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<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#sphx-glr-download-auto-examples-plot-debias-sink-div-py"><span class="std std-ref">Go to the end</span></a>
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<section class="sphx-glr-example-title" id="sinkhorn-divergence-and-debiased-ot-solvers">
<span id="sphx-glr-auto-examples-plot-debias-sink-div-py"></span><h1>Sinkhorn Divergence and Debiased OT solvers<a class="headerlink" href="#sinkhorn-divergence-and-debiased-ot-solvers" title="Link to this heading"></a></h1>
<p>This example shows how to use the debiased OT solvers in <cite>ot.solve_sample</cite> to
compute Sinkhorn divergences and debiased Minibatch solutions. The debiased OT solvers
can be used with balanced and unbalanced OT problems, and with different
regularization types (entropic, L2, group lasso).</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Remi Flamary <remi.flamary@polytechnique.edu></span>
<span class="c1">#</span>
<span class="c1"># License: MIT License</span>
<span class="c1"># sphinx_gallery_thumbnail_number = 3</span>
</pre></div>
</div>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pylab</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">pl</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">ot</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">ot.plot</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">ot.datasets</span><span class="w"> </span><span class="kn">import</span> <span class="n">make_1D_gauss</span> <span class="k">as</span> <span class="n">gauss</span>
</pre></div>
</div>
<section id="generate-data">
<h2>Generate data<a class="headerlink" href="#generate-data" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">sample_ball</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">,</span> <span class="n">radius</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">)):</span>
<a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.seed.html#numpy.random.seed" title="numpy.random.seed" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span></a><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">theta</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.rand.html#numpy.random.rand" title="numpy.random.rand" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">)</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">radius</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.rand.html#numpy.random.rand" title="numpy.random.rand" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">))</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">cos</span></a><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">+</span> <span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">+</span> <span class="n">center</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="k">return</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.stack.html#numpy.stack" title="numpy.stack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">stack</span></a><span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">sample_two_balls</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">,</span> <span class="n">radius</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">sep</span></a><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="k">assert</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"n must be even"</span>
<span class="n">centers</span> <span class="o">=</span> <span class="p">((</span><span class="o">-</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">sep</span></a><span class="p">,</span> <span class="o">-</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">sep</span></a><span class="p">),</span> <span class="p">(</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">sep</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">sep</span></a><span class="p">))</span>
<span class="n">n_half</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a> <span class="o">//</span> <span class="mi">2</span>
<span class="n">X1</span> <span class="o">=</span> <span class="n">sample_ball</span><span class="p">(</span><span class="n">n_half</span><span class="p">,</span> <span class="n">radius</span><span class="p">,</span> <span class="n">centers</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">X2</span> <span class="o">=</span> <span class="n">sample_ball</span><span class="p">(</span><span class="n">n_half</span><span class="p">,</span> <span class="n">radius</span><span class="p">,</span> <span class="n">centers</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">perm</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.permutation.html#numpy.random.permutation" title="numpy.random.permutation" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">permutation</span></a><span class="p">(</span><span class="n">n_half</span> <span class="o">*</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.vstack.html#numpy.vstack" title="numpy.vstack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">vstack</span></a><span class="p">((</span><span class="n">X1</span><span class="p">,</span> <span class="n">X2</span><span class="p">))</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">perm</span><span class="p">]</span>
<span class="k">return</span> <span class="n">X</span>
<a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a> <span class="o">=</span> <span class="mi">50</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a> <span class="o">=</span> <span class="n">sample_ball</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">,</span> <span class="n">radius</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a> <span class="o">=</span> <span class="n">sample_two_balls</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">,</span> <span class="n">radius</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">sep</span></a><span class="o">=</span><span class="mf">1.5</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Source distribution"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.7</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Target distribution"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.7</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Two distributions"</span><span class="p">)</span>
<a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span></a> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">()</span>
</pre></div>
</div>
<img src="../_images/sphx_glr_plot_debias_sink_div_001.png" srcset="../_images/sphx_glr_plot_debias_sink_div_001.png" alt="Two distributions" class = "sphx-glr-single-img"/></section>
<section id="compute-sinkhorn-divergence-and-visualize-plans">
<h2>Compute Sinkhorn divergence and visualize plans<a class="headerlink" href="#compute-sinkhorn-divergence-and-visualize-plans" title="Link to this heading"></a></h2>
<p>The Sinkhorn divergence is computed by setting the <cite>debias</cite> parameter to
<cite>True</cite> in the <cite>ot.solve_sample</cite> function. The resulting value is the Sinkhorn
divergence. The Sinkhorn divergences is computed as:</p>
<div class="math notranslate nohighlight">
\[S_\epsilon(\mu, \nu) = OT_\epsilon(\mu, \nu) - \frac{1}{2} OT_\epsilon(\mu, \mu) - \frac{1}{2} OT_\epsilon(\nu, \nu)\]</div>
<p>The entropic OT plans for each of those terms can be accessed in the <cite>log</cite>
attribute of the result, and can be visualized using the
<cite>ot.plot.plot2D_samples_mat</cite> function.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="../gen_modules/ot.utils.html#id56" title="ot.utils.OTResult" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">res</span></a> <span class="o">=</span> <a href="../all.html#ot.solve_sample" title="ot.solve_sample" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">solve_sample</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">reg</span></a><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">debias</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Sinkhorn divergence: "</span><span class="p">,</span> <a href="../gen_modules/ot.utils.html#id83" title="ot.utils.OTResult.value" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">value</span></a><span class="p">)</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_11</span></a> <span class="o">=</span> <a href="../gen_modules/ot.utils.html#id73" title="ot.utils.OTResult.log" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">log</span></a><span class="p">[</span><span class="s2">"res_aa"</span><span class="p">]</span><span class="o">.</span><span class="n">plan</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_12</span></a> <span class="o">=</span> <a href="../gen_modules/ot.utils.html#id73" title="ot.utils.OTResult.log" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">log</span></a><span class="p">[</span><span class="s2">"res_ab"</span><span class="p">]</span><span class="o">.</span><span class="n">plan</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_22</span></a> <span class="o">=</span> <a href="../gen_modules/ot.utils.html#id73" title="ot.utils.OTResult.log" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">log</span></a><span class="p">[</span><span class="s2">"res_bb"</span><span class="p">]</span><span class="o">.</span><span class="n">plan</span>
<span class="c1">#</span>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#id1" title="ot.plot.plot2D_samples_mat" class="sphx-glr-backref-module-ot-plot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">plot2D_samples_mat</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_11</span></a><span class="p">,</span> <span class="n">thr</span><span class="o">=</span><span class="mf">0.05</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Source distribution"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Plan between source and source"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#id1" title="ot.plot.plot2D_samples_mat" class="sphx-glr-backref-module-ot-plot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">plot2D_samples_mat</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_12</span></a><span class="p">,</span> <span class="n">thr</span><span class="o">=</span><span class="mf">0.05</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Source distribution"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Target distribution"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Plan between source and target"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#id1" title="ot.plot.plot2D_samples_mat" class="sphx-glr-backref-module-ot-plot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">plot2D_samples_mat</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_22</span></a><span class="p">,</span> <span class="n">thr</span><span class="o">=</span><span class="mf">0.05</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Target distribution"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Plan between target and target"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../_images/sphx_glr_plot_debias_sink_div_002.png" srcset="../_images/sphx_glr_plot_debias_sink_div_002.png" alt="Plan between source and source, Plan between source and target, Plan between target and target" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>/home/circleci/project/ot/bregman/_sinkhorn.py:902: UserWarning: Sinkhorn did not converge. You might want to increase the number of iterations `numItermax` or the regularization parameter `reg`.
warnings.warn(
Sinkhorn divergence: 3.1176410736749864
Text(0.5, 1.0, 'Plan between target and target')
</pre></div>
</div>
</section>
<section id="debiased-minibatch-ot">
<h2>Debiased Minibatch OT<a class="headerlink" href="#debiased-minibatch-ot" title="Link to this heading"></a></h2>
<p>Doing OT on minibatches leads to a similar bias than using entropic
regularization since the average OT plan is densified due to the stochasticity
of the minibatch sampling. On a given minibatch, the debiased loss can be
computed by setting the <cite>debias</cite> parameter to <a href="#id1"><span class="problematic" id="id2">`</span></a>’split’<a href="#id3"><span class="problematic" id="id4">`</span></a>that split the data
points in each distributions in two and computes the debias OT loss as:</p>
<div class="math notranslate nohighlight">
\[\tilde{OT}_m(\mu, \nu) = \frac{1}{2}(\hat{OT}_m(\mu_1, \nu_1) + \hat{OT}_m(\mu_2, \nu_2) - \hat{OT}_m(\nu_1, \nu_2) - \hat{OT}_m(\mu_1, \nu_2))\]</div>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="../gen_modules/ot.utils.html#id56" title="ot.utils.OTResult" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">res</span></a> <span class="o">=</span> <a href="../all.html#ot.solve_sample" title="ot.solve_sample" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">solve_sample</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">,</span> <span class="n">debias</span><span class="o">=</span><span class="s2">"split"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Debiased minibatch OT loss: "</span><span class="p">,</span> <a href="../gen_modules/ot.utils.html#id83" title="ot.utils.OTResult.value" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">value</span></a><span class="p">)</span>
<span class="c1"># recover the plans for each of the four terms in the debiased loss</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_11</span></a> <span class="o">=</span> <a href="../gen_modules/ot.utils.html#id73" title="ot.utils.OTResult.log" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">log</span></a><span class="p">[</span><span class="s2">"res_aa"</span><span class="p">]</span><span class="o">.</span><span class="n">plan</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_12</span></a> <span class="o">=</span> <a href="../gen_modules/ot.utils.html#id73" title="ot.utils.OTResult.log" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">log</span></a><span class="p">[</span><span class="s2">"res_ab1"</span><span class="p">]</span><span class="o">.</span><span class="n">plan</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_21</span></a> <span class="o">=</span> <a href="../gen_modules/ot.utils.html#id73" title="ot.utils.OTResult.log" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">log</span></a><span class="p">[</span><span class="s2">"res_ab2"</span><span class="p">]</span><span class="o">.</span><span class="n">plan</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_22</span></a> <span class="o">=</span> <a href="../gen_modules/ot.utils.html#id73" title="ot.utils.OTResult.log" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">log</span></a><span class="p">[</span><span class="s2">"res_bb"</span><span class="p">]</span><span class="o">.</span><span class="n">plan</span>
<a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a1</span></a> <span class="o">=</span> <a href="../gen_modules/ot.utils.html#id73" title="ot.utils.OTResult.log" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">log</span></a><span class="p">[</span><span class="s2">"sel_a1"</span><span class="p">]</span>
<a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a2</span></a> <span class="o">=</span> <a href="../gen_modules/ot.utils.html#id73" title="ot.utils.OTResult.log" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">log</span></a><span class="p">[</span><span class="s2">"sel_a2"</span><span class="p">]</span>
<a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b1</span></a> <span class="o">=</span> <a href="../gen_modules/ot.utils.html#id73" title="ot.utils.OTResult.log" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">log</span></a><span class="p">[</span><span class="s2">"sel_b1"</span><span class="p">]</span>
<a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b2</span></a> <span class="o">=</span> <a href="../gen_modules/ot.utils.html#id73" title="ot.utils.OTResult.log" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-property"><span class="n">res</span><span class="o">.</span><span class="n">log</span></a><span class="p">[</span><span class="s2">"sel_b2"</span><span class="p">]</span>
<a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">nb1</span></a> <span class="o">=</span> <a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_11</span><span class="o">.</span><span class="n">shape</span></a><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">nb2</span></a> <span class="o">=</span> <a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_22</span><span class="o">.</span><span class="n">shape</span></a><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
<span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a1</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a1</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"$\mu_1$"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a2</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a2</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$\mu_2$"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C0"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b1</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b1</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$\nu_1$"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b2</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b2</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$\nu_2$"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Minibatch split"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#id1" title="ot.plot.plot2D_samples_mat" class="sphx-glr-backref-module-ot-plot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">plot2D_samples_mat</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a1</span></a><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a2</span></a><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_11</span></a><span class="p">,</span> <span class="n">thr</span><span class="o">=</span><span class="mf">0.05</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a1</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a1</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a2</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a2</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
<span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"C0"</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Plan between source and source"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#id1" title="ot.plot.plot2D_samples_mat" class="sphx-glr-backref-module-ot-plot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">plot2D_samples_mat</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a1</span></a><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b1</span></a><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_12</span></a><span class="p">,</span> <span class="n">thr</span><span class="o">=</span><span class="mf">0.05</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#id1" title="ot.plot.plot2D_samples_mat" class="sphx-glr-backref-module-ot-plot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">plot2D_samples_mat</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a2</span></a><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b2</span></a><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_21</span></a><span class="p">,</span> <span class="n">thr</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a1</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a1</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Source distribution"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b1</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b1</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Target distribution"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a2</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_a2</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"Source distribution"</span><span class="p">,</span>
<span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"C0"</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b2</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b2</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"Target distribution"</span><span class="p">,</span>
<span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Plan between source and target"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#id1" title="ot.plot.plot2D_samples_mat" class="sphx-glr-backref-module-ot-plot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">plot2D_samples_mat</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b1</span></a><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b2</span></a><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plan_22</span></a><span class="p">,</span> <span class="n">thr</span><span class="o">=</span><span class="mf">0.05</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b1</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b1</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Target distribution"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b2</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#slice" title="builtins.slice" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sel_b2</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"Target distribution"</span><span class="p">,</span>
<span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Plan between target and target"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../_images/sphx_glr_plot_debias_sink_div_003.png" srcset="../_images/sphx_glr_plot_debias_sink_div_003.png" alt="Minibatch split, Plan between source and source, Plan between source and target, Plan between target and target" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>/home/circleci/project/examples/plot_debias_sink_div.py:148: SyntaxWarning: invalid escape sequence '\m'
pl.scatter(x1[sel_a1, 0], x1[sel_a1, 1], label="$\mu_1$", zorder=2)
Debiased minibatch OT loss: 1.5822357572175718
Text(0.5, 1.0, 'Plan between target and target')
</pre></div>
</div>
</section>
<section id="comparison-of-the-divergences">
<h2>Comparison of the divergences<a class="headerlink" href="#comparison-of-the-divergences" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">reg</span></a> <span class="o">=</span> <span class="mf">0.1</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sep_list</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sink_list</span></a> <span class="o">=</span> <span class="p">[]</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sink_div_list</span></a> <span class="o">=</span> <span class="p">[]</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ot_mb_list</span></a> <span class="o">=</span> <span class="p">[]</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ot_mb_sink_list</span></a> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">sep</span></a> <span class="ow">in</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sep_list</span></a><span class="p">:</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2sep</span></a> <span class="o">=</span> <span class="n">sample_two_balls</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">,</span> <span class="n">radius</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">sep</span></a><span class="o">=</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">sep</span></a><span class="p">)</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sink_list</span></a><span class="o">.</span><span class="n">append</span><span class="p">(</span>
<a href="../all.html#ot.solve_sample" title="ot.solve_sample" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">solve_sample</span></a><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">,</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2sep</span></a><span class="p">,</span>
<a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">reg</span></a><span class="o">=</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">reg</span></a><span class="p">,</span>
<span class="p">)</span><span class="o">.</span><span class="n">value</span>
<span class="p">)</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sink_div_list</span></a><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="../all.html#ot.solve_sample" title="ot.solve_sample" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">solve_sample</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2sep</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">reg</span></a><span class="o">=</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">reg</span></a><span class="p">,</span> <span class="n">debias</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span><span class="o">.</span><span class="n">value</span><span class="p">)</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ot_mb_list</span></a><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="../all.html#ot.solve_sample" title="ot.solve_sample" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">solve_sample</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2sep</span></a><span class="p">,</span> <span class="n">debias</span><span class="o">=</span><span class="s2">"split"</span><span class="p">)</span><span class="o">.</span><span class="n">value</span><span class="p">)</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ot_mb_sink_list</span></a><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="../all.html#ot.solve_sample" title="ot.solve_sample" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">solve_sample</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x1</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x2sep</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">reg</span></a><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">debias</span><span class="o">=</span><span class="s2">"split"</span><span class="p">)</span><span class="o">.</span><span class="n">value</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sep_list</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sink_list</span></a><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Sinkhorn loss"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C0"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sep_list</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sink_div_list</span></a><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Sinkhorn divergence"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sep_list</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ot_mb_list</span></a><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Debiased MB OT"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C2"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sep_list</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ot_mb_sink_list</span></a><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Debiased MB Sinkhorn"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C3"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"Separation between distributions"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"Loss/Divergence"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Comparison of biased VS debiased OT losses"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
<span class="n">pl</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
</pre></div>
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<img src="../_images/sphx_glr_plot_debias_sink_div_004.png" srcset="../_images/sphx_glr_plot_debias_sink_div_004.png" alt="Comparison of biased VS debiased OT losses" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span><matplotlib.legend.Legend object at 0x7e97aaa2ef60>
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