (n_source_samples, n_features)</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="ot.da.BaseTransport.inverse_transform_labels">
<span class="sig-name descname"><span class="pre">inverse_transform_labels</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">yt</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 internal" href="../_modules/ot/da.html#BaseTransport.inverse_transform_labels"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.BaseTransport.inverse_transform_labels" title="Link to this definition"></a></dt>
<dd><p>Propagate target labels <span class="math notranslate nohighlight">\(\mathbf{y_t}\)</span> to obtain estimated source labels
<span class="math notranslate nohighlight">\(\mathbf{y_s}\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>yt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>,</em><em>)</em>)</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>transp_ys</strong> – Estimated soft source labels.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (n_source_samples, nb_classes)</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="ot.da.BaseTransport.transform">
<span class="sig-name descname"><span class="pre">transform</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Xs</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">ys</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">Xt</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">yt</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">batch_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">128</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/da.html#BaseTransport.transform"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.BaseTransport.transform" title="Link to this definition"></a></dt>
<dd><p>Transports source samples <span class="math notranslate nohighlight">\(\mathbf{X_s}\)</span> onto target ones <span class="math notranslate nohighlight">\(\mathbf{X_t}\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>Xs</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>, </em><em>n_features</em><em>)</em>) – The source input samples.</p></li>
<li><p><strong>ys</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>,</em><em>)</em>) – The class labels for source samples</p></li>
<li><p><strong>Xt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>, </em><em>n_features</em><em>)</em>) – The target input samples.</p></li>
<li><p><strong>yt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>,</em><em>)</em>) – <p>The class labels for target. If some target samples are unlabelled, fill the
<span class="math notranslate nohighlight">\(\mathbf{y_t}\)</span>’s elements with -1.</p>
<p>Warning: Note that, due to this convention -1 cannot be used as a
class label</p>
</p></li>
<li><p><strong>batch_size</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em><em> (</em><em>default=128</em><em>)</em>) – The batch size for out of sample inverse transform</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>transp_Xs</strong> – The transport source samples.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (n_source_samples, n_features)</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="ot.da.BaseTransport.transform_labels">
<span class="sig-name descname"><span class="pre">transform_labels</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ys</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 internal" href="../_modules/ot/da.html#BaseTransport.transform_labels"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.BaseTransport.transform_labels" title="Link to this definition"></a></dt>
<dd><p>Propagate source labels <span class="math notranslate nohighlight">\(\mathbf{y_s}\)</span> to obtain estimated target labels as in
<span class="xref std std-ref">[27]</span>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>ys</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>,</em><em>)</em>) – The source class labels</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>transp_ys</strong> – Estimated soft target labels.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (n_target_samples, nb_classes)</p>
</dd>
</dl>
<p class="rubric" id="references-basetransport-transform-labels">References</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id7" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>27<span class="fn-bracket">]</span></span>
<p>Ievgen Redko, Nicolas Courty, Rémi Flamary, Devis Tuia
“Optimal transport for multi-source domain adaptation under target shift”,
International Conference on Artificial Intelligence and Statistics (AISTATS), 2019.</p>
</aside>
</aside>
</dd></dl>
</dd></dl>
<section id="examples-using-ot-da-basetransport">
<h3>Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.BaseTransport</span></code><a class="headerlink" href="#examples-using-ot-da-basetransport" title="Link to this heading"></a></h3>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting and OTDA approach with Laplacian regularization."><img alt="" src="../_images/sphx_glr_plot_otda_laplacian_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_laplacian.html"><span class="doc">OT with Laplacian regularization for domain adaptation</span></a></p>
<div class="sphx-glr-thumbnail-title">OT with Laplacian regularization for domain adaptation</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example presents a way of transferring colors between two images with Optimal Transport as introduced in [6]"><img alt="" src="../_images/sphx_glr_plot_otda_color_images_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_color_images.html"><span class="doc">OT for image color adaptation</span></a></p>
<div class="sphx-glr-thumbnail-title">OT for image color adaptation</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="OT for domain adaptation with image color adaptation [6] with mapping estimation [8]."><img alt="" src="../_images/sphx_glr_plot_otda_mapping_colors_images_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_mapping_colors_images.html"><span class="doc">OT for image color adaptation with mapping estimation</span></a></p>
<div class="sphx-glr-thumbnail-title">OT for image color adaptation with mapping estimation</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Linear OT mapping estimation"><img alt="" src="../_images/sphx_glr_plot_otda_linear_mapping_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_linear_mapping.html"><span class="doc">Linear OT mapping estimation</span></a></p>
<div class="sphx-glr-thumbnail-title">Linear OT mapping estimation</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example introduces a semi supervised domain adaptation in a 2D setting. It explicit the problem of semi supervised domain adaptation and introduces some optimal transport approaches to solve it."><img alt="" src="../_images/sphx_glr_plot_otda_semi_supervised_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_semi_supervised.html"><span class="doc">OTDA unsupervised vs semi-supervised setting</span></a></p>
<div class="sphx-glr-thumbnail-title">OTDA unsupervised vs semi-supervised setting</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting and the 4 OTDA approaches currently supported in POT."><img alt="" src="../_images/sphx_glr_plot_otda_classes_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_classes.html"><span class="doc">OT for domain adaptation</span></a></p>
<div class="sphx-glr-thumbnail-title">OT for domain adaptation</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting. It explicit the problem of domain adaptation and introduces some optimal transport approaches to solve it."><img alt="" src="../_images/sphx_glr_plot_otda_d2_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_d2.html"><span class="doc">OT for domain adaptation on empirical distributions</span></a></p>
<div class="sphx-glr-thumbnail-title">OT for domain adaptation on empirical distributions</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example introduces a target shift problem with two 2D source and 1 target domain."><img alt="" src="../_images/sphx_glr_plot_otda_jcpot_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_jcpot.html"><span class="doc">OT for multi-source target shift</span></a></p>
<div class="sphx-glr-thumbnail-title">OT for multi-source target shift</div>
</div></div><div class="sphx-glr-clear"></div><dl class="py class">
<dt class="sig sig-object py" id="ot.da.EMDLaplaceTransport">
<span class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></span><span class="sig-prename descclassname"><span class="pre">ot.da.</span></span><span class="sig-name descname"><span class="pre">EMDLaplaceTransport</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">reg_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'pos'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">reg_lap</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">reg_src</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">metric</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'sqeuclidean'</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">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">similarity</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'knn'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">similarity_param</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">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">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-09</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_inner_iter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100000</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inner_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-09</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log</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">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">distribution_estimation</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre"><function</span> <span class="pre">distribution_estimation_uniform></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out_of_sample_map</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'ferradans'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/da.html#EMDLaplaceTransport"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.EMDLaplaceTransport" title="Link to this definition"></a></dt>
<dd><p>Domain Adaptation OT method based on Earth Mover’s Distance with Laplacian regularization</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>reg_type</strong> (<em>string optional</em><em> (</em><em>default='pos'</em><em>)</em>) – Type of the regularization term: ‘pos’ and ‘disp’ for
regularization term defined in <span class="xref std std-ref">[2]</span> and
<span class="xref std std-ref">[6]</span>, respectively.</p></li>
<li><p><strong>reg_lap</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=1</em><em>)</em>) – Laplacian regularization parameter</p></li>
<li><p><strong>reg_src</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=0.5</em><em>)</em>) – Source relative importance in regularization</p></li>
<li><p><strong>metric</strong> (<em>string</em><em>, </em><em>optional</em><em> (</em><em>default="sqeuclidean"</em><em>)</em>) – The ground metric for the Wasserstein problem</p></li>
<li><p><strong>norm</strong> (<em>string</em><em>, </em><em>optional</em><em> (</em><em>default=None</em><em>)</em>) – If given, normalize the ground metric to avoid numerical errors that
can occur with large metric values.</p></li>
<li><p><strong>similarity</strong> (<em>string</em><em>, </em><em>optional</em><em> (</em><em>default="knn"</em><em>)</em>) – The similarity to use either knn or gaussian</p></li>
<li><p><strong>similarity_param</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=None</em><em>)</em>) – Parameter for the similarity: number of nearest neighbors or bandwidth
if similarity=”knn” or “gaussian”, respectively. If None is provided,
it is set to 3 or the average pairwise squared Euclidean distance, respectively.</p></li>
<li><p><strong>max_iter</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em><em> (</em><em>default=100</em><em>)</em>) – Max number of BCD iterations</p></li>
<li><p><strong>tol</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=1e-5</em><em>)</em>) – Stop threshold on relative loss decrease (>0)</p></li>
<li><p><strong>max_inner_iter</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em><em> (</em><em>default=10</em><em>)</em>) – Max number of iterations (inner CG solver)</p></li>
<li><p><strong>inner_tol</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=1e-6</em><em>)</em>) – Stop threshold on error (inner CG solver) (>0)</p></li>
<li><p><strong>log</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em><em> (</em><em>default=False</em><em>)</em>) – Controls the logs of the optimization algorithm</p></li>
<li><p><strong>distribution_estimation</strong> (<em>callable</em><em>, </em><em>optional</em><em> (</em><em>defaults to the uniform</em><em>)</em>) – The kind of distribution estimation to employ</p></li>
<li><p><strong>out_of_sample_map</strong> (<em>string</em><em>, </em><em>optional</em><em> (</em><em>default="ferradans"</em><em>)</em>) – The kind of out of sample mapping to apply to transport samples
from a domain into another one. Currently the only possible option is
“ferradans” which uses the method proposed in <span class="xref std std-ref">[6]</span>.</p></li>
</ul>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="ot.da.EMDLaplaceTransport.coupling_">
<span class="sig-name descname"><span class="pre">coupling_</span></span><a class="headerlink" href="#ot.da.EMDLaplaceTransport.coupling_" title="Link to this definition"></a></dt>
<dd><p>The optimal coupling</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (n_source_samples, n_target_samples)</p>
</dd>
</dl>
</dd></dl>
<p class="rubric" id="references-emdlaplacetransport">References</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id8" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy,
“Optimal Transport for Domain Adaptation,” in IEEE Transactions
on Pattern Analysis and Machine Intelligence , vol.PP, no.99, pp.1-1</p>
</aside>
<aside class="footnote brackets" id="id9" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<p>R. Flamary, N. Courty, D. Tuia, A. Rakotomamonjy,
“Optimal transport with Laplacian regularization: Applications to domain adaptation and shape matching,”
in NIPS Workshop on Optimal Transport and Machine Learning OTML, 2014.</p>
</aside>
<aside class="footnote brackets" id="id10" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>6<span class="fn-bracket">]</span></span>
<p>Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014).
Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882.</p>
</aside>
</aside>
<dl class="py method">
<dt class="sig sig-object py" id="ot.da.EMDLaplaceTransport.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">Xs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ys</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">Xt</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">yt</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 internal" href="../_modules/ot/da.html#EMDLaplaceTransport.fit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.EMDLaplaceTransport.fit" title="Link to this definition"></a></dt>
<dd><p>Build a coupling matrix from source and target sets of samples
<span class="math notranslate nohighlight">\((\mathbf{X_s}, \mathbf{y_s})\)</span> and <span class="math notranslate nohighlight">\((\mathbf{X_t}, \mathbf{y_t})\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>Xs</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>, </em><em>n_features</em><em>)</em>) – The training input samples.</p></li>
<li><p><strong>ys</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>,</em><em>)</em>) – The class labels</p></li>
<li><p><strong>Xt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>, </em><em>n_features</em><em>)</em>) – The training input samples.</p></li>
<li><p><strong>yt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>,</em><em>)</em>) – <p>The class labels. If some target samples are unlabelled, fill the
<span class="math notranslate nohighlight">\(\mathbf{y_t}\)</span>’s elements with -1.</p>
<p>Warning: Note that, due to this convention -1 cannot be used as a
class label</p>
</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>self</strong> – Returns self.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#object" title="(in Python v3.15)">object</a></p>
</dd>
</dl>
</dd></dl>
</dd></dl>
</section>
<section id="examples-using-ot-da-emdlaplacetransport">
<h3>Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.EMDLaplaceTransport</span></code><a class="headerlink" href="#examples-using-ot-da-emdlaplacetransport" title="Link to this heading"></a></h3>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting and OTDA approach with Laplacian regularization."><img alt="" src="../_images/sphx_glr_plot_otda_laplacian_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_laplacian.html"><span class="doc">OT with Laplacian regularization for domain adaptation</span></a></p>
<div class="sphx-glr-thumbnail-title">OT with Laplacian regularization for domain adaptation</div>
</div></div><div class="sphx-glr-clear"></div><dl class="py class">
<dt class="sig sig-object py" id="ot.da.EMDTransport">
<span class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></span><span class="sig-prename descclassname"><span class="pre">ot.da.</span></span><span class="sig-name descname"><span class="pre">EMDTransport</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">metric</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'sqeuclidean'</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">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log</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">distribution_estimation</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre"><function</span> <span class="pre">distribution_estimation_uniform></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out_of_sample_map</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'ferradans'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">limit_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</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">100000</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/da.html#EMDTransport"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.EMDTransport" title="Link to this definition"></a></dt>
<dd><p>Domain Adaptation OT method based on Earth Mover’s Distance</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>metric</strong> (<em>string</em><em>, </em><em>optional</em><em> (</em><em>default="sqeuclidean"</em><em>)</em>) – The ground metric for the Wasserstein problem</p></li>
<li><p><strong>norm</strong> (<em>string</em><em>, </em><em>optional</em><em> (</em><em>default=None</em><em>)</em>) – If given, normalize the ground metric to avoid numerical errors that
can occur with large metric values.</p></li>
<li><p><strong>log</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em><em> (</em><em>default=False</em><em>)</em>) – Controls the logs of the optimization algorithm</p></li>
<li><p><strong>distribution_estimation</strong> (<em>callable</em><em>, </em><em>optional</em><em> (</em><em>defaults to the uniform</em><em>)</em>) – The kind of distribution estimation to employ</p></li>
<li><p><strong>out_of_sample_map</strong> (<em>string</em><em>, </em><em>optional</em><em> (</em><em>default="ferradans"</em><em>)</em>) – The kind of out of sample mapping to apply to transport samples
from a domain into another one. Currently the only possible option is
“ferradans” which uses the method proposed in <span class="xref std std-ref">[6]</span>.</p></li>
<li><p><strong>limit_max</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=10</em><em>)</em>) – Controls the semi supervised mode. Transport between labeled source
and target samples of different classes will exhibit an infinite cost
(10 times the maximum value of the cost matrix)</p></li>
<li><p><strong>max_iter</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em><em> (</em><em>default=100000</em><em>)</em>) – The maximum number of iterations before stopping the optimization
algorithm if it has not converged.</p></li>
</ul>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="ot.da.EMDTransport.coupling_">
<span class="sig-name descname"><span class="pre">coupling_</span></span><a class="headerlink" href="#ot.da.EMDTransport.coupling_" title="Link to this definition"></a></dt>
<dd><p>The optimal coupling</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (n_source_samples, n_target_samples)</p>
</dd>
</dl>
</dd></dl>
<p class="rubric" id="references-emdtransport">References</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id11" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy,
“Optimal Transport for Domain Adaptation,” in IEEE Transactions
on Pattern Analysis and Machine Intelligence , vol.PP, no.99, pp.1-1</p>
</aside>
<aside class="footnote brackets" id="id12" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>6<span class="fn-bracket">]</span></span>
<p>Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014).
Regularized discrete optimal transport. SIAM Journal on Imaging
Sciences, 7(3), 1853-1882.</p>
</aside>
</aside>
<dl class="py method">
<dt class="sig sig-object py" id="ot.da.EMDTransport.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">Xs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ys</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">Xt</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">yt</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 internal" href="../_modules/ot/da.html#EMDTransport.fit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.EMDTransport.fit" title="Link to this definition"></a></dt>
<dd><p>Build a coupling matrix from source and target sets of samples
<span class="math notranslate nohighlight">\((\mathbf{X_s}, \mathbf{y_s})\)</span> and <span class="math notranslate nohighlight">\((\mathbf{X_t}, \mathbf{y_t})\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>Xs</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>, </em><em>n_features</em><em>)</em>) – The training input samples.</p></li>
<li><p><strong>ys</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_source_samples</em><em>,</em><em>)</em>) – The class labels</p></li>
<li><p><strong>Xt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>, </em><em>n_features</em><em>)</em>) – The training input samples.</p></li>
<li><p><strong>yt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>,</em><em>)</em>) – <p>The class labels. If some target samples are unlabelled, fill the
<span class="math notranslate nohighlight">\(\mathbf{y_t}\)</span>’s elements with -1.</p>
<p>Warning: Note that, due to this convention -1 cannot be used as a
class label</p>
</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>self</strong> – Returns self.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#object" title="(in Python v3.15)">object</a></p>
</dd>
</dl>
</dd></dl>
</dd></dl>
</section>
<section id="examples-using-ot-da-emdtransport">
<h3>Examples using <code class="docutils literal notranslate"><span class="pre">ot.da.EMDTransport</span></code><a class="headerlink" href="#examples-using-ot-da-emdtransport" title="Link to this heading"></a></h3>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting and OTDA approach with Laplacian regularization."><img alt="" src="../_images/sphx_glr_plot_otda_laplacian_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_laplacian.html"><span class="doc">OT with Laplacian regularization for domain adaptation</span></a></p>
<div class="sphx-glr-thumbnail-title">OT with Laplacian regularization for domain adaptation</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example presents a way of transferring colors between two images with Optimal Transport as introduced in [6]"><img alt="" src="../_images/sphx_glr_plot_otda_color_images_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_color_images.html"><span class="doc">OT for image color adaptation</span></a></p>
<div class="sphx-glr-thumbnail-title">OT for image color adaptation</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="OT for domain adaptation with image color adaptation [6] with mapping estimation [8]."><img alt="" src="../_images/sphx_glr_plot_otda_mapping_colors_images_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_mapping_colors_images.html"><span class="doc">OT for image color adaptation with mapping estimation</span></a></p>
<div class="sphx-glr-thumbnail-title">OT for image color adaptation with mapping estimation</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting and the 4 OTDA approaches currently supported in POT."><img alt="" src="../_images/sphx_glr_plot_otda_classes_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_classes.html"><span class="doc">OT for domain adaptation</span></a></p>
<div class="sphx-glr-thumbnail-title">OT for domain adaptation</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting. It explicit the problem of domain adaptation and introduces some optimal transport approaches to solve it."><img alt="" src="../_images/sphx_glr_plot_otda_d2_thumb.png" />
<p><a class="reference internal" href="../auto_examples/domain-adaptation/plot_otda_d2.html"><span class="doc">OT for domain adaptation on empirical distributions</span></a></p>
<div class="sphx-glr-thumbnail-title">OT for domain adaptation on empirical distributions</div>
</div></div><div class="sphx-glr-clear"></div><dl class="py class">
<dt class="sig sig-object py" id="ot.da.JCPOTTransport">
<span class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></span><span class="sig-prename descclassname"><span class="pre">ot.da.</span></span><span class="sig-name descname"><span class="pre">JCPOTTransport</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">reg_e</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.1</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">10</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">1e-08</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">log</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">metric</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'sqeuclidean'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out_of_sample_map</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'ferradans'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/da.html#JCPOTTransport"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.JCPOTTransport" title="Link to this definition"></a></dt>
<dd><p>Domain Adaptation OT method for multi-source target shift based on Wasserstein barycenter algorithm.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>reg_e</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=1</em><em>)</em>) – Entropic regularization parameter</p></li>
<li><p><strong>max_iter</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=10</em><em>)</em>) – The minimum number of iteration before stopping the optimization
algorithm if it has not converged</p></li>
<li><p><strong>tol</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=10e-9</em><em>)</em>) – Stop threshold on error (inner sinkhorn solver) (>0)</p></li>
<li><p><strong>verbose</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#bool" title="(in Python v3.15)"><em>bool</em></a><em>, </em><em>optional</em><em> (</em><em>default=False</em><em>)</em>) – Controls the verbosity of the optimization algorithm</p></li>
<li><p><strong>log</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#bool" title="(in Python v3.15)"><em>bool</em></a><em>, </em><em>optional</em><em> (</em><em>default=False</em><em>)</em>) – Controls the logs of the optimization algorithm</p></li>
<li><p><strong>metric</strong> (<em>string</em><em>, </em><em>optional</em><em> (</em><em>default="sqeuclidean"</em><em>)</em>) – The ground metric for the Wasserstein problem</p></li>
<li><p><strong>norm</strong> (<em>string</em><em>, </em><em>optional</em><em> (</em><em>default=None</em><em>)</em>) – If given, normalize the ground metric to avoid numerical errors that
can occur with large metric values.</p></li>
<li><p><strong>distribution_estimation</strong> (<em>callable</em><em>, </em><em>optional</em><em> (</em><em>defaults to the uniform</em><em>)</em>) – The kind of distribution estimation to employ</p></li>
<li><p><strong>out_of_sample_map</strong> (<em>string</em><em>, </em><em>optional</em><em> (</em><em>default="ferradans"</em><em>)</em>) – The kind of out of sample mapping to apply to transport samples
from a domain into another one. Currently the only possible option is
“ferradans” which uses the method proposed in <span class="xref std std-ref">[6]</span>.</p></li>
</ul>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="ot.da.JCPOTTransport.coupling_">
<span class="sig-name descname"><span class="pre">coupling_</span></span><a class="headerlink" href="#ot.da.JCPOTTransport.coupling_" title="Link to this definition"></a></dt>
<dd><p>A set of optimal couplings between each source domain and the target domain</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#list" title="(in Python v3.15)">list</a> of array-like objects, shape K x (n_source_samples, n_target_samples)</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="ot.da.JCPOTTransport.proportions_">
<span class="sig-name descname"><span class="pre">proportions_</span></span><a class="headerlink" href="#ot.da.JCPOTTransport.proportions_" title="Link to this definition"></a></dt>
<dd><p>Estimated class proportions in the target domain</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (n_classes,)</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="ot.da.JCPOTTransport.log_">
<span class="sig-name descname"><span class="pre">log_</span></span><a class="headerlink" href="#ot.da.JCPOTTransport.log_" title="Link to this definition"></a></dt>
<dd><p>The dictionary of log, empty dict if parameter log is not True</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dictionary</p>
</dd>
</dl>
</dd></dl>
<p class="rubric" id="references-jcpottransport">References</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id13" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>Ievgen Redko, Nicolas Courty, Rémi Flamary, Devis Tuia
“Optimal transport for multi-source domain adaptation under target shift”,
International Conference on Artificial Intelligence and Statistics (AISTATS),
vol. 89, p.849-858, 2019.</p>
</aside>
<aside class="footnote brackets" id="id14" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>6<span class="fn-bracket">]</span></span>
<p>Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014).
Regularized discrete optimal transport. SIAM Journal on Imaging
Sciences, 7(3), 1853-1882.</p>
</aside>
</aside>
<dl class="py method">
<dt class="sig sig-object py" id="ot.da.JCPOTTransport.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">Xs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ys</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">Xt</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">yt</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 internal" href="../_modules/ot/da.html#JCPOTTransport.fit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.JCPOTTransport.fit" title="Link to this definition"></a></dt>
<dd><p>Building coupling matrices from a list of source and target sets of samples
<span class="math notranslate nohighlight">\((\mathbf{X_s}, \mathbf{y_s})\)</span> and <span class="math notranslate nohighlight">\((\mathbf{X_t}, \mathbf{y_t})\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>Xs</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#list" title="(in Python v3.15)"><em>list</em></a><em> of </em><em>K array-like objects</em><em>, </em><em>shape K x</em><em> (</em><em>nk_source_samples</em><em>, </em><em>n_features</em><em>)</em>) – A list of the training input samples.</p></li>
<li><p><strong>ys</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#list" title="(in Python v3.15)"><em>list</em></a><em> of </em><em>K array-like objects</em><em>, </em><em>shape K x</em><em> (</em><em>nk_source_samples</em><em>,</em><em>)</em>) – A list of the class labels</p></li>
<li><p><strong>Xt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>, </em><em>n_features</em><em>)</em>) – The training input samples.</p></li>
<li><p><strong>yt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>,</em><em>)</em>) – <p>The class labels. If some target samples are unlabelled, fill the
<span class="math notranslate nohighlight">\(\mathbf{y_t}\)</span>’s elements with -1.</p>
<p>Warning: Note that, due to this convention -1 cannot be used as a
class label</p>
</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>self</strong> – Returns self.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#object" title="(in Python v3.15)">object</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="ot.da.JCPOTTransport.inverse_transform_labels">
<span class="sig-name descname"><span class="pre">inverse_transform_labels</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">yt</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 internal" href="../_modules/ot/da.html#JCPOTTransport.inverse_transform_labels"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.JCPOTTransport.inverse_transform_labels" title="Link to this definition"></a></dt>
<dd><p>Propagate target labels <span class="math notranslate nohighlight">\(\mathbf{y_t}\)</span> to obtain estimated source labels
<span class="math notranslate nohighlight">\(\mathbf{y_s}\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>yt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>,</em><em>)</em>) – The target class labels</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>transp_ys</strong> – A list of estimated soft source labels</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#list" title="(in Python v3.15)">list</a> of K array-like objects, shape K x (nk_source_samples, nb_classes)</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="ot.da.JCPOTTransport.transform">
<span class="sig-name descname"><span class="pre">transform</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Xs</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">ys</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">Xt</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">yt</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">batch_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">128</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/da.html#JCPOTTransport.transform"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.da.JCPOTTransport.transform" title="Link to this definition"></a></dt>
<dd><p>Transports source samples <span class="math notranslate nohighlight">\(\mathbf{X_s}\)</span> onto target ones <span class="math notranslate nohighlight">\(\mathbf{X_t}\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>Xs</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#list" title="(in Python v3.15)"><em>list</em></a><em> of </em><em>K array-like objects</em><em>, </em><em>shape K x</em><em> (</em><em>nk_source_samples</em><em>, </em><em>n_features</em><em>)</em>) – A list of the training input samples.</p></li>
<li><p><strong>ys</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#list" title="(in Python v3.15)"><em>list</em></a><em> of </em><em>K array-like objects</em><em>, </em><em>shape K x</em><em> (</em><em>nk_source_samples</em><em>,</em><em>)</em>) – A list of the class labels</p></li>
<li><p><strong>Xt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>, </em><em>n_features</em><em>)</em>) – The training input samples.</p></li>
<li><p><strong>yt</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_target_samples</em><em>,</em><em>)</em>) – <p>The class labels. If some target samples are unlabelled, fill the
<span class="math notranslate nohighlight">\(\mathbf{y_t}\)</span>’s elements with -1.</p>