diff --git a/_downloads/071683bb9f5d321841ee9dd62eee27a4/plot_sim_red_syn.zip b/_downloads/071683bb9f5d321841ee9dd62eee27a4/plot_sim_red_syn.zip
index e942f58a..42f8c7eb 100644
Binary files a/_downloads/071683bb9f5d321841ee9dd62eee27a4/plot_sim_red_syn.zip and b/_downloads/071683bb9f5d321841ee9dd62eee27a4/plot_sim_red_syn.zip differ
diff --git a/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip b/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip
index 6d949b11..bd851080 100644
Binary files a/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip and b/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip differ
diff --git a/_downloads/17dd9833b54c0c0905f696d14e67b05d/plot_bootstrapping.zip b/_downloads/17dd9833b54c0c0905f696d14e67b05d/plot_bootstrapping.zip
index d4dd7405..9920f4db 100644
Binary files a/_downloads/17dd9833b54c0c0905f696d14e67b05d/plot_bootstrapping.zip and b/_downloads/17dd9833b54c0c0905f696d14e67b05d/plot_bootstrapping.zip differ
diff --git a/_downloads/1e58f0eaeee8456990c2959bfc1babe9/plot_oinfo.zip b/_downloads/1e58f0eaeee8456990c2959bfc1babe9/plot_oinfo.zip
index 083ad736..d44d7e2c 100644
Binary files a/_downloads/1e58f0eaeee8456990c2959bfc1babe9/plot_oinfo.zip and b/_downloads/1e58f0eaeee8456990c2959bfc1babe9/plot_oinfo.zip differ
diff --git a/_downloads/31d2b25c7ef60a5789246c25d83787c6/plot_ml_vs_it.zip b/_downloads/31d2b25c7ef60a5789246c25d83787c6/plot_ml_vs_it.zip
index 37d0035a..429f0bae 100644
Binary files a/_downloads/31d2b25c7ef60a5789246c25d83787c6/plot_ml_vs_it.zip and b/_downloads/31d2b25c7ef60a5789246c25d83787c6/plot_ml_vs_it.zip differ
diff --git a/_downloads/34da59110fbcc6d2797595ef80bd7328/plot_inspect_results.zip b/_downloads/34da59110fbcc6d2797595ef80bd7328/plot_inspect_results.zip
index 107731dc..fe3ceb54 100644
Binary files a/_downloads/34da59110fbcc6d2797595ef80bd7328/plot_inspect_results.zip and b/_downloads/34da59110fbcc6d2797595ef80bd7328/plot_inspect_results.zip differ
diff --git a/_downloads/4edd620b8310fd78193d26c454d1ca13/plot_rsi.zip b/_downloads/4edd620b8310fd78193d26c454d1ca13/plot_rsi.zip
index dc1e70fa..1636eaae 100644
Binary files a/_downloads/4edd620b8310fd78193d26c454d1ca13/plot_rsi.zip and b/_downloads/4edd620b8310fd78193d26c454d1ca13/plot_rsi.zip differ
diff --git a/_downloads/523f753ee18fc36accf251c60a59f685/tuto_jax.zip b/_downloads/523f753ee18fc36accf251c60a59f685/tuto_jax.zip
index b5933395..4a7e952d 100644
Binary files a/_downloads/523f753ee18fc36accf251c60a59f685/tuto_jax.zip and b/_downloads/523f753ee18fc36accf251c60a59f685/tuto_jax.zip differ
diff --git a/_downloads/58edfc8265b6af8f03b242ea4656b10f/plot_syn_phiID.zip b/_downloads/58edfc8265b6af8f03b242ea4656b10f/plot_syn_phiID.zip
index 94f415cd..1e533fb6 100644
Binary files a/_downloads/58edfc8265b6af8f03b242ea4656b10f/plot_syn_phiID.zip and b/_downloads/58edfc8265b6af8f03b242ea4656b10f/plot_syn_phiID.zip differ
diff --git a/_downloads/675ecb045af78b81dbd01cbea1d59fa1/plot_entropies_mvar.zip b/_downloads/675ecb045af78b81dbd01cbea1d59fa1/plot_entropies_mvar.zip
index 954a49a3..a79982f8 100644
Binary files a/_downloads/675ecb045af78b81dbd01cbea1d59fa1/plot_entropies_mvar.zip and b/_downloads/675ecb045af78b81dbd01cbea1d59fa1/plot_entropies_mvar.zip differ
diff --git a/_downloads/69a8436c098192f96580d8e9cd2f5d4d/plot_entropies.zip b/_downloads/69a8436c098192f96580d8e9cd2f5d4d/plot_entropies.zip
index fc5e9971..7268eec0 100644
Binary files a/_downloads/69a8436c098192f96580d8e9cd2f5d4d/plot_entropies.zip and b/_downloads/69a8436c098192f96580d8e9cd2f5d4d/plot_entropies.zip differ
diff --git a/_downloads/6df867479300c4bb75728e18f2fcc139/plot_infotopo.zip b/_downloads/6df867479300c4bb75728e18f2fcc139/plot_infotopo.zip
index 433953b6..ec4ea5a5 100644
Binary files a/_downloads/6df867479300c4bb75728e18f2fcc139/plot_infotopo.zip and b/_downloads/6df867479300c4bb75728e18f2fcc139/plot_infotopo.zip differ
diff --git a/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip b/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip
index 9a64af66..39293b1f 100644
Binary files a/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip and b/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip differ
diff --git a/_downloads/88e7424e21f0645541ebb2bb32c0cfda/plot_mi_high_dimensional.zip b/_downloads/88e7424e21f0645541ebb2bb32c0cfda/plot_mi_high_dimensional.zip
index d51ed954..d53e66f0 100644
Binary files a/_downloads/88e7424e21f0645541ebb2bb32c0cfda/plot_mi_high_dimensional.zip and b/_downloads/88e7424e21f0645541ebb2bb32c0cfda/plot_mi_high_dimensional.zip differ
diff --git a/_downloads/cb54325e1a49091788b29a83388e5628/plot_mi.zip b/_downloads/cb54325e1a49091788b29a83388e5628/plot_mi.zip
index 96a7c2e1..acd4d902 100644
Binary files a/_downloads/cb54325e1a49091788b29a83388e5628/plot_mi.zip and b/_downloads/cb54325e1a49091788b29a83388e5628/plot_mi.zip differ
diff --git a/_downloads/e45bdd4f8818a611325b90cc89a08e31/tuto_core.zip b/_downloads/e45bdd4f8818a611325b90cc89a08e31/tuto_core.zip
index 67d63810..eafbecec 100644
Binary files a/_downloads/e45bdd4f8818a611325b90cc89a08e31/tuto_core.zip and b/_downloads/e45bdd4f8818a611325b90cc89a08e31/tuto_core.zip differ
diff --git a/_downloads/f599913a46208f71dc47a6311a232f10/plot_syn_red_mmi.zip b/_downloads/f599913a46208f71dc47a6311a232f10/plot_syn_red_mmi.zip
index d0b33eba..4c3f11ae 100644
Binary files a/_downloads/f599913a46208f71dc47a6311a232f10/plot_syn_red_mmi.zip and b/_downloads/f599913a46208f71dc47a6311a232f10/plot_syn_red_mmi.zip differ
diff --git a/_downloads/f97532cb8c6e95a143612bdc254c6548/plot_entropy_high_dimensional.zip b/_downloads/f97532cb8c6e95a143612bdc254c6548/plot_entropy_high_dimensional.zip
index f1503a36..2a3c09be 100644
Binary files a/_downloads/f97532cb8c6e95a143612bdc254c6548/plot_entropy_high_dimensional.zip and b/_downloads/f97532cb8c6e95a143612bdc254c6548/plot_entropy_high_dimensional.zip differ
diff --git a/_modules/hoi/utils/stats.html b/_modules/hoi/utils/stats.html
index e21d4fa0..803b3bfe 100644
--- a/_modules/hoi/utils/stats.html
+++ b/_modules/hoi/utils/stats.html
@@ -617,6 +617,8 @@ <h1>Source code for hoi.utils.stats</h1><div class="highlight"><pre>
     <span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
 
     <span class="n">hoi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">hoi</span><span class="p">)</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
+    <span class="k">if</span> <span class="ow">not</span> <span class="n">hoi</span><span class="o">.</span><span class="n">ndim</span><span class="p">:</span>
+        <span class="n">hoi</span> <span class="o">=</span> <span class="n">hoi</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
 
     <span class="c1"># get order and multiplets</span>
     <span class="k">if</span> <span class="n">model</span><span class="p">:</span>
diff --git a/auto_examples/it/plot_entropies.html b/auto_examples/it/plot_entropies.html
index cb68bb11..9c48a5a1 100644
--- a/auto_examples/it/plot_entropies.html
+++ b/auto_examples/it/plot_entropies.html
@@ -591,7 +591,7 @@ <h2>Entropy of data sampled from an exponential distribution<a class="headerlink
 <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
 </pre></div>
 </div>
-<img src="../../_images/sphx_glr_plot_entropies_003.png" srcset="../../_images/sphx_glr_plot_entropies_003.png" alt="Comparison of entropy estimators when the data are sampled from a exponential distribution" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 20.308 seconds)</p>
+<img src="../../_images/sphx_glr_plot_entropies_003.png" srcset="../../_images/sphx_glr_plot_entropies_003.png" alt="Comparison of entropy estimators when the data are sampled from a exponential distribution" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 20.392 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-it-plot-entropies-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/a1ef8dbbc19c785bec2a5cc12335798e/plot_entropies.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_entropies.ipynb</span></code></a></p>
diff --git a/auto_examples/it/plot_entropies_mvar.html b/auto_examples/it/plot_entropies_mvar.html
index 4fc23fd4..3ecaa542 100644
--- a/auto_examples/it/plot_entropies_mvar.html
+++ b/auto_examples/it/plot_entropies_mvar.html
@@ -567,7 +567,7 @@ <h2>Comparison of estimators<a class="headerlink" href="#comparison-of-estimator
 <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
 </pre></div>
 </div>
-<img src="../../_images/sphx_glr_plot_entropies_mvar_001.png" srcset="../../_images/sphx_glr_plot_entropies_mvar_001.png" alt="2-dimensional multivariate normal, 4-dimensional multivariate normal, 6-dimensional multivariate normal, 8-dimensional multivariate normal" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 31.995 seconds)</p>
+<img src="../../_images/sphx_glr_plot_entropies_mvar_001.png" srcset="../../_images/sphx_glr_plot_entropies_mvar_001.png" alt="2-dimensional multivariate normal, 4-dimensional multivariate normal, 6-dimensional multivariate normal, 8-dimensional multivariate normal" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 32.313 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-it-plot-entropies-mvar-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/4a44859767d9a5abc2a411d84f3464c0/plot_entropies_mvar.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_entropies_mvar.ipynb</span></code></a></p>
diff --git a/auto_examples/it/plot_entropy_high_dimensional.html b/auto_examples/it/plot_entropy_high_dimensional.html
index 33227e26..c96346b2 100644
--- a/auto_examples/it/plot_entropy_high_dimensional.html
+++ b/auto_examples/it/plot_entropy_high_dimensional.html
@@ -564,7 +564,7 @@ <h2>Definition of entropy estimators<a class="headerlink" href="#definition-of-e
 <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
 </pre></div>
 </div>
-<img src="../../_images/sphx_glr_plot_entropy_high_dimensional_001.png" srcset="../../_images/sphx_glr_plot_entropy_high_dimensional_001.png" alt="Comparison of entropy estimators when the data is high-dimensional, Mode: dense, Mode: sparse" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 24.189 seconds)</p>
+<img src="../../_images/sphx_glr_plot_entropy_high_dimensional_001.png" srcset="../../_images/sphx_glr_plot_entropy_high_dimensional_001.png" alt="Comparison of entropy estimators when the data is high-dimensional, Mode: dense, Mode: sparse" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 24.213 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-it-plot-entropy-high-dimensional-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/5643cba16e58fee7f03fd86cb1cd9854/plot_entropy_high_dimensional.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_entropy_high_dimensional.ipynb</span></code></a></p>
diff --git a/auto_examples/it/plot_mi.html b/auto_examples/it/plot_mi.html
index 684495ca..07f307cd 100644
--- a/auto_examples/it/plot_mi.html
+++ b/auto_examples/it/plot_mi.html
@@ -556,7 +556,7 @@ <h2>MI of data sampled from normal distribution<a class="headerlink" href="#mi-o
 <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
 </pre></div>
 </div>
-<img src="../../_images/sphx_glr_plot_mi_001.png" srcset="../../_images/sphx_glr_plot_mi_001.png" alt="Comparison of MI estimators when the data are sampled from a normal distribution" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 20.547 seconds)</p>
+<img src="../../_images/sphx_glr_plot_mi_001.png" srcset="../../_images/sphx_glr_plot_mi_001.png" alt="Comparison of MI estimators when the data are sampled from a normal distribution" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 20.688 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-it-plot-mi-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/f14e92090ebeb63084124f7809315b90/plot_mi.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_mi.ipynb</span></code></a></p>
diff --git a/auto_examples/it/plot_mi_high_dimensional.html b/auto_examples/it/plot_mi_high_dimensional.html
index b6a037c4..327105ed 100644
--- a/auto_examples/it/plot_mi_high_dimensional.html
+++ b/auto_examples/it/plot_mi_high_dimensional.html
@@ -568,7 +568,7 @@ <h2>MI of data sampled from splitted multinormal distribution<a class="headerlin
 <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
 </pre></div>
 </div>
-<img src="../../_images/sphx_glr_plot_mi_high_dimensional_001.png" srcset="../../_images/sphx_glr_plot_mi_high_dimensional_001.png" alt="Comparison of MI estimators when the data is high-dimensional, Mode: dense, Mode: sparse" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 29.919 seconds)</p>
+<img src="../../_images/sphx_glr_plot_mi_high_dimensional_001.png" srcset="../../_images/sphx_glr_plot_mi_high_dimensional_001.png" alt="Comparison of MI estimators when the data is high-dimensional, Mode: dense, Mode: sparse" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 30.009 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-it-plot-mi-high-dimensional-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/c2e64540f3d3ca92b3a73d57756734af/plot_mi_high_dimensional.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_mi_high_dimensional.ipynb</span></code></a></p>
diff --git a/auto_examples/it/sg_execution_times.html b/auto_examples/it/sg_execution_times.html
index afd6ccca..f1ee3d59 100644
--- a/auto_examples/it/sg_execution_times.html
+++ b/auto_examples/it/sg_execution_times.html
@@ -404,7 +404,7 @@ <h1>Computation times</h1>
                   
   <section id="computation-times">
 <span id="sphx-glr-auto-examples-it-sg-execution-times"></span><h1>Computation times<a class="headerlink" href="#computation-times" title="Link to this heading">#</a></h1>
-<p><strong>02:07.188</strong> total execution time for 6 files <strong>from auto_examples/it</strong>:</p>
+<p><strong>02:07.848</strong> total execution time for 6 files <strong>from auto_examples/it</strong>:</p>
 <div class="docutils container">
 <style scoped>
 <link href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/5.3.0/css/bootstrap.min.css" rel="stylesheet" />
@@ -426,27 +426,27 @@ <h1>Computation times</h1>
 </thead>
 <tbody>
 <tr class="row-even"><td><p><a class="reference internal" href="plot_entropies_mvar.html#sphx-glr-auto-examples-it-plot-entropies-mvar-py"><span class="std std-ref">Comparison of entropy estimators for a multivariate normal</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_entropies_mvar.py</span></code>)</p></td>
-<td><p>00:31.995</p></td>
+<td><p>00:32.313</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="plot_mi_high_dimensional.html#sphx-glr-auto-examples-it-plot-mi-high-dimensional-py"><span class="std std-ref">Comparison of MI estimators with high-dimensional data</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_mi_high_dimensional.py</span></code>)</p></td>
-<td><p>00:29.919</p></td>
+<td><p>00:30.009</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="plot_entropy_high_dimensional.html#sphx-glr-auto-examples-it-plot-entropy-high-dimensional-py"><span class="std std-ref">Comparison of entropy estimators with high-dimensional data</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_entropy_high_dimensional.py</span></code>)</p></td>
-<td><p>00:24.189</p></td>
+<td><p>00:24.213</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="plot_mi.html#sphx-glr-auto-examples-it-plot-mi-py"><span class="std std-ref">Comparison of mutual-information estimators</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_mi.py</span></code>)</p></td>
-<td><p>00:20.547</p></td>
+<td><p>00:20.688</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="plot_entropies.html#sphx-glr-auto-examples-it-plot-entropies-py"><span class="std std-ref">Comparison of entropy estimators for various distributions</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_entropies.py</span></code>)</p></td>
-<td><p>00:20.308</p></td>
+<td><p>00:20.392</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="tuto_core.html#sphx-glr-auto-examples-it-tuto-core-py"><span class="std std-ref">Introduction to core information theoretical metrics</span></a> (<code class="docutils literal notranslate"><span class="pre">tuto_core.py</span></code>)</p></td>
-<td><p>00:00.231</p></td>
+<td><p>00:00.232</p></td>
 <td><p>0.0</p></td>
 </tr>
 </tbody>
diff --git a/auto_examples/it/tuto_core.html b/auto_examples/it/tuto_core.html
index 2586df9d..621416e6 100644
--- a/auto_examples/it/tuto_core.html
+++ b/auto_examples/it/tuto_core.html
@@ -494,7 +494,7 @@ <h2>Mutual information<a class="headerlink" href="#mutual-information" title="Li
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Mutual information between x and y: 0.00
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 0.231 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 0.232 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-it-tuto-core-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/c07170058282c5cf6f9dde4efceadb96/tuto_core.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">tuto_core.ipynb</span></code></a></p>
diff --git a/auto_examples/metrics/plot_infotopo.html b/auto_examples/metrics/plot_infotopo.html
index ac99ec02..f809880d 100644
--- a/auto_examples/metrics/plot_infotopo.html
+++ b/auto_examples/metrics/plot_infotopo.html
@@ -471,11 +471,11 @@ <h2>Spatial spreading : the problem with the O-information<a class="headerlink"
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/5 [00:00&lt;?,       ?it/s]
- 20%|██        | Oinfo (3):  1/5 [00:00&lt;00:01,    2.78it/s]
- 40%|████      | Oinfo (4):  2/5 [00:00&lt;00:00,    3.45it/s]
- 60%|██████    | Oinfo (5):  3/5 [00:01&lt;00:00,    2.80it/s]
- 80%|████████  | Oinfo (6):  4/5 [00:01&lt;00:00,    2.60it/s]
-100%|██████████| Oinfo (7):  5/5 [00:01&lt;00:00,    2.63it/s]
+ 20%|██        | Oinfo (3):  1/5 [00:00&lt;00:01,    2.80it/s]
+ 40%|████      | Oinfo (4):  2/5 [00:00&lt;00:00,    3.47it/s]
+ 60%|██████    | Oinfo (5):  3/5 [00:01&lt;00:00,    2.82it/s]
+ 80%|████████  | Oinfo (6):  4/5 [00:01&lt;00:00,    2.57it/s]
+100%|██████████| Oinfo (7):  5/5 [00:01&lt;00:00,    2.58it/s]
 </pre></div>
 </div>
 <p>Now we can plot the landscape. This landscape show the values of HOI for
@@ -528,19 +528,19 @@ <h2>Multiplet isolation using the Topological Information<a class="headerlink" h
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/7 [00:00&lt;?,       ?it/s]
- 14%|█▍        | Entropy H(1):  1/7 [00:00&lt;00:00,    7.78it/s]
- 29%|██▊       | Entropy H(2):  2/7 [00:00&lt;00:00,    7.87it/s]
- 43%|████▎     | Entropy H(3):  3/7 [00:00&lt;00:00,    8.02it/s]
- 57%|█████▋    | Entropy H(4):  4/7 [00:00&lt;00:00,    8.47it/s]
- 71%|███████▏  | Entropy H(5):  5/7 [00:00&lt;00:00,    8.74it/s]
- 86%|████████▌ | Entropy H(6):  6/7 [00:00&lt;00:00,    8.99it/s]
-100%|██████████| Entropy H(7):  7/7 [00:00&lt;00:00,    9.23it/s]
+ 14%|█▍        | Entropy H(1):  1/7 [00:00&lt;00:00,    8.35it/s]
+ 29%|██▊       | Entropy H(2):  2/7 [00:00&lt;00:00,    8.05it/s]
+ 43%|████▎     | Entropy H(3):  3/7 [00:00&lt;00:00,    8.06it/s]
+ 57%|█████▋    | Entropy H(4):  4/7 [00:00&lt;00:00,    8.45it/s]
+ 71%|███████▏  | Entropy H(5):  5/7 [00:00&lt;00:00,    8.76it/s]
+ 86%|████████▌ | Entropy H(6):  6/7 [00:00&lt;00:00,    8.98it/s]
+100%|██████████| Entropy H(7):  7/7 [00:00&lt;00:00,    9.24it/s]
 
 
 Mutual information:   0%|          | 0/99 [00:00&lt;?, ?it/s]
 
 
-Mutual information: 100%|██████████| 99/99 [00:00&lt;00:00, 30482.76it/s]
+Mutual information: 100%|██████████| 99/99 [00:00&lt;00:00, 29493.29it/s]
 </pre></div>
 </div>
 <p>Again, we can plot the landscape. This time, as we can see, there’s no more
@@ -574,7 +574,7 @@ <h2>Multiplet isolation using the Topological Information<a class="headerlink" h
 9     32      3 -0.090620     [3, 4, 6]
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.378 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.402 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-metrics-plot-infotopo-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/ece4d51dfdf0dbf7235e94595766e7c5/plot_infotopo.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_infotopo.ipynb</span></code></a></p>
diff --git a/auto_examples/metrics/plot_oinfo.html b/auto_examples/metrics/plot_oinfo.html
index be1d12d2..a0e20533 100644
--- a/auto_examples/metrics/plot_oinfo.html
+++ b/auto_examples/metrics/plot_oinfo.html
@@ -496,7 +496,7 @@ <h3>Total Correlation (TC)<a class="headerlink" href="#total-correlation-tc" tit
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| TC (3):  1/1 [00:00&lt;00:00,    3.89it/s]
+100%|██████████| TC (3):  1/1 [00:00&lt;00:00,    4.01it/s]
 
    index  order       hoi  multiplet
 0      0      3  0.948908  [0, 1, 2]
@@ -534,7 +534,7 @@ <h3>Dual Total Correlation (DTC)<a class="headerlink" href="#dual-total-correlat
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| DTC (3):  1/1 [00:00&lt;00:00,    6.16it/s]
+100%|██████████| DTC (3):  1/1 [00:00&lt;00:00,    6.24it/s]
 
    index  order       hoi  multiplet
 0     19      3  0.824267  [3, 4, 5]
@@ -569,7 +569,7 @@ <h3>O-information<a class="headerlink" href="#o-information" title="Link to this
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.79it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.89it/s]
 
    index  order       hoi  multiplet
 0      0      3  0.199325  [0, 1, 2]
@@ -604,7 +604,7 @@ <h3>S-information<a class="headerlink" href="#s-information" title="Link to this
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Sinfo (3):  1/1 [00:00&lt;00:00,    4.84it/s]
+100%|██████████| Sinfo (3):  1/1 [00:00&lt;00:00,    4.88it/s]
 
    index  order       hoi  multiplet
 0      0      3  1.698491  [0, 1, 2]
@@ -657,11 +657,11 @@ <h3>Simulating redundant encoding<a class="headerlink" href="#simulating-redunda
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.84it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.92it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.33it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.28it/s]
 
    index  order       hoi  multiplet
 0      0      3  0.387095  [0, 1, 2]
@@ -694,11 +694,11 @@ <h3>Simulating synergistic encoding<a class="headerlink" href="#simulating-syner
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.82it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.87it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.87it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.86it/s]
 
    index  order       hoi  multiplet
 0      3      3  0.002729  [0, 1, 5]
@@ -737,11 +737,11 @@ <h3>Combining redundant and synergistic codings using a multivariate target<a cl
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.86it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.85it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.40it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.39it/s]
 
    index  order       hoi  multiplet
 0      0      3  0.371283  [0, 1, 2]
@@ -789,14 +789,14 @@ <h3>Dynamic redundant and synergistic codings<a class="headerlink" href="#dynami
 </pre></div>
 </div>
 <img src="../../_images/sphx_glr_plot_oinfo_001.png" srcset="../../_images/sphx_glr_plot_oinfo_001.png" alt="Dynamic gradient O-information" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    2.67it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    2.77it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.23it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.22it/s]
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.764 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.730 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-metrics-plot-oinfo-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/2d62e710e011551b615a935858a62b71/plot_oinfo.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_oinfo.ipynb</span></code></a></p>
diff --git a/auto_examples/metrics/plot_rsi.html b/auto_examples/metrics/plot_rsi.html
index 1de10882..d053b242 100644
--- a/auto_examples/metrics/plot_rsi.html
+++ b/auto_examples/metrics/plot_rsi.html
@@ -479,9 +479,9 @@ <h2>Simulate univariate redundancy<a class="headerlink" href="#simulate-univaria
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/3 [00:00&lt;?,       ?it/s]
- 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    2.20it/s]
- 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    2.85it/s]
-100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    3.08it/s]
+ 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    2.14it/s]
+ 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    2.82it/s]
+100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    3.06it/s]
 
    index  order       hoi  multiplet
 0      5      3  0.010098  [0, 2, 3]
@@ -522,9 +522,9 @@ <h2>Simulate multivariate redundancy<a class="headerlink" href="#simulate-multiv
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/3 [00:00&lt;?,       ?it/s]
- 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    3.30it/s]
- 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.40it/s]
-100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    4.95it/s]
+ 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    3.31it/s]
+ 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.39it/s]
+100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    4.94it/s]
 
    index  order       hoi  multiplet
 0     11      3 -0.305800  [0, 3, 6]
@@ -555,9 +555,9 @@ <h2>Simulate univariate and multivariate synergy<a class="headerlink" href="#sim
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/3 [00:00&lt;?,       ?it/s]
- 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    4.00it/s]
- 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    5.20it/s]
-100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.72it/s]
+ 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    3.98it/s]
+ 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    5.21it/s]
+100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.80it/s]
 
    index  order       hoi  multiplet
 0     10      3  1.273890  [0, 3, 5]
@@ -586,9 +586,9 @@ <h2>Simulate univariate and multivariate synergy<a class="headerlink" href="#sim
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/3 [00:00&lt;?,       ?it/s]
- 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    3.60it/s]
- 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.77it/s]
-100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.35it/s]
+ 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    3.57it/s]
+ 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.74it/s]
+100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.34it/s]
 
    index  order       hoi  multiplet
 0     18      3  1.559214  [1, 2, 6]
@@ -632,8 +632,8 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 </div>
 <img src="../../_images/sphx_glr_plot_rsi_001.png" srcset="../../_images/sphx_glr_plot_rsi_001.png" alt="plot rsi" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/3 [00:00&lt;?,       ?it/s]
  33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    3.62it/s]
- 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.65it/s]
-100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.25it/s]
+ 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.78it/s]
+100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.36it/s]
 
    index  order       hoi  multiplet
 0      0      3  1.312485  [0, 1, 2]
@@ -644,7 +644,7 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 5     31      3 -0.498634  [3, 4, 5]
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.981 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.968 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-metrics-plot-rsi-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/4e89a3c451ce8407889de983108afa1c/plot_rsi.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_rsi.ipynb</span></code></a></p>
diff --git a/auto_examples/metrics/plot_syn_phiID.html b/auto_examples/metrics/plot_syn_phiID.html
index 04fd7e34..7bf3ae13 100644
--- a/auto_examples/metrics/plot_syn_phiID.html
+++ b/auto_examples/metrics/plot_syn_phiID.html
@@ -486,7 +486,7 @@ <h2>Simulate synergy<a class="headerlink" href="#simulate-synergy" title="Link t
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| SynPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    2.34it/s]
+100%|██████████| SynPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    2.36it/s]
 
    index  order       hoi multiplet
 0      0      2  0.545935    [0, 1]
@@ -523,7 +523,7 @@ <h2>Simulate redundancy<a class="headerlink" href="#simulate-redundancy" title="
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| RedPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    4.47it/s]
+100%|██████████| RedPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    4.49it/s]
 
    index  order       hoi multiplet
 0      0      2  1.698441    [0, 1]
@@ -574,7 +574,7 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 </pre></div>
 </div>
 <img src="../../_images/sphx_glr_plot_syn_phiID_001.png" srcset="../../_images/sphx_glr_plot_syn_phiID_001.png" alt="plot syn phiID" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| SynPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    3.63it/s]
+100%|██████████| SynPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    3.77it/s]
 
    index  order       hoi multiplet
 0      0      2  1.698441    [0, 1]
@@ -606,7 +606,7 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 </pre></div>
 </div>
 <img src="../../_images/sphx_glr_plot_syn_phiID_002.png" srcset="../../_images/sphx_glr_plot_syn_phiID_002.png" alt="plot syn phiID" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| RedPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    5.87it/s]
+100%|██████████| RedPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    5.84it/s]
 
    index  order       hoi multiplet
 0      1      2  1.134994    [0, 2]
@@ -614,7 +614,7 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 2      6      2  0.597383    [1, 2]
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 1.541 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 1.581 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-metrics-plot-syn-phiid-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/fc28b610171f69bef0470c1f4ae19f0c/plot_syn_phiID.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_syn_phiID.ipynb</span></code></a></p>
diff --git a/auto_examples/metrics/plot_syn_red_mmi.html b/auto_examples/metrics/plot_syn_red_mmi.html
index d62b8748..9c1b7fb4 100644
--- a/auto_examples/metrics/plot_syn_red_mmi.html
+++ b/auto_examples/metrics/plot_syn_red_mmi.html
@@ -485,8 +485,8 @@ <h2>Simulate univariate redundancy<a class="headerlink" href="#simulate-univaria
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/3 [00:00&lt;?,       ?it/s]
- 33%|███▎      | RedMMI order 3:  1/3 [00:00&lt;00:00,    7.68it/s]
-100%|██████████| RedMMI order 5:  3/3 [00:00&lt;00:00,   19.48it/s]
+ 33%|███▎      | RedMMI order 3:  1/3 [00:00&lt;00:00,    7.76it/s]
+100%|██████████| RedMMI order 5:  3/3 [00:00&lt;00:00,   19.82it/s]
 
    index  order       hoi  multiplet
 0     20      3  0.392336  [1, 3, 5]
@@ -524,7 +524,7 @@ <h2>Simulate multivariate redundancy<a class="headerlink" href="#simulate-multiv
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/3 [00:00&lt;?,       ?it/s]
- 33%|███▎      | RedMMI order 3:  1/3 [00:00&lt;00:00,    7.33it/s]
+ 33%|███▎      | RedMMI order 3:  1/3 [00:00&lt;00:00,    7.46it/s]
 
    index  order       hoi  multiplet
 0     27      3  0.483097  [2, 3, 6]
@@ -562,9 +562,9 @@ <h2>Simulate univariate and multivariate synergy<a class="headerlink" href="#sim
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/3 [00:00&lt;?,       ?it/s]
- 33%|███▎      | SynMMI order 3:  1/3 [00:00&lt;00:00,    3.84it/s]
- 67%|██████▋   | SynMMI order 4:  2/3 [00:00&lt;00:00,    3.91it/s]
-100%|██████████| SynMMI order 5:  3/3 [00:00&lt;00:00,    3.93it/s]
+ 33%|███▎      | SynMMI order 3:  1/3 [00:00&lt;00:00,    3.88it/s]
+ 67%|██████▋   | SynMMI order 4:  2/3 [00:00&lt;00:00,    3.94it/s]
+100%|██████████| SynMMI order 5:  3/3 [00:00&lt;00:00,    3.94it/s]
 
    index  order           hoi  multiplet
 0     10      3  1.365911e+00  [0, 3, 5]
@@ -591,9 +591,9 @@ <h2>Simulate univariate and multivariate synergy<a class="headerlink" href="#sim
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/3 [00:00&lt;?,       ?it/s]
- 33%|███▎      | SynMMI order 3:  1/3 [00:00&lt;00:00,    3.65it/s]
- 67%|██████▋   | SynMMI order 4:  2/3 [00:00&lt;00:00,    3.61it/s]
-100%|██████████| SynMMI order 5:  3/3 [00:00&lt;00:00,    3.59it/s]
+ 33%|███▎      | SynMMI order 3:  1/3 [00:00&lt;00:00,    3.68it/s]
+ 67%|██████▋   | SynMMI order 4:  2/3 [00:00&lt;00:00,    3.63it/s]
+100%|██████████| SynMMI order 5:  3/3 [00:00&lt;00:00,    3.61it/s]
 
    index  order       hoi  multiplet
 0     18      3  1.600548  [1, 2, 6]
@@ -636,9 +636,9 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/3 [00:00&lt;?,       ?it/s]
- 33%|███▎      | SynMMI order 3:  1/3 [00:00&lt;00:00,    3.72it/s]
- 67%|██████▋   | SynMMI order 4:  2/3 [00:00&lt;00:00,    3.65it/s]
-100%|██████████| SynMMI order 5:  3/3 [00:00&lt;00:00,    3.61it/s]
+ 33%|███▎      | SynMMI order 3:  1/3 [00:00&lt;00:00,    3.80it/s]
+ 67%|██████▋   | SynMMI order 4:  2/3 [00:00&lt;00:00,    3.68it/s]
+100%|██████████| SynMMI order 5:  3/3 [00:00&lt;00:00,    3.64it/s]
 
 
 Synergy results
@@ -649,7 +649,7 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 2      8      3  0.002230  [0, 2, 6]
 
   0%|          |  0/3 [00:00&lt;?,       ?it/s]
- 33%|███▎      | RedMMI order 3:  1/3 [00:00&lt;00:00,    7.35it/s]
+ 33%|███▎      | RedMMI order 3:  1/3 [00:00&lt;00:00,    7.33it/s]
 
 
 Redundancy results
@@ -684,7 +684,7 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
 </pre></div>
 </div>
-<img src="../../_images/sphx_glr_plot_syn_red_mmi_002.png" srcset="../../_images/sphx_glr_plot_syn_red_mmi_002.png" alt="plot syn red mmi" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.054 seconds)</p>
+<img src="../../_images/sphx_glr_plot_syn_red_mmi_002.png" srcset="../../_images/sphx_glr_plot_syn_red_mmi_002.png" alt="plot syn red mmi" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.046 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-metrics-plot-syn-red-mmi-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/506e66570f568588cfe575362572604a/plot_syn_red_mmi.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_syn_red_mmi.ipynb</span></code></a></p>
diff --git a/auto_examples/metrics/sg_execution_times.html b/auto_examples/metrics/sg_execution_times.html
index 31b3e9df..4f8c898f 100644
--- a/auto_examples/metrics/sg_execution_times.html
+++ b/auto_examples/metrics/sg_execution_times.html
@@ -404,7 +404,7 @@ <h1>Computation times</h1>
                   
   <section id="computation-times">
 <span id="sphx-glr-auto-examples-metrics-sg-execution-times"></span><h1>Computation times<a class="headerlink" href="#computation-times" title="Link to this heading">#</a></h1>
-<p><strong>00:15.718</strong> total execution time for 5 files <strong>from auto_examples/metrics</strong>:</p>
+<p><strong>00:15.726</strong> total execution time for 5 files <strong>from auto_examples/metrics</strong>:</p>
 <div class="docutils container">
 <style scoped>
 <link href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/5.3.0/css/bootstrap.min.css" rel="stylesheet" />
@@ -426,23 +426,23 @@ <h1>Computation times</h1>
 </thead>
 <tbody>
 <tr class="row-even"><td><p><a class="reference internal" href="plot_rsi.html#sphx-glr-auto-examples-metrics-plot-rsi-py"><span class="std std-ref">Redundancy-Synergy Index</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_rsi.py</span></code>)</p></td>
-<td><p>00:03.981</p></td>
+<td><p>00:03.968</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="plot_oinfo.html#sphx-glr-auto-examples-metrics-plot-oinfo-py"><span class="std std-ref">O-information and its derivatives for network behavior and encoding</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_oinfo.py</span></code>)</p></td>
-<td><p>00:03.764</p></td>
+<td><p>00:03.730</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="plot_infotopo.html#sphx-glr-auto-examples-metrics-plot-infotopo-py"><span class="std std-ref">Topological Information : conditioning on orders</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_infotopo.py</span></code>)</p></td>
-<td><p>00:03.378</p></td>
+<td><p>00:03.402</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="plot_syn_red_mmi.html#sphx-glr-auto-examples-metrics-plot-syn-red-mmi-py"><span class="std std-ref">Redundancy and Synergy MMI</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_syn_red_mmi.py</span></code>)</p></td>
-<td><p>00:03.054</p></td>
+<td><p>00:03.046</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="plot_syn_phiID.html#sphx-glr-auto-examples-metrics-plot-syn-phiid-py"><span class="std std-ref">Integrated Information Decomposition</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_syn_phiID.py</span></code>)</p></td>
-<td><p>00:01.541</p></td>
+<td><p>00:01.581</p></td>
 <td><p>0.0</p></td>
 </tr>
 </tbody>
diff --git a/auto_examples/miscellaneous/plot_inspect_results.html b/auto_examples/miscellaneous/plot_inspect_results.html
index 3cd723ee..9e34fb0b 100644
--- a/auto_examples/miscellaneous/plot_inspect_results.html
+++ b/auto_examples/miscellaneous/plot_inspect_results.html
@@ -466,18 +466,18 @@ <h2>Estimate HOI<a class="headerlink" href="#estimate-hoi" title="Link to this h
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/6 [00:00&lt;?,       ?it/s]
- 17%|█▋        | Entropy H(1):  1/6 [00:00&lt;00:00,    5.29it/s]
- 33%|███▎      | Entropy H(2):  2/6 [00:00&lt;00:00,    5.11it/s]
- 50%|█████     | Entropy H(3):  3/6 [00:00&lt;00:00,    5.69it/s]
- 67%|██████▋   | Entropy H(4):  4/6 [00:00&lt;00:00,    6.38it/s]
- 83%|████████▎ | Entropy H(5):  5/6 [00:00&lt;00:00,    6.76it/s]
-100%|██████████| Entropy H(6):  6/6 [00:00&lt;00:00,    7.09it/s]
+ 17%|█▋        | Entropy H(1):  1/6 [00:00&lt;00:00,    5.16it/s]
+ 33%|███▎      | Entropy H(2):  2/6 [00:00&lt;00:00,    4.98it/s]
+ 50%|█████     | Entropy H(3):  3/6 [00:00&lt;00:00,    5.55it/s]
+ 67%|██████▋   | Entropy H(4):  4/6 [00:00&lt;00:00,    6.22it/s]
+ 83%|████████▎ | Entropy H(5):  5/6 [00:00&lt;00:00,    6.61it/s]
+100%|██████████| Entropy H(6):  6/6 [00:00&lt;00:00,    6.76it/s]
 
 
 Mutual information:   0%|          | 0/42 [00:00&lt;?, ?it/s]
 
 
-Mutual information: 100%|██████████| 42/42 [00:00&lt;00:00, 16046.71it/s]
+Mutual information: 100%|██████████| 42/42 [00:00&lt;00:00, 16243.50it/s]
 </pre></div>
 </div>
 </section>
@@ -558,7 +558,7 @@ <h2>Plotting individual multiplets<a class="headerlink" href="#plotting-individu
 <span class="c1"># sphinx_gallery_thumbnail_number = 2</span>
 </pre></div>
 </div>
-<img src="../../_images/sphx_glr_plot_inspect_results_002.png" srcset="../../_images/sphx_glr_plot_inspect_results_002.png" alt="plot inspect results" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 1.627 seconds)</p>
+<img src="../../_images/sphx_glr_plot_inspect_results_002.png" srcset="../../_images/sphx_glr_plot_inspect_results_002.png" alt="plot inspect results" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 1.767 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-miscellaneous-plot-inspect-results-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/ad4b98878b000f24685a5165bd000d07/plot_inspect_results.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_inspect_results.ipynb</span></code></a></p>
diff --git a/auto_examples/miscellaneous/sg_execution_times.html b/auto_examples/miscellaneous/sg_execution_times.html
index dcfe35a8..450a9b95 100644
--- a/auto_examples/miscellaneous/sg_execution_times.html
+++ b/auto_examples/miscellaneous/sg_execution_times.html
@@ -404,7 +404,7 @@ <h1>Computation times</h1>
                   
   <section id="computation-times">
 <span id="sphx-glr-auto-examples-miscellaneous-sg-execution-times"></span><h1>Computation times<a class="headerlink" href="#computation-times" title="Link to this heading">#</a></h1>
-<p><strong>00:02.877</strong> total execution time for 2 files <strong>from auto_examples/miscellaneous</strong>:</p>
+<p><strong>00:03.042</strong> total execution time for 2 files <strong>from auto_examples/miscellaneous</strong>:</p>
 <div class="docutils container">
 <style scoped>
 <link href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/5.3.0/css/bootstrap.min.css" rel="stylesheet" />
@@ -426,11 +426,11 @@ <h1>Computation times</h1>
 </thead>
 <tbody>
 <tr class="row-even"><td><p><a class="reference internal" href="plot_inspect_results.html#sphx-glr-auto-examples-miscellaneous-plot-inspect-results-py"><span class="std std-ref">Inspect and plot Higher-Order Interactions</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_inspect_results.py</span></code>)</p></td>
-<td><p>00:01.627</p></td>
+<td><p>00:01.767</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="tuto_jax.html#sphx-glr-auto-examples-miscellaneous-tuto-jax-py"><span class="std std-ref">Quick introduction to jax</span></a> (<code class="docutils literal notranslate"><span class="pre">tuto_jax.py</span></code>)</p></td>
-<td><p>00:01.250</p></td>
+<td><p>00:01.274</p></td>
 <td><p>0.0</p></td>
 </tr>
 </tbody>
diff --git a/auto_examples/miscellaneous/tuto_jax.html b/auto_examples/miscellaneous/tuto_jax.html
index 7915deb0..da4398cc 100644
--- a/auto_examples/miscellaneous/tuto_jax.html
+++ b/auto_examples/miscellaneous/tuto_jax.html
@@ -521,8 +521,8 @@ <h2>Compiling functions using jit<a class="headerlink" href="#compiling-function
 <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Time taken by jitted function: </span><span class="si">{</span><span class="n">t2</span><span class="si">}</span><span class="s2"> seconds&quot;</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Time taken by pure NumPy function: 0.5845532199999752 seconds
-Time taken by jitted function: 0.26873912700000346 seconds
+<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Time taken by pure NumPy function: 0.5857170439999777 seconds
+Time taken by jitted function: 0.282138118999967 seconds
 </pre></div>
 </div>
 <p>if the function takes optional argument, you can use the <cite>static_argnums</cite>
@@ -622,7 +622,7 @@ <h2>For loops with jax<a class="headerlink" href="#for-loops-with-jax" title="Li
 nice introduction to <cite>jax.lax.scan</cite></p></li>
 </ul>
 </div></blockquote>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 1.250 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 1.274 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-miscellaneous-tuto-jax-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/c9df0fdd61c061c32221dcc575a693a9/tuto_jax.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">tuto_jax.ipynb</span></code></a></p>
diff --git a/auto_examples/statistics/plot_bootstrapping.html b/auto_examples/statistics/plot_bootstrapping.html
index 5da03988..629c0708 100644
--- a/auto_examples/statistics/plot_bootstrapping.html
+++ b/auto_examples/statistics/plot_bootstrapping.html
@@ -665,7 +665,7 @@ <h3>Plot the O-information with the confidence interval<a class="headerlink" hre
 <div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># sphinx_gallery_thumbnail_number = 2</span>
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 15.886 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 15.654 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-statistics-plot-bootstrapping-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/d2e94d8bac717c85e2a37d7d973930a2/plot_bootstrapping.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_bootstrapping.ipynb</span></code></a></p>
diff --git a/auto_examples/statistics/sg_execution_times.html b/auto_examples/statistics/sg_execution_times.html
index ae511856..8eefd65b 100644
--- a/auto_examples/statistics/sg_execution_times.html
+++ b/auto_examples/statistics/sg_execution_times.html
@@ -404,7 +404,7 @@ <h1>Computation times</h1>
                   
   <section id="computation-times">
 <span id="sphx-glr-auto-examples-statistics-sg-execution-times"></span><h1>Computation times<a class="headerlink" href="#computation-times" title="Link to this heading">#</a></h1>
-<p><strong>00:15.886</strong> total execution time for 1 file <strong>from auto_examples/statistics</strong>:</p>
+<p><strong>00:15.654</strong> total execution time for 1 file <strong>from auto_examples/statistics</strong>:</p>
 <div class="docutils container">
 <style scoped>
 <link href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/5.3.0/css/bootstrap.min.css" rel="stylesheet" />
@@ -426,7 +426,7 @@ <h1>Computation times</h1>
 </thead>
 <tbody>
 <tr class="row-even"><td><p><a class="reference internal" href="plot_bootstrapping.html#sphx-glr-auto-examples-statistics-plot-bootstrapping-py"><span class="std std-ref">Bootstrapping and confidence interval</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_bootstrapping.py</span></code>)</p></td>
-<td><p>00:15.886</p></td>
+<td><p>00:15.654</p></td>
 <td><p>0.0</p></td>
 </tr>
 </tbody>
diff --git a/auto_examples/tutorials/plot_ml_vs_it.html b/auto_examples/tutorials/plot_ml_vs_it.html
index 98e35bcc..a052b267 100644
--- a/auto_examples/tutorials/plot_ml_vs_it.html
+++ b/auto_examples/tutorials/plot_ml_vs_it.html
@@ -602,7 +602,7 @@ <h2>Using information-theoretic approaches<a class="headerlink" href="#using-inf
 <img src="../../_images/sphx_glr_plot_ml_vs_it_003.png" srcset="../../_images/sphx_glr_plot_ml_vs_it_003.png" alt="Redundant interactions, Synergistic interactions" class = "sphx-glr-single-img"/><p>We retrieve the bump of information around sample 50 however this time, the
 bump is positive in case of redundant interactions and negative in case of
 synergistic interactions.</p>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 9.287 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 9.273 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-tutorials-plot-ml-vs-it-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/007eb65766f3b4811d99ff5b36a7b49b/plot_ml_vs_it.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_ml_vs_it.ipynb</span></code></a></p>
diff --git a/auto_examples/tutorials/plot_sim_red_syn.html b/auto_examples/tutorials/plot_sim_red_syn.html
index e8bcf7a0..5f801c24 100644
--- a/auto_examples/tutorials/plot_sim_red_syn.html
+++ b/auto_examples/tutorials/plot_sim_red_syn.html
@@ -490,7 +490,7 @@ <h3>Simulating synergistic behavior<a class="headerlink" href="#simulating-syner
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    1.60it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    1.76it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -520,7 +520,7 @@ <h3>Simulating redundant behavior<a class="headerlink" href="#simulating-redunda
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.17it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.26it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -552,7 +552,7 @@ <h3>Simulating synergistic behavior by sum operation<a class="headerlink" href="
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.24it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.33it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -583,7 +583,7 @@ <h3>Simulating redundant behavior by copy operator<a class="headerlink" href="#s
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.17it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.27it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -630,7 +630,7 @@ <h3>Simulating dynamic redundancy and synergy<a class="headerlink" href="#simula
 </pre></div>
 </div>
 <img src="../../_images/sphx_glr_plot_sim_red_syn_001.png" srcset="../../_images/sphx_glr_plot_sim_red_syn_001.png" alt="Dynamic HOI" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    2.41it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    2.49it/s]
 
 Text(0.5, 1.0, &#39;Dynamic HOI&#39;)
 </pre></div>
@@ -670,11 +670,11 @@ <h3>Simulating redundant encoding<a class="headerlink" href="#simulating-redunda
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.26it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.28it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.06it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.04it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -702,11 +702,11 @@ <h3>Simulating synergistic encoding<a class="headerlink" href="#simulating-syner
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.20it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.22it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.27it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.35it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -737,11 +737,11 @@ <h3>Simulating redundant encoding by copy operation<a class="headerlink" href="#
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.25it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.22it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.36it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.39it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -767,11 +767,11 @@ <h3>Simulating synergistic encoding by sum operation<a class="headerlink" href="
 </pre></div>
 </div>
 <div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.24it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.26it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.38it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.39it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -822,14 +822,14 @@ <h3>Simulating dynamic redundant and synergistic encoding<a class="headerlink" h
 </pre></div>
 </div>
 <img src="../../_images/sphx_glr_plot_sim_red_syn_002.png" srcset="../../_images/sphx_glr_plot_sim_red_syn_002.png" alt="Dynamic HOI" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>  0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.64it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.63it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.64it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.72it/s]
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 4.738 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 4.654 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-tutorials-plot-sim-red-syn-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/2a4afa62d27b153aa605e093f9600e6b/plot_sim_red_syn.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_sim_red_syn.ipynb</span></code></a></p>
diff --git a/auto_examples/tutorials/sg_execution_times.html b/auto_examples/tutorials/sg_execution_times.html
index 3bf82b63..6ad9bb05 100644
--- a/auto_examples/tutorials/sg_execution_times.html
+++ b/auto_examples/tutorials/sg_execution_times.html
@@ -404,7 +404,7 @@ <h1>Computation times</h1>
                   
   <section id="computation-times">
 <span id="sphx-glr-auto-examples-tutorials-sg-execution-times"></span><h1>Computation times<a class="headerlink" href="#computation-times" title="Link to this heading">#</a></h1>
-<p><strong>00:14.025</strong> total execution time for 2 files <strong>from auto_examples/tutorials</strong>:</p>
+<p><strong>00:13.927</strong> total execution time for 2 files <strong>from auto_examples/tutorials</strong>:</p>
 <div class="docutils container">
 <style scoped>
 <link href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/5.3.0/css/bootstrap.min.css" rel="stylesheet" />
@@ -426,11 +426,11 @@ <h1>Computation times</h1>
 </thead>
 <tbody>
 <tr class="row-even"><td><p><a class="reference internal" href="plot_ml_vs_it.html#sphx-glr-auto-examples-tutorials-plot-ml-vs-it-py"><span class="std std-ref">Machine-learning vs. Information theoretic approaches for HOI</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_ml_vs_it.py</span></code>)</p></td>
-<td><p>00:09.287</p></td>
+<td><p>00:09.273</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="plot_sim_red_syn.html#sphx-glr-auto-examples-tutorials-plot-sim-red-syn-py"><span class="std std-ref">How to simulate redundancy and synergy</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_sim_red_syn.py</span></code>)</p></td>
-<td><p>00:04.738</p></td>
+<td><p>00:04.654</p></td>
 <td><p>0.0</p></td>
 </tr>
 </tbody>
diff --git a/contributors.html b/contributors.html
index e1b5fbc5..02b2176c 100644
--- a/contributors.html
+++ b/contributors.html
@@ -408,7 +408,7 @@ <h1>List of contributors<a class="headerlink" href="#list-of-contributors" title
 <li class="sphinx-contributors_list__item"><div class="sphinx-contributors_contributor docutils container">
 <img alt="https://avatars.githubusercontent.com/u/15892073?v=4" class="sphinx-contributors_contributor__image" src="https://avatars.githubusercontent.com/u/15892073?v=4" />
 <p class="sphinx-contributors_contributor__username"><a class="reference external" href="https://github.com/EtienneCmb">EtienneCmb</a></p>
-<p class="sphinx-contributors_contributor__contributions">286 contributions</p>
+<p class="sphinx-contributors_contributor__contributions">288 contributions</p>
 </div>
 </li>
 <li class="sphinx-contributors_list__item"><div class="sphinx-contributors_contributor docutils container">
diff --git a/searchindex.js b/searchindex.js
index f04d5633..446a36f6 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"Bibliography": [[70, "bibliography"]], "Bootstrapping and confidence interval": [[56, null]], "CPU vs. GPU : Performance comparison": [[67, "cpu-vs-gpu-performance-comparison"]], "Combinatorics": [[0, "combinatorics"]], "Combining redundancy and synergy": [[46, "combining-redundancy-and-synergy"], [47, "combining-redundancy-and-synergy"], [48, "combining-redundancy-and-synergy"]], "Combining redundant and synergistic codings using a multivariate target": [[45, "combining-redundant-and-synergistic-codings-using-a-multivariate-target"]], "Comparison of MI estimators with high-dimensional data": [[40, null]], "Comparison of entropy estimators for a multivariate normal": [[37, null]], "Comparison of entropy estimators for various distributions": [[36, null]], "Comparison of entropy estimators with high-dimensional data": [[38, null]], "Comparison of estimators": [[37, "comparison-of-estimators"]], "Comparison of mutual-information estimators": [[39, null]], "Compiling functions using jit": [[53, "compiling-functions-using-jit"]], "Computation times": [[41, null], [49, null], [52, null], [54, null], [57, null], [61, null], [69, null]], "Compute Higher-Order Interactions": [[68, "compute-higher-order-interactions"]], "Compute bootstrap": [[56, "compute-bootstrap"]], "Computing Higher-Order Interactions on large multiplets": [[67, "computing-higher-order-interactions-on-large-multiplets"]], "Computing entropy on large multi-dimensional arrays": [[67, "computing-entropy-on-large-multi-dimensional-arrays"]], "Contributing code using pull requests": [[62, "contributing-code-using-pull-requests"]], "Contributing to HOI": [[62, "contributing-to-hoi"]], "Core information theoretic measures": [[70, "core-information-theoretic-measures"]], "Data simulation": [[45, "data-simulation"], [59, "data-simulation"]], "Decoding Y using X": [[59, "decoding-y-using-x"]], "Definition": [[46, "definition"], [47, "definition"], [48, "definition"]], "Definition of MI estimators": [[39, "definition-of-mi-estimators"], [40, "definition-of-mi-estimators"]], "Definition of entropy estimators": [[38, "definition-of-entropy-estimators"]], "Definition of estimators of entropy": [[36, "definition-of-estimators-of-entropy"], [37, "definition-of-estimators-of-entropy"]], "Dependencies": [[66, "dependencies"]], "Developer Documentation": [[62, null]], "Dual Total Correlation (DTC)": [[45, "dual-total-correlation-dtc"]], "Dual Total correlation": [[70, "dual-total-correlation"]], "Dynamic redundant and synergistic codings": [[45, "dynamic-redundant-and-synergistic-codings"]], "Entropy": [[42, "entropy"]], "Entropy and mutual information": [[34, "entropy-and-mutual-information"], [35, null]], "Entropy of data sampled from a uniform distribution": [[36, "entropy-of-data-sampled-from-a-uniform-distribution"]], "Entropy of data sampled from an exponential distribution": [[36, "entropy-of-data-sampled-from-an-exponential-distribution"]], "Entropy of data sampled from normal distribution": [[36, "entropy-of-data-sampled-from-normal-distribution"]], "Estimate HOI": [[51, "estimate-hoi"]], "Estimation of the confidence interval using a bootstrapping approach": [[56, "estimation-of-the-confidence-interval-using-a-bootstrapping-approach"]], "Examples": [[34, null]], "Examples using hoi.core.get_entropy": [[12, "examples-using-hoi-core-get-entropy"]], "Examples using hoi.core.get_mi": [[13, "examples-using-hoi-core-get-mi"]], "Examples using hoi.metrics.DTC": [[15, "examples-using-hoi-metrics-dtc"]], "Examples using hoi.metrics.GradientOinfo": [[16, "examples-using-hoi-metrics-gradientoinfo"]], "Examples using hoi.metrics.InfoTopo": [[17, "examples-using-hoi-metrics-infotopo"]], "Examples using hoi.metrics.Oinfo": [[19, "examples-using-hoi-metrics-oinfo"]], "Examples using hoi.metrics.RSI": [[20, "examples-using-hoi-metrics-rsi"]], "Examples using hoi.metrics.RedundancyMMI": [[21, "examples-using-hoi-metrics-redundancymmi"]], "Examples using hoi.metrics.RedundancyphiID": [[22, "examples-using-hoi-metrics-redundancyphiid"]], "Examples using hoi.metrics.Sinfo": [[23, "examples-using-hoi-metrics-sinfo"]], "Examples using hoi.metrics.SynergyMMI": [[24, "examples-using-hoi-metrics-synergymmi"]], "Examples using hoi.metrics.SynergyphiID": [[25, "examples-using-hoi-metrics-synergyphiid"]], "Examples using hoi.metrics.TC": [[26, "examples-using-hoi-metrics-tc"]], "Examples using hoi.plot.plot_landscape": [[27, "examples-using-hoi-plot-plot-landscape"]], "Examples using hoi.simulation.simulate_hoi_gauss": [[28, "examples-using-hoi-simulation-simulate-hoi-gauss"]], "Examples using hoi.utils.digitize": [[29, "examples-using-hoi-utils-digitize"]], "Examples using hoi.utils.get_nbest_mult": [[30, "examples-using-hoi-utils-get-nbest-mult"]], "For loops with jax": [[53, "for-loops-with-jax"]], "From pairwise to higher-order interactions": [[70, "from-pairwise-to-higher-order-interactions"]], "Funding": [[65, "funding"]], "Get a summary of the results": [[51, "get-a-summary-of-the-results"]], "Get involved": [[65, "get-involved"]], "Glossary": [[64, null]], "Gradient of O-information": [[70, "gradient-of-o-information"]], "HOI : High-Performance Estimation of Higher-Order Interactions": [[65, null]], "How to simulate redundancy and synergy": [[60, null]], "Inspect and plot Higher-Order Interactions": [[51, null]], "Inspect the results": [[68, "inspect-the-results"]], "Installation": [[66, null], [68, "installation"]], "Installation for developers": [[62, "installation-for-developers"]], "Integrated Information Decomposition": [[47, null]], "Introduction to core information theoretical metrics": [[42, null]], "Jax.numpy module": [[53, "jax-numpy-module"]], "Jax: linear algebra backend": [[67, null]], "Landscape plot": [[51, "landscape-plot"]], "License": [[65, "license"]], "List of classes and functions": [[33, null]], "List of contributors": [[63, null]], "MI of data sampled from normal distribution": [[39, "mi-of-data-sampled-from-normal-distribution"]], "MI of data sampled from splitted multinormal distribution": [[40, "mi-of-data-sampled-from-splitted-multinormal-distribution"]], "Machine-learning vs. Information theoretic approaches for HOI": [[59, null]], "Measures of Entropy": [[0, "measures-of-entropy"]], "Measures of Mutual Information": [[0, "measures-of-mutual-information"]], "Measuring Entropy": [[70, "measuring-entropy"]], "Measuring Mutual Information (MI)": [[70, "measuring-mutual-information-mi"]], "Metrics of HOI": [[34, "metrics-of-hoi"], [43, null]], "Miscellaneous": [[34, "miscellaneous"], [50, null]], "Multiplet isolation using the Topological Information": [[44, "multiplet-isolation-using-the-topological-information"]], "Mutual information": [[42, "mutual-information"]], "Network behavior": [[1, "network-behavior"], [70, "network-behavior"]], "Network encoding": [[1, "network-encoding"], [70, "network-encoding"]], "O-information": [[45, "o-information"], [70, "o-information"]], "O-information : Redundancy and synergy spread to higher orders": [[56, "o-information-redundancy-and-synergy-spread-to-higher-orders"]], "O-information and its derivatives for network behavior and encoding": [[45, null]], "O-information for network behavior": [[45, "o-information-for-network-behavior"]], "O-information for network encoding": [[45, "o-information-for-network-encoding"]], "Other softwares for the analysis of higher-order interactions": [[68, "other-softwares-for-the-analysis-of-higher-order-interactions"]], "Plot the O-information with the confidence interval": [[56, "plot-the-o-information-with-the-confidence-interval"]], "Plotting individual multiplets": [[51, "plotting-individual-multiplets"]], "Postprocessing": [[4, "postprocessing"]], "Practical recommendations": [[68, "practical-recommendations"]], "Preprocessing": [[4, "preprocessing"]], "Quick introduction to jax": [[53, null]], "Quickstart": [[68, null]], "Redundancy and Synergy MMI": [[48, null]], "Redundancy-Synergy Index": [[46, null]], "Redundancy-Synergy index (RSI)": [[70, "redundancy-synergy-index-rsi"]], "Redundant and synergistic network behavior": [[60, "redundant-and-synergistic-network-behavior"]], "Redundant and synergistic network encoding": [[60, "redundant-and-synergistic-network-encoding"]], "S information": [[70, "s-information"]], "S-information": [[45, "s-information"]], "Simulate data": [[51, "simulate-data"], [68, "simulate-data"]], "Simulate multivariate redundancy": [[46, "simulate-multivariate-redundancy"], [48, "simulate-multivariate-redundancy"]], "Simulate redundancy": [[47, "simulate-redundancy"]], "Simulate redundant and synergistic interactions": [[44, "simulate-redundant-and-synergistic-interactions"]], "Simulate synergy": [[47, "simulate-synergy"]], "Simulate univariate and multivariate synergy": [[46, "simulate-univariate-and-multivariate-synergy"], [48, "simulate-univariate-and-multivariate-synergy"]], "Simulate univariate redundancy": [[46, "simulate-univariate-redundancy"], [48, "simulate-univariate-redundancy"]], "Simulating dynamic redundancy and synergy": [[60, "simulating-dynamic-redundancy-and-synergy"]], "Simulating dynamic redundant and synergistic encoding": [[60, "simulating-dynamic-redundant-and-synergistic-encoding"]], "Simulating redundant behavior": [[60, "simulating-redundant-behavior"]], "Simulating redundant behavior by copy operator": [[60, "simulating-redundant-behavior-by-copy-operator"]], "Simulating redundant encoding": [[45, "simulating-redundant-encoding"], [60, "simulating-redundant-encoding"]], "Simulating redundant encoding by copy operation": [[60, "simulating-redundant-encoding-by-copy-operation"]], "Simulating synergistic behavior": [[60, "simulating-synergistic-behavior"]], "Simulating synergistic behavior by sum operation": [[60, "simulating-synergistic-behavior-by-sum-operation"]], "Simulating synergistic encoding": [[45, "simulating-synergistic-encoding"], [60, "simulating-synergistic-encoding"]], "Simulating synergistic encoding by sum operation": [[60, "simulating-synergistic-encoding-by-sum-operation"]], "Spatial spreading : the problem with the O-information": [[44, "spatial-spreading-the-problem-with-the-o-information"]], "Statistics : bootstrapping and permutations": [[34, "statistics-bootstrapping-and-permutations"], [55, null]], "Synergy and redundancy (MMI)": [[70, "synergy-and-redundancy-mmi"]], "Synergy and redundancy integrated Information Decomposition (MMI)": [[70, "synergy-and-redundancy-integrated-information-decomposition-mmi"]], "Theoretical background": [[70, null]], "Topological Information : conditioning on orders": [[44, null]], "Topological information": [[70, "topological-information"]], "Total Correlation (TC)": [[45, "total-correlation-tc"]], "Total correlation": [[70, "total-correlation"]], "Tutorials": [[34, "tutorials"], [58, null]], "User installation": [[66, "user-installation"]], "Using information-theoretic approaches": [[59, "using-information-theoretic-approaches"]], "hoi.core": [[0, null]], "hoi.core.combinations": [[5, null]], "hoi.core.entropy_bin": [[6, null]], "hoi.core.entropy_gauss": [[7, null]], "hoi.core.entropy_gc": [[8, null]], "hoi.core.entropy_hist": [[9, null]], "hoi.core.entropy_kernel": [[10, null]], "hoi.core.entropy_knn": [[11, null]], "hoi.core.get_entropy": [[12, null]], "hoi.core.get_mi": [[13, null]], "hoi.core.prepare_for_it": [[14, null]], "hoi.metrics": [[1, null]], "hoi.metrics.DTC": [[15, null]], "hoi.metrics.GradientOinfo": [[16, null]], "hoi.metrics.InfoTopo": [[17, null]], "hoi.metrics.InfoTot": [[18, null]], "hoi.metrics.Oinfo": [[19, null]], "hoi.metrics.RSI": [[20, null]], "hoi.metrics.RedundancyMMI": [[21, null]], "hoi.metrics.RedundancyphiID": [[22, null]], "hoi.metrics.Sinfo": [[23, null]], "hoi.metrics.SynergyMMI": [[24, null]], "hoi.metrics.SynergyphiID": [[25, null]], "hoi.metrics.TC": [[26, null]], "hoi.plot": [[2, null]], "hoi.plot.plot_landscape": [[27, null]], "hoi.simulation": [[3, null]], "hoi.simulation.simulate_hoi_gauss": [[28, null]], "hoi.utils": [[4, null]], "hoi.utils.digitize": [[29, null]], "hoi.utils.get_nbest_mult": [[30, null]], "hoi.utils.landscape": [[31, null]], "hoi.utils.normalize": [[32, null]], "vmap : vectorize a function": [[53, "vmap-vectorize-a-function"]]}, "docnames": ["api/api_core", "api/api_metrics", "api/api_plot", "api/api_sim", "api/api_utils", "api/generated/hoi.core.combinations", "api/generated/hoi.core.entropy_bin", "api/generated/hoi.core.entropy_gauss", "api/generated/hoi.core.entropy_gc", "api/generated/hoi.core.entropy_hist", "api/generated/hoi.core.entropy_kernel", "api/generated/hoi.core.entropy_knn", "api/generated/hoi.core.get_entropy", "api/generated/hoi.core.get_mi", "api/generated/hoi.core.prepare_for_it", "api/generated/hoi.metrics.DTC", "api/generated/hoi.metrics.GradientOinfo", "api/generated/hoi.metrics.InfoTopo", "api/generated/hoi.metrics.InfoTot", "api/generated/hoi.metrics.Oinfo", "api/generated/hoi.metrics.RSI", "api/generated/hoi.metrics.RedundancyMMI", "api/generated/hoi.metrics.RedundancyphiID", "api/generated/hoi.metrics.Sinfo", "api/generated/hoi.metrics.SynergyMMI", "api/generated/hoi.metrics.SynergyphiID", "api/generated/hoi.metrics.TC", "api/generated/hoi.plot.plot_landscape", "api/generated/hoi.simulation.simulate_hoi_gauss", "api/generated/hoi.utils.digitize", "api/generated/hoi.utils.get_nbest_mult", "api/generated/hoi.utils.landscape", "api/generated/hoi.utils.normalize", "api/modules", "auto_examples/index", "auto_examples/it/index", "auto_examples/it/plot_entropies", "auto_examples/it/plot_entropies_mvar", "auto_examples/it/plot_entropy_high_dimensional", "auto_examples/it/plot_mi", "auto_examples/it/plot_mi_high_dimensional", "auto_examples/it/sg_execution_times", "auto_examples/it/tuto_core", "auto_examples/metrics/index", "auto_examples/metrics/plot_infotopo", "auto_examples/metrics/plot_oinfo", "auto_examples/metrics/plot_rsi", "auto_examples/metrics/plot_syn_phiID", "auto_examples/metrics/plot_syn_red_mmi", "auto_examples/metrics/sg_execution_times", "auto_examples/miscellaneous/index", "auto_examples/miscellaneous/plot_inspect_results", "auto_examples/miscellaneous/sg_execution_times", "auto_examples/miscellaneous/tuto_jax", "auto_examples/sg_execution_times", "auto_examples/statistics/index", "auto_examples/statistics/plot_bootstrapping", "auto_examples/statistics/sg_execution_times", "auto_examples/tutorials/index", "auto_examples/tutorials/plot_ml_vs_it", "auto_examples/tutorials/plot_sim_red_syn", "auto_examples/tutorials/sg_execution_times", "contributor_guide", "contributors", "glossary", "index", "install", "jax", "quickstart", "sg_execution_times", "theory"], "envversion": {"sphinx": 62, "sphinx.domains.c": 3, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 9, "sphinx.domains.index": 1, "sphinx.domains.javascript": 3, "sphinx.domains.math": 2, "sphinx.domains.python": 4, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx.ext.todo": 2, "sphinx.ext.viewcode": 1, "sphinxcontrib.bibtex": 9}, "filenames": ["api/api_core.rst", "api/api_metrics.rst", "api/api_plot.rst", "api/api_sim.rst", "api/api_utils.rst", "api/generated/hoi.core.combinations.rst", "api/generated/hoi.core.entropy_bin.rst", "api/generated/hoi.core.entropy_gauss.rst", "api/generated/hoi.core.entropy_gc.rst", "api/generated/hoi.core.entropy_hist.rst", "api/generated/hoi.core.entropy_kernel.rst", "api/generated/hoi.core.entropy_knn.rst", "api/generated/hoi.core.get_entropy.rst", "api/generated/hoi.core.get_mi.rst", "api/generated/hoi.core.prepare_for_it.rst", "api/generated/hoi.metrics.DTC.rst", "api/generated/hoi.metrics.GradientOinfo.rst", "api/generated/hoi.metrics.InfoTopo.rst", "api/generated/hoi.metrics.InfoTot.rst", "api/generated/hoi.metrics.Oinfo.rst", "api/generated/hoi.metrics.RSI.rst", "api/generated/hoi.metrics.RedundancyMMI.rst", "api/generated/hoi.metrics.RedundancyphiID.rst", "api/generated/hoi.metrics.Sinfo.rst", "api/generated/hoi.metrics.SynergyMMI.rst", "api/generated/hoi.metrics.SynergyphiID.rst", "api/generated/hoi.metrics.TC.rst", "api/generated/hoi.plot.plot_landscape.rst", "api/generated/hoi.simulation.simulate_hoi_gauss.rst", "api/generated/hoi.utils.digitize.rst", "api/generated/hoi.utils.get_nbest_mult.rst", "api/generated/hoi.utils.landscape.rst", "api/generated/hoi.utils.normalize.rst", "api/modules.rst", "auto_examples/index.rst", "auto_examples/it/index.rst", "auto_examples/it/plot_entropies.rst", "auto_examples/it/plot_entropies_mvar.rst", "auto_examples/it/plot_entropy_high_dimensional.rst", "auto_examples/it/plot_mi.rst", "auto_examples/it/plot_mi_high_dimensional.rst", "auto_examples/it/sg_execution_times.rst", "auto_examples/it/tuto_core.rst", "auto_examples/metrics/index.rst", "auto_examples/metrics/plot_infotopo.rst", "auto_examples/metrics/plot_oinfo.rst", "auto_examples/metrics/plot_rsi.rst", "auto_examples/metrics/plot_syn_phiID.rst", "auto_examples/metrics/plot_syn_red_mmi.rst", "auto_examples/metrics/sg_execution_times.rst", "auto_examples/miscellaneous/index.rst", "auto_examples/miscellaneous/plot_inspect_results.rst", "auto_examples/miscellaneous/sg_execution_times.rst", "auto_examples/miscellaneous/tuto_jax.rst", "auto_examples/sg_execution_times.rst", "auto_examples/statistics/index.rst", "auto_examples/statistics/plot_bootstrapping.rst", "auto_examples/statistics/sg_execution_times.rst", "auto_examples/tutorials/index.rst", "auto_examples/tutorials/plot_ml_vs_it.rst", "auto_examples/tutorials/plot_sim_red_syn.rst", "auto_examples/tutorials/sg_execution_times.rst", "contributor_guide.rst", "contributors.rst", "glossary.rst", "index.rst", "install.rst", "jax.rst", "quickstart.rst", "sg_execution_times.rst", "theory.rst"], "indexentries": {"__iter__() (hoi.metrics.dtc method)": [[15, "hoi.metrics.DTC.__iter__", false]], "__iter__() (hoi.metrics.gradientoinfo method)": [[16, "hoi.metrics.GradientOinfo.__iter__", false]], "__iter__() (hoi.metrics.infotopo method)": [[17, "hoi.metrics.InfoTopo.__iter__", false]], "__iter__() (hoi.metrics.infotot method)": [[18, "hoi.metrics.InfoTot.__iter__", false]], "__iter__() (hoi.metrics.oinfo method)": [[19, "hoi.metrics.Oinfo.__iter__", false]], "__iter__() (hoi.metrics.redundancymmi method)": [[21, "hoi.metrics.RedundancyMMI.__iter__", false]], "__iter__() (hoi.metrics.redundancyphiid method)": [[22, "hoi.metrics.RedundancyphiID.__iter__", false]], "__iter__() (hoi.metrics.rsi method)": [[20, "hoi.metrics.RSI.__iter__", false]], "__iter__() (hoi.metrics.sinfo method)": [[23, "hoi.metrics.Sinfo.__iter__", false]], "__iter__() (hoi.metrics.synergymmi method)": [[24, "hoi.metrics.SynergyMMI.__iter__", false]], "__iter__() (hoi.metrics.synergyphiid method)": [[25, "hoi.metrics.SynergyphiID.__iter__", false]], "__iter__() (hoi.metrics.tc method)": [[26, "hoi.metrics.TC.__iter__", false]], "combinations() (in module hoi.core)": [[5, "hoi.core.combinations", false]], "compute_entropies() (hoi.metrics.dtc method)": [[15, "hoi.metrics.DTC.compute_entropies", false]], "compute_entropies() (hoi.metrics.gradientoinfo method)": [[16, "hoi.metrics.GradientOinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.infotopo method)": [[17, "hoi.metrics.InfoTopo.compute_entropies", false]], "compute_entropies() (hoi.metrics.infotot method)": [[18, "hoi.metrics.InfoTot.compute_entropies", false]], "compute_entropies() (hoi.metrics.oinfo method)": [[19, "hoi.metrics.Oinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.redundancymmi method)": [[21, "hoi.metrics.RedundancyMMI.compute_entropies", false]], "compute_entropies() (hoi.metrics.redundancyphiid method)": [[22, "hoi.metrics.RedundancyphiID.compute_entropies", false]], "compute_entropies() (hoi.metrics.rsi method)": [[20, "hoi.metrics.RSI.compute_entropies", false]], "compute_entropies() (hoi.metrics.sinfo method)": [[23, "hoi.metrics.Sinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.synergymmi method)": [[24, "hoi.metrics.SynergyMMI.compute_entropies", false]], "compute_entropies() (hoi.metrics.synergyphiid method)": [[25, "hoi.metrics.SynergyphiID.compute_entropies", false]], "compute_entropies() (hoi.metrics.tc method)": [[26, "hoi.metrics.TC.compute_entropies", false]], "digitize() (in module hoi.utils)": [[29, "hoi.utils.digitize", false]], "dtc (class in hoi.metrics)": [[15, "hoi.metrics.DTC", false]], "entropies (hoi.metrics.dtc property)": [[15, "hoi.metrics.DTC.entropies", false]], "entropies (hoi.metrics.gradientoinfo property)": [[16, "hoi.metrics.GradientOinfo.entropies", false]], "entropies (hoi.metrics.infotopo property)": [[17, "hoi.metrics.InfoTopo.entropies", false]], "entropies (hoi.metrics.infotot property)": [[18, "hoi.metrics.InfoTot.entropies", false]], "entropies (hoi.metrics.oinfo property)": [[19, "hoi.metrics.Oinfo.entropies", false]], "entropies (hoi.metrics.redundancymmi property)": [[21, "hoi.metrics.RedundancyMMI.entropies", false]], "entropies (hoi.metrics.redundancyphiid property)": [[22, "hoi.metrics.RedundancyphiID.entropies", false]], "entropies (hoi.metrics.rsi property)": [[20, "hoi.metrics.RSI.entropies", false]], "entropies (hoi.metrics.sinfo property)": [[23, "hoi.metrics.Sinfo.entropies", false]], "entropies (hoi.metrics.synergymmi property)": [[24, "hoi.metrics.SynergyMMI.entropies", false]], "entropies (hoi.metrics.synergyphiid property)": [[25, "hoi.metrics.SynergyphiID.entropies", false]], "entropies (hoi.metrics.tc property)": [[26, "hoi.metrics.TC.entropies", false]], "entropy": [[64, "term-Entropy", true]], "entropy_bin() (in module hoi.core)": [[6, "hoi.core.entropy_bin", false]], "entropy_gauss() (in module hoi.core)": [[7, "hoi.core.entropy_gauss", false]], "entropy_gc() (in module hoi.core)": [[8, "hoi.core.entropy_gc", false]], "entropy_hist() (in module hoi.core)": [[9, "hoi.core.entropy_hist", false]], "entropy_kernel() (in module hoi.core)": [[10, "hoi.core.entropy_kernel", false]], "entropy_knn() (in module hoi.core)": [[11, "hoi.core.entropy_knn", false]], "fit() (hoi.metrics.dtc method)": [[15, "hoi.metrics.DTC.fit", false]], "fit() (hoi.metrics.gradientoinfo method)": [[16, "hoi.metrics.GradientOinfo.fit", false]], "fit() (hoi.metrics.infotopo method)": [[17, "hoi.metrics.InfoTopo.fit", false]], "fit() (hoi.metrics.infotot method)": [[18, "hoi.metrics.InfoTot.fit", false]], "fit() (hoi.metrics.oinfo method)": [[19, "hoi.metrics.Oinfo.fit", false]], "fit() (hoi.metrics.redundancymmi method)": [[21, "hoi.metrics.RedundancyMMI.fit", false]], "fit() (hoi.metrics.redundancyphiid method)": [[22, "hoi.metrics.RedundancyphiID.fit", false]], "fit() (hoi.metrics.rsi method)": [[20, "hoi.metrics.RSI.fit", false]], "fit() (hoi.metrics.sinfo method)": [[23, "hoi.metrics.Sinfo.fit", false]], "fit() (hoi.metrics.synergymmi method)": [[24, "hoi.metrics.SynergyMMI.fit", false]], "fit() (hoi.metrics.synergyphiid method)": [[25, "hoi.metrics.SynergyphiID.fit", false]], "fit() (hoi.metrics.tc method)": [[26, "hoi.metrics.TC.fit", false]], "get_combinations() (hoi.metrics.dtc method)": [[15, "hoi.metrics.DTC.get_combinations", false]], "get_combinations() (hoi.metrics.gradientoinfo method)": [[16, "hoi.metrics.GradientOinfo.get_combinations", false]], "get_combinations() (hoi.metrics.infotopo method)": [[17, "hoi.metrics.InfoTopo.get_combinations", false]], "get_combinations() (hoi.metrics.infotot method)": [[18, "hoi.metrics.InfoTot.get_combinations", false]], "get_combinations() (hoi.metrics.oinfo method)": [[19, "hoi.metrics.Oinfo.get_combinations", false]], "get_combinations() (hoi.metrics.redundancymmi method)": [[21, "hoi.metrics.RedundancyMMI.get_combinations", false]], "get_combinations() (hoi.metrics.redundancyphiid method)": [[22, "hoi.metrics.RedundancyphiID.get_combinations", false]], "get_combinations() (hoi.metrics.rsi method)": [[20, "hoi.metrics.RSI.get_combinations", false]], "get_combinations() (hoi.metrics.sinfo method)": [[23, "hoi.metrics.Sinfo.get_combinations", false]], "get_combinations() (hoi.metrics.synergymmi method)": [[24, "hoi.metrics.SynergyMMI.get_combinations", false]], "get_combinations() (hoi.metrics.synergyphiid method)": [[25, "hoi.metrics.SynergyphiID.get_combinations", false]], "get_combinations() (hoi.metrics.tc method)": [[26, "hoi.metrics.TC.get_combinations", false]], "get_entropy() (in module hoi.core)": [[12, "hoi.core.get_entropy", false]], "get_mi() (in module hoi.core)": [[13, "hoi.core.get_mi", false]], "get_nbest_mult() (in module hoi.utils)": [[30, "hoi.utils.get_nbest_mult", false]], "gradientoinfo (class in hoi.metrics)": [[16, "hoi.metrics.GradientOinfo", false]], "higher order interactions": [[64, "term-Higher-Order-Interactions", true]], "hoi.metrics": [[1, "module-hoi.metrics", false]], "information theory": [[64, "term-Information-Theory", true]], "infotopo (class in hoi.metrics)": [[17, "hoi.metrics.InfoTopo", false]], "infotot (class in hoi.metrics)": [[18, "hoi.metrics.InfoTot", false]], "landscape() (in module hoi.utils)": [[31, "hoi.utils.landscape", false]], "module": [[1, "module-hoi.metrics", false]], "multiplets (hoi.metrics.dtc property)": [[15, "hoi.metrics.DTC.multiplets", false]], "multiplets (hoi.metrics.gradientoinfo property)": [[16, "hoi.metrics.GradientOinfo.multiplets", false]], "multiplets (hoi.metrics.infotopo property)": [[17, "hoi.metrics.InfoTopo.multiplets", false]], "multiplets (hoi.metrics.infotot property)": [[18, "hoi.metrics.InfoTot.multiplets", false]], "multiplets (hoi.metrics.oinfo property)": [[19, "hoi.metrics.Oinfo.multiplets", false]], "multiplets (hoi.metrics.redundancymmi property)": [[21, "hoi.metrics.RedundancyMMI.multiplets", false]], "multiplets (hoi.metrics.redundancyphiid property)": [[22, "hoi.metrics.RedundancyphiID.multiplets", false]], "multiplets (hoi.metrics.rsi property)": [[20, "hoi.metrics.RSI.multiplets", false]], "multiplets (hoi.metrics.sinfo property)": [[23, "hoi.metrics.Sinfo.multiplets", false]], "multiplets (hoi.metrics.synergymmi property)": [[24, "hoi.metrics.SynergyMMI.multiplets", false]], "multiplets (hoi.metrics.synergyphiid property)": [[25, "hoi.metrics.SynergyphiID.multiplets", false]], "multiplets (hoi.metrics.tc property)": [[26, "hoi.metrics.TC.multiplets", false]], "mutual information": [[64, "term-Mutual-Information", true]], "network behavior": [[64, "term-Network-behavior", true]], "network encoding": [[64, "term-Network-encoding", true]], "normalize() (in module hoi.utils)": [[32, "hoi.utils.normalize", false]], "oinfo (class in hoi.metrics)": [[19, "hoi.metrics.Oinfo", false]], "order (hoi.metrics.dtc property)": [[15, "hoi.metrics.DTC.order", false]], "order (hoi.metrics.gradientoinfo property)": [[16, "hoi.metrics.GradientOinfo.order", false]], "order (hoi.metrics.infotopo property)": [[17, "hoi.metrics.InfoTopo.order", false]], "order (hoi.metrics.infotot property)": [[18, "hoi.metrics.InfoTot.order", false]], "order (hoi.metrics.oinfo property)": [[19, "hoi.metrics.Oinfo.order", false]], "order (hoi.metrics.redundancymmi property)": [[21, "hoi.metrics.RedundancyMMI.order", false]], "order (hoi.metrics.redundancyphiid property)": [[22, "hoi.metrics.RedundancyphiID.order", false]], "order (hoi.metrics.rsi property)": [[20, "hoi.metrics.RSI.order", false]], "order (hoi.metrics.sinfo property)": [[23, "hoi.metrics.Sinfo.order", false]], "order (hoi.metrics.synergymmi property)": [[24, "hoi.metrics.SynergyMMI.order", false]], "order (hoi.metrics.synergyphiid property)": [[25, "hoi.metrics.SynergyphiID.order", false]], "order (hoi.metrics.tc property)": [[26, "hoi.metrics.TC.order", false]], "partial information decomposition": [[64, "term-Partial-Information-Decomposition", true]], "plot_landscape() (in module hoi.plot)": [[27, "hoi.plot.plot_landscape", false]], "prepare_for_it() (in module hoi.core)": [[14, "hoi.core.prepare_for_it", false]], "redundancy": [[64, "term-Redundancy", true]], "redundancymmi (class in hoi.metrics)": [[21, "hoi.metrics.RedundancyMMI", false]], "redundancyphiid (class in hoi.metrics)": [[22, "hoi.metrics.RedundancyphiID", false]], "rsi (class in hoi.metrics)": [[20, "hoi.metrics.RSI", false]], "simulate_hoi_gauss() (in module hoi.simulation)": [[28, "hoi.simulation.simulate_hoi_gauss", false]], "sinfo (class in hoi.metrics)": [[23, "hoi.metrics.Sinfo", false]], "synergy": [[64, "term-Synergy", true]], "synergymmi (class in hoi.metrics)": [[24, "hoi.metrics.SynergyMMI", false]], "synergyphiid (class in hoi.metrics)": [[25, "hoi.metrics.SynergyphiID", false]], "tc (class in hoi.metrics)": [[26, "hoi.metrics.TC", false]], "undersampling (hoi.metrics.dtc property)": [[15, "hoi.metrics.DTC.undersampling", false]], "undersampling (hoi.metrics.gradientoinfo property)": [[16, "hoi.metrics.GradientOinfo.undersampling", false]], "undersampling (hoi.metrics.infotopo property)": [[17, "hoi.metrics.InfoTopo.undersampling", false]], "undersampling (hoi.metrics.infotot property)": [[18, "hoi.metrics.InfoTot.undersampling", false]], "undersampling (hoi.metrics.oinfo property)": [[19, "hoi.metrics.Oinfo.undersampling", false]], "undersampling (hoi.metrics.redundancymmi property)": [[21, "hoi.metrics.RedundancyMMI.undersampling", false]], "undersampling (hoi.metrics.redundancyphiid property)": [[22, "hoi.metrics.RedundancyphiID.undersampling", false]], "undersampling (hoi.metrics.rsi property)": [[20, "hoi.metrics.RSI.undersampling", false]], "undersampling (hoi.metrics.sinfo property)": [[23, "hoi.metrics.Sinfo.undersampling", false]], "undersampling (hoi.metrics.synergymmi property)": [[24, "hoi.metrics.SynergyMMI.undersampling", false]], "undersampling (hoi.metrics.synergyphiid property)": [[25, "hoi.metrics.SynergyphiID.undersampling", false]], "undersampling (hoi.metrics.tc property)": [[26, "hoi.metrics.TC.undersampling", false]]}, "objects": {"hoi": [[1, 1, 0, "-", "metrics"]], "hoi.core": [[5, 0, 1, "", "combinations"], [6, 0, 1, "", "entropy_bin"], [7, 0, 1, "", "entropy_gauss"], [8, 0, 1, "", "entropy_gc"], [9, 0, 1, "", "entropy_hist"], [10, 0, 1, "", "entropy_kernel"], [11, 0, 1, "", "entropy_knn"], [12, 0, 1, "", "get_entropy"], [13, 0, 1, "", "get_mi"], [14, 0, 1, "", "prepare_for_it"]], "hoi.metrics": [[15, 2, 1, "", "DTC"], [16, 2, 1, "", "GradientOinfo"], [17, 2, 1, "", "InfoTopo"], [18, 2, 1, "", "InfoTot"], [19, 2, 1, "", "Oinfo"], [20, 2, 1, "", "RSI"], [21, 2, 1, "", "RedundancyMMI"], [22, 2, 1, "", "RedundancyphiID"], [23, 2, 1, "", "Sinfo"], [24, 2, 1, "", "SynergyMMI"], [25, 2, 1, "", "SynergyphiID"], [26, 2, 1, "", "TC"]], "hoi.metrics.DTC": [[15, 3, 1, "", "__iter__"], [15, 3, 1, "", "compute_entropies"], [15, 4, 1, "", "entropies"], [15, 3, 1, "", "fit"], [15, 3, 1, "", "get_combinations"], [15, 4, 1, "", "multiplets"], [15, 4, 1, "", "order"], [15, 4, 1, "", "undersampling"]], "hoi.metrics.GradientOinfo": [[16, 3, 1, "", "__iter__"], [16, 3, 1, "", "compute_entropies"], [16, 4, 1, "", "entropies"], [16, 3, 1, "", "fit"], [16, 3, 1, "", "get_combinations"], [16, 4, 1, "", "multiplets"], [16, 4, 1, "", "order"], [16, 4, 1, "", "undersampling"]], "hoi.metrics.InfoTopo": [[17, 3, 1, "", "__iter__"], [17, 3, 1, "", "compute_entropies"], [17, 4, 1, "", "entropies"], [17, 3, 1, "", "fit"], [17, 3, 1, "", "get_combinations"], [17, 4, 1, "", "multiplets"], [17, 4, 1, "", "order"], [17, 4, 1, "", "undersampling"]], "hoi.metrics.InfoTot": [[18, 3, 1, "", "__iter__"], [18, 3, 1, "", "compute_entropies"], [18, 4, 1, "", "entropies"], [18, 3, 1, "", "fit"], [18, 3, 1, "", "get_combinations"], [18, 4, 1, "", "multiplets"], [18, 4, 1, "", "order"], [18, 4, 1, "", "undersampling"]], "hoi.metrics.Oinfo": [[19, 3, 1, "", "__iter__"], [19, 3, 1, "", "compute_entropies"], [19, 4, 1, "", "entropies"], [19, 3, 1, "", "fit"], [19, 3, 1, "", "get_combinations"], [19, 4, 1, "", "multiplets"], [19, 4, 1, "", "order"], [19, 4, 1, "", "undersampling"]], "hoi.metrics.RSI": [[20, 3, 1, "", "__iter__"], [20, 3, 1, "", "compute_entropies"], [20, 4, 1, "", "entropies"], [20, 3, 1, "", "fit"], [20, 3, 1, "", "get_combinations"], [20, 4, 1, "", "multiplets"], [20, 4, 1, "", "order"], [20, 4, 1, "", "undersampling"]], "hoi.metrics.RedundancyMMI": [[21, 3, 1, "", "__iter__"], [21, 3, 1, "", "compute_entropies"], [21, 4, 1, "", "entropies"], [21, 3, 1, "", "fit"], [21, 3, 1, "", "get_combinations"], [21, 4, 1, "", "multiplets"], [21, 4, 1, "", "order"], [21, 4, 1, "", "undersampling"]], "hoi.metrics.RedundancyphiID": [[22, 3, 1, "", "__iter__"], [22, 3, 1, "", "compute_entropies"], [22, 4, 1, "", "entropies"], [22, 3, 1, "", "fit"], [22, 3, 1, "", "get_combinations"], [22, 4, 1, "", "multiplets"], [22, 4, 1, "", "order"], [22, 4, 1, "", "undersampling"]], "hoi.metrics.Sinfo": [[23, 3, 1, "", "__iter__"], [23, 3, 1, "", "compute_entropies"], [23, 4, 1, "", "entropies"], [23, 3, 1, "", "fit"], [23, 3, 1, "", "get_combinations"], [23, 4, 1, "", "multiplets"], [23, 4, 1, "", "order"], [23, 4, 1, "", "undersampling"]], "hoi.metrics.SynergyMMI": [[24, 3, 1, "", "__iter__"], [24, 3, 1, "", "compute_entropies"], [24, 4, 1, "", "entropies"], [24, 3, 1, "", "fit"], [24, 3, 1, "", "get_combinations"], [24, 4, 1, "", "multiplets"], [24, 4, 1, "", "order"], [24, 4, 1, "", "undersampling"]], "hoi.metrics.SynergyphiID": [[25, 3, 1, "", "__iter__"], [25, 3, 1, "", "compute_entropies"], [25, 4, 1, "", "entropies"], [25, 3, 1, "", "fit"], [25, 3, 1, "", "get_combinations"], [25, 4, 1, "", "multiplets"], [25, 4, 1, "", "order"], [25, 4, 1, "", "undersampling"]], "hoi.metrics.TC": [[26, 3, 1, "", "__iter__"], [26, 3, 1, "", "compute_entropies"], [26, 4, 1, "", "entropies"], [26, 3, 1, "", "fit"], [26, 3, 1, "", "get_combinations"], [26, 4, 1, "", "multiplets"], [26, 4, 1, "", "order"], [26, 4, 1, "", "undersampling"]], "hoi.plot": [[27, 0, 1, "", "plot_landscape"]], "hoi.simulation": [[28, 0, 1, "", "simulate_hoi_gauss"]], "hoi.utils": [[29, 0, 1, "", "digitize"], [30, 0, 1, "", "get_nbest_mult"], [31, 0, 1, "", "landscape"], [32, 0, 1, "", "normalize"]]}, "objnames": {"0": ["py", "function", "Python function"], "1": ["py", "module", "Python module"], "2": ["py", "class", "Python class"], "3": ["py", "method", "Python method"], "4": ["py", "property", "Python property"]}, "objtypes": {"0": "py:function", "1": "py:module", "2": "py:class", "3": "py:method", "4": "py:property"}, "terms": {"": [18, 20, 23, 36, 37, 38, 39, 40, 42, 44, 46, 47, 48, 51, 53, 56, 59, 60, 62, 65, 66, 67], "0": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 32, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 59, 60, 61, 62, 65, 67, 69, 70], "00": [41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 54, 57, 60, 61, 69], "000": 54, "000008": 45, "000013": 45, "000068": 45, "000292": 45, "000440": 56, "000526": 56, "000540": 45, "000792": 56, "000795": 44, "000867": 48, "000945": 44, "000955": 44, "001132": 51, "001188": 45, "001248": 46, "001291": 44, "001332": 44, "001399": 51, "001460": 45, "001482": 46, "001514": 45, "001530": 45, "001593": 51, "001624": 46, "001628": 45, "001651": 46, "001666": 45, "001671": 51, "001762": 51, "002230": 48, "002443": 48, "002511": 51, "002614": 45, "002717": 45, "002729": 45, "002837": 47, "004202": 51, "004351": 51, "008568": 46, "009364": 46, "009812": 48, "00it": 46, "01": [44, 49, 52, 69], "010098": 46, "013025": 70, "014264": 47, "02": [41, 48, 52, 69], "025": 61, "02it": 44, "03": [48, 49, 69], "030847": 47, "032305": 70, "04": [61, 69], "05": 47, "052802": 70, "054": [48, 49, 69], "055869": 44, "066138": 70, "06it": 60, "07": 41, "070711": 44, "071": 65, "07140": 70, "08": 48, "087830": 44, "08it": 46, "09": [61, 69], "090282": 45, "090620": 44, "092037": 45, "09it": 51, "1": [5, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 32, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 57, 59, 60, 62, 66, 67, 70], "10": [20, 36, 37, 38, 39, 40, 46, 47, 48, 51, 53, 56, 63, 67, 70], "100": [31, 44, 45, 46, 47, 48, 51, 59, 60, 67, 70], "1000": [28, 36, 37, 38, 39, 40, 42, 44, 45, 53, 56, 60, 67, 68], "100000": 53, "1004": 70, "101147319": 65, "106": 70, "107": 36, "1093": 70, "1098": 70, "1099": 70, "10e2": 67, "11": [45, 46, 51, 56, 67, 70], "1103": 70, "1134": 70, "119": 70, "11it": 51, "12": [20, 42, 46, 48, 53, 56, 59, 70], "12482": 70, "13": [45, 51, 56, 67, 70], "1315": 70, "13186": 70, "1321": 70, "133": 70, "134994": 47, "13637": 70, "14": [23, 37, 44, 45, 46, 48, 51, 56, 61, 63, 70], "140": 70, "146471": 56, "148361": 56, "15": [36, 38, 40, 46, 48, 49, 56, 57, 67, 69, 70], "152": 70, "1541": 70, "156": 70, "1573": 70, "159": 70, "16": [45, 46, 56, 69, 70], "16046": 51, "16it": 45, "17": [25, 46, 51, 56, 70], "17019176483154297": 60, "177": 70, "177947": 45, "179842": 45, "17it": 60, "18": [46, 48, 53, 56, 64, 70], "180913": 45, "188": 41, "189": [38, 41, 69], "189541": 46, "19": [22, 45, 48, 51, 56, 70], "190": [47, 70], "192637": 48, "193685": 46, "1940": 64, "1948": 70, "1960": [26, 70], "196290": 51, "1963": 70, "1975": 70, "197775": 46, "1978": [15, 70], "1986": 70, "199325": 45, "1995": 70, "1998": 70, "1999": 70, "2": [6, 9, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 52, 53, 56, 59, 60, 61, 63, 65, 67, 70], "20": [36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 53, 56, 60, 69, 70], "200": [46, 47, 48, 51, 56], "2001": [20, 70], "2003": 70, "2004": [11, 70], "2005": 70, "2009": 70, "2010": 70, "2011": [23, 70], "2014": [20, 70], "2015": 70, "2017": 70, "2018": [17, 70], "2019": [17, 19, 44, 45, 70], "2020": [65, 70], "2021": [22, 70], "20210246": 70, "2022": [25, 70], "2023": [16, 40, 65, 70], "2024": 70, "203173": 44, "203503": 44, "203644": 44, "203772": 44, "203808": 44, "205925": 44, "20it": [46, 60], "20th": 70, "21": [48, 70], "2109": 70, "211186": 46, "214246": 45, "214289": 45, "216": 53, "22": [64, 65, 66, 70], "22015380859375": 60, "22138118743896484": 60, "222631": 51, "2227": 70, "223212242126465": 60, "225347": 46, "23": [46, 70], "2304": 70, "231": [41, 42, 69], "2318": 70, "232792": 46, "233146": 46, "236016e": 48, "238701": 70, "23it": [44, 45], "24": [38, 41, 51, 69, 70], "2404": 70, "241095": 45, "241659": 45, "24it": 60, "25": [19, 44, 45, 46, 53, 70], "250": [52, 53, 69], "2515": 70, "25it": [46, 60], "26": [16, 44, 46, 48, 70], "261": 70, "26873912700000346": 53, "26it": 60, "27": [20, 46, 48, 51, 53, 70], "273890": 46, "27it": 60, "28": [64, 70], "286": 63, "28618431091308594": 60, "287": [59, 61, 69], "29": [40, 41, 44, 69, 70], "297": 70, "29it": 51, "2d": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 53], "2f": 42, "2\u03c0e": 37, "2\u03c0e\u03c3": 36, "3": [11, 28, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 64, 65, 66, 67, 68, 70], "30": [45, 48, 51, 53, 60, 70], "300": 59, "30482": 44, "305800": 46, "308": [36, 41, 69], "30it": 46, "31": [17, 36, 37, 41, 44, 46, 69, 70], "312485": 46, "314976": 46, "315670": 46, "32": [15, 44, 46, 70], "329931": 48, "33": [20, 44, 46, 48, 51, 53, 70], "337": 70, "3390": 70, "33it": [45, 48], "34": [64, 70], "34401702880859375": 60, "347109": 45, "3490": 70, "3495": 70, "34it": 47, "35": [44, 64, 70], "35it": [46, 48], "36": [44, 53, 70], "365911e": 48, "36it": 60, "37": [26, 70], "371283": 45, "3766": 70, "3779": 70, "378": [44, 49, 69], "379": 70, "379484": 46, "38": [64, 70], "380": 70, "381920": 46, "387095": 45, "38it": [51, 60], "390869": 44, "392231": 44, "392336": 48, "392670": 44, "392677": 44, "392874": 44, "397405": 45, "3d": 53, "4": [17, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 67, 68, 70], "40": [44, 59], "40it": [45, 46], "41it": 60, "42": [51, 60], "420686": 48, "423": 70, "43": 44, "4300": 70, "439481e": 48, "444745": 48, "45": [56, 70], "450861": 48, "45it": 44, "46": 63, "470587": 45, "476": 70, "477": 70, "47it": [44, 47], "483097": 48, "484223": 45, "484230": 45, "485553": 45, "485621": 45, "485729": 45, "486022": 45, "48it": 48, "498634": 46, "5": [20, 30, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 51, 56, 59, 60, 67, 70], "50": [45, 51, 59, 60], "51": 70, "52": 70, "533365": 48, "54": 53, "541": [47, 49, 69], "545935": 47, "547": [39, 41, 69], "55": 69, "559214": 46, "569149": 46, "57": 44, "5714287757873535": 53, "573858": 46, "5845532199999752": 53, "597383": 47, "59it": 48, "6": [37, 38, 40, 41, 42, 44, 45, 46, 47, 48, 51, 53, 56, 60, 67, 70], "60": [44, 59], "600548": 48, "603431": 47, "60it": [44, 46, 60], "61it": 48, "627": [51, 52, 69], "62it": 46, "63it": [44, 47], "646320": 45, "64it": 60, "65it": [46, 48], "66": 70, "67": [46, 48, 51], "67it": 45, "68": 70, "68it": 48, "69": [44, 70], "695": 69, "698441": 47, "698491": 45, "69it": 51, "7": [15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 44, 45, 46, 47, 48, 51, 56, 59, 63, 67, 70], "70": 44, "705744e": 48, "71": 44, "718": 49, "71it": 51, "72": 44, "729": 53, "72it": [46, 48], "73": 44, "738": [60, 61, 69], "749583": 45, "74it": 44, "764": [45, 49, 69], "76it": [44, 51], "77": 63, "771": 70, "77it": 46, "782": 70, "78it": 44, "79it": 45, "8": [9, 15, 16, 18, 19, 20, 21, 23, 24, 26, 28, 37, 44, 45, 46, 48, 51, 53, 56, 59, 62, 66, 70], "80": [44, 45, 60], "80it": 44, "81": 53, "82": 70, "824267": 45, "82it": 45, "83": 51, "84": 44, "84it": [45, 48], "8529834747314453": 60, "85it": 46, "86": 44, "869": 70, "86it": 45, "874": 70, "877": 52, "87it": [44, 45, 47], "886": [56, 57, 69], "89": 44, "89it": 45, "9": [15, 16, 18, 19, 20, 21, 23, 24, 26, 44, 45, 51, 53, 56, 59, 66, 70], "90": [44, 59], "91": 70, "919": [40, 41, 69], "91it": 48, "92": 70, "9361505508422852": 60, "93it": 48, "948908": 45, "95": [36, 37, 38, 39, 40, 44, 56], "95it": 46, "968453": 45, "971174": 45, "971751": 45, "981": [46, 49, 69], "99": 44, "995": [37, 41, 69], "99it": 44, "A": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 46, 47, 48, 54, 60, 65, 68, 70], "As": [44, 45, 51, 53, 56, 59, 60, 68, 70], "Be": 60, "But": 45, "By": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29], "For": [12, 25, 29, 36, 37, 42, 44, 45, 46, 47, 48, 51, 56, 59, 62, 68, 70], "IT": [64, 70], "If": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 62, 65, 66, 68, 70], "In": [28, 36, 38, 39, 40, 42, 44, 46, 48, 51, 53, 56, 60, 64, 67, 68, 70], "It": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 37, 47, 48, 64, 70], "Its": 70, "No": 65, "On": 67, "One": [46, 48, 53, 67, 70], "That": [45, 46, 48, 60], "The": [6, 9, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 37, 42, 44, 45, 46, 47, 51, 53, 56, 59, 62, 64, 65, 67, 70], "Their": 47, "Then": [37, 44, 45, 53, 60, 62, 70], "There": 44, "These": [42, 64, 70], "To": [45, 51, 56, 59, 60, 62, 66, 67, 68, 70], "_": [16, 45, 59], "__iter__": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "_autosummari": 53, "_hoi": 56, "_trial": 59, "aa": 70, "ab": [60, 65], "abil": 64, "abl": [44, 48], "about": [20, 25, 28, 44, 45, 46, 47, 48, 56, 59, 60, 64, 70], "abov": [45, 46, 48, 56, 60, 70], "academi": 70, "accur": [68, 70], "accuraci": 59, "achiev": [46, 47, 48, 56, 70], "acknowledg": 65, "across": [51, 56, 68], "activ": [60, 70], "acuiti": 68, "ad": 70, "adam": 70, "adapt": 70, "add": [27, 45, 46, 48, 51, 62], "add_edges_from": 51, "add_nodes_from": 51, "add_subplot": [38, 40], "addit": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 56, 62, 68], "address": [64, 70], "adopt": 65, "adrian": 70, "advanc": [64, 70], "advantag": 70, "advis": 70, "after": 70, "again": [44, 45, 46, 47, 48], "aggreg": 31, "agreement": 65, "aim": [64, 70], "aix": 65, "al": [11, 16, 17, 19, 20, 22, 23, 25, 40, 44, 45, 70], "alain": 70, "alexand": 70, "alford": 70, "algebra": [53, 68], "alic": 70, "all": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 34, 38, 40, 44, 45, 48, 56, 59, 60, 62, 67, 69, 70], "allanson": 70, "allow": [45, 53, 64, 65, 68, 70], "along": [29, 53], "alpha": [36, 37, 38, 39, 40, 51, 56], "alreadi": [6, 9, 66, 70], "also": [11, 20, 23, 37, 44, 45, 46, 47, 48, 56, 64, 65, 66, 68, 70], "altern": 51, "although": 68, "alwai": 70, "am": [22, 70], "american": 70, "amico": 70, "amir": 70, "ammount": 48, "among": [64, 70], "amount": [45, 47, 64, 70], "amx": 65, "an": [5, 15, 26, 31, 37, 42, 45, 48, 51, 53, 56, 60, 62, 64, 67, 68, 70], "analys": 51, "analysi": 70, "analyt": [42, 64], "analyz": 68, "anatomi": 70, "anderson": 70, "andrea": 70, "andrew": 70, "ani": [15, 44, 51, 56, 67, 70], "anil": 70, "annal": 70, "anoth": [15, 42, 64, 70], "answer": 59, "antonacci": 70, "anywher": 65, "aopi": 63, "ap": 70, "apart": 70, "api": [65, 68], "append": [56, 67], "appli": [8, 53, 70], "applic": 70, "approach": [16, 25, 34, 39, 48, 58, 61, 68, 69, 70], "approxim": [47, 48, 70], "ar": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 48, 51, 53, 56, 59, 60, 62, 64, 67, 68, 70], "arang": [51, 56, 59, 67], "arbitrari": [15, 26, 70], "architectur": 70, "area": [31, 56, 68], "areg": 60, "argument": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 53], "around": [31, 56, 59], "arrai": [5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 42, 53, 59], "array_lik": [6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 59], "array_split": 59, "arruda": 70, "arxiv": 70, "asarrai": [53, 67], "ask": 45, "aspect": [47, 70], "assert": 59, "associ": [27, 30, 31, 47, 64, 70], "assum": 62, "assumpt": 68, "astyp": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 67], "atric": 70, "attent": 70, "attractor": 70, "attribut": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "auditori": 70, "auto": 47, "auto_exampl": [41, 49, 52, 54, 57, 61], "auto_examples_jupyt": 34, "auto_examples_python": 34, "autocorrel": 47, "automat": 53, "avail": [42, 70], "averag": 56, "avoid": [44, 70], "ax": [27, 37, 38, 40, 51, 53, 56, 59], "axhlin": [36, 37, 38, 39, 40], "axi": [22, 25, 27, 29, 31, 36, 37, 38, 39, 40, 53, 56], "b": [36, 60, 62, 70], "backend": [65, 68], "background": 68, "balaji": 70, "bandwidth": 10, "bar": 31, "barrat": 70, "barrett": 70, "base": [6, 9, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 42, 44, 48, 62, 70], "base_model": 16, "basic": [53, 62], "battiston": 70, "baudot": [17, 44, 70], "bayesian": 70, "becam": 70, "becaus": [39, 45, 60], "becom": 70, "been": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 65, 70], "beer": 70, "beerenwinkel": 70, "befor": [14, 60], "begg": 70, "behavior": [15, 16, 19, 23, 26, 30, 34, 43, 49, 64, 68, 69], "behaviour": 70, "behind": [45, 70], "being": 44, "bell": 70, "bellow": 68, "below": [37, 44, 51], "benchmark": 68, "benedetta": 70, "benjamin": 70, "bennequin": 70, "berri": 70, "besid": 70, "best": [30, 46, 47, 48], "better": 56, "between": [15, 16, 17, 18, 19, 23, 26, 32, 36, 37, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 64, 65, 68, 70], "beyond": [64, 65, 68, 70], "bia": 8, "bialek": 70, "bianconi": 70, "biascorrect": [8, 38, 39, 40], "bibtex": 62, "big": 70, "bin": [6, 9, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 39, 70], "binar": [9, 70], "binari": 39, "bind": 70, "binom": 67, "biolog": 64, "biologi": [64, 70], "biorxiv": 70, "bit": [6, 7, 8, 9, 10, 11, 36, 37, 38, 39, 40, 42, 45, 46, 48, 56, 59, 60, 70], "bivari": [45, 46, 48], "black": [37, 62], "blakeaw": 11, "block": 70, "blog": 53, "bodi": 70, "bold": [36, 37, 38, 39, 40, 45, 56, 59, 60, 67], "book": 62, "bool": [5, 8, 27, 28, 29, 31], "boostrap": 56, "bootstrap": [19, 27, 30, 57, 68, 69, 70], "bor": 70, "both": [15, 44, 45, 60, 67, 68, 70], "bound": [36, 37, 38, 39, 40, 70], "boundari": 36, "brain": [68, 70], "brainet": [62, 66], "branch": 62, "branch_nam": 62, "brien": 70, "bring": 56, "broad": 70, "brovelli": 63, "browser": 62, "bruno": 70, "bsd": 65, "bug": 62, "build": [31, 42, 62, 70], "built": [65, 68], "bump": 59, "button": 62, "bw_method": 10, "c": [36, 37, 38, 39, 40, 42, 59, 60, 68], "c0": 59, "c_": [46, 48], "calcul": 37, "call": [23, 42, 53, 68, 70], "callabl": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 42], "can": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 37, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 64, 66, 67, 68, 70], "cancel": 39, "cannot": [64, 70], "capabl": [44, 45, 46], "capac": 64, "captur": 68, "card": [17, 44, 70], "care": [60, 70], "carhart": 70, "carri": [20, 45, 46, 47, 48, 56, 59, 60, 64, 70], "case": [28, 31, 39, 42, 48, 59, 64, 70], "categori": [64, 70], "causal": 70, "cbar": 27, "cd": 62, "cell": 67, "cencetti": 70, "center": 31, "central": 31, "centuri": 70, "certain": [37, 70], "challeng": 70, "chang": [53, 62], "channel": 64, "chao": 70, "charact": [28, 45], "character": [45, 70], "characteris": 70, "characterist": [44, 70], "chechik": [20, 70], "check": [31, 44, 48, 62], "checkout": [44, 45, 46, 48, 56, 59, 62, 65, 68], "chichek": 70, "choic": 70, "choos": 28, "chrisferreyra13": 63, "christin": 70, "christof": 70, "christoph": 70, "circular": 51, "circular_layout": 51, "claim": 68, "class": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 65, 68], "claud": [64, 70], "claus": 65, "clear": 70, "clf": 59, "click": 62, "clone": 62, "close": 42, "closest": 11, "cmap": [44, 46, 48, 56], "code": [11, 34, 36, 37, 38, 39, 40, 42, 44, 46, 47, 48, 51, 53, 56, 59, 60, 65, 67, 70], "codecov": 62, "cognit": 70, "colab": 67, "collect": [45, 51, 70], "color": [36, 37, 38, 39, 40, 59], "colorbar": [27, 47], "column": [45, 46, 48], "com": [53, 62, 66, 70], "comb": 5, "combin": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 64, 68], "combinatori": 33, "come": 70, "command": [62, 68], "commit": 62, "common": 70, "commun": [64, 70], "compar": [36, 37, 38, 39, 40, 59, 67, 70], "comparison": [12, 13, 29, 34, 35, 41, 42, 56, 68, 69, 70], "compil": 67, "complet": 70, "complex": [64, 67, 68, 70], "complic": 70, "compon": [64, 70], "compos": 68, "compress": 64, "comput": [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 31, 36, 37, 38, 39, 40, 42, 44, 45, 47, 48, 60, 62, 65, 70], "computation": 56, "compute_entropi": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37], "compute_hoi_beh": 60, "compute_hoi_enc": 60, "compute_tim": 67, "compute_true_entropi": 38, "compute_true_mi": 40, "concept": [64, 70], "concern": 45, "concis": 70, "conclud": 56, "concret": 70, "condit": [17, 19, 27, 30, 34, 43, 45, 49, 56, 69, 70], "confid": [19, 27, 30, 34, 55, 57, 68, 69, 70], "connect": 70, "conscious": 70, "consequ": 45, "consid": [9, 22, 25, 47, 48, 64, 67, 70], "consist": [60, 70], "constant": [36, 37], "constraint": [45, 70], "contain": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 31, 37, 44, 45, 70], "content": 70, "context": [60, 70], "continu": [29, 39, 70], "contrast": 44, "contribut": [60, 63, 64, 65, 68, 70], "control": 70, "convei": [28, 70], "convent": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "converg": [36, 38, 39, 40], "convers": 44, "cooper": 64, "coordin": 70, "copi": [45, 46, 47, 48, 59, 64, 70], "copnorm": 8, "copula": [8, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 42, 67, 68, 70], "core": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 33, 34, 35, 36, 37, 38, 39, 40, 41, 62, 67, 69], "correct": [8, 39, 64, 70], "correctli": 44, "correl": [15, 19, 23, 26], "correspond": 44, "cost": [67, 70], "could": 45, "count": 31, "coupl": [25, 47, 70], "cov": [37, 38, 40, 42, 62], "cov_matrix": [38, 39, 40], "covari": [37, 38, 39, 40, 42, 60], "cpu": [53, 65, 66], "craig": 70, "creat": [37, 38, 39, 40, 47, 51, 56, 59, 60, 62, 67], "create_cov_matrix": [38, 40], "creation": 68, "cross_val_scor": 59, "crucial": 70, "crutchfield": 70, "cryptographi": 64, "current": 27, "custom": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "cut": 65, "cv": 59, "czy": 70, "czyz": 40, "d": [37, 42, 70], "da": 59, "da_": 59, "daniel": 70, "darbellai": 70, "data": [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 31, 34, 35, 37, 41, 42, 56, 60, 64, 67, 69, 70], "data_s": 67, "dataarrai": 31, "datafram": [30, 31, 51], "dataset": 37, "date": 65, "david": 70, "de": 70, "deal": [67, 70], "deciph": 70, "decode_i": 59, "decompos": [64, 70], "decomposit": [22, 25, 30, 34, 43, 49, 64, 69], "def": [36, 37, 38, 39, 40, 53, 59, 60, 67], "default": [5, 6, 9, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30], "default_devic": 67, "defin": [15, 16, 17, 19, 20, 22, 23, 25, 26, 36, 37, 38, 39, 40, 42, 45, 46, 47, 48, 51, 53, 56, 60, 67, 68, 70], "definit": [44, 45, 68, 70], "degre": 70, "delai": [22, 25, 70], "delv": 70, "demonstr": 37, "dens": [38, 40], "densiti": [10, 31, 70], "depend": [17, 31, 59, 65, 68, 70], "depict": 56, "deriv": [15, 16, 19, 23, 26, 30, 34, 43, 49, 69, 70], "describ": [37, 64, 68, 70], "descript": 70, "descriptor": 70, "design": [20, 70], "despit": 44, "det": [37, 38, 40, 42], "det_cov": 38, "det_i": 40, "det_x": 40, "det_xi": 40, "detail": [12, 68, 70], "detect": 64, "determin": 37, "develop": [64, 65, 67, 68, 70], "deviat": 36, "devic": 67, "df": [46, 47, 48], "df_best": 30, "diag": 37, "diag_indic": [38, 40], "diagon": [37, 38, 40], "dict": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 44, 46, 48, 56], "did": 44, "differ": [15, 16, 19, 39, 42, 44, 45, 53, 56, 59, 60, 64, 67, 70], "differenti": [12, 39], "differnt": [38, 40], "digit": 39, "dim": 38, "dimens": [37, 38, 40, 53, 56], "dimension": [12, 13, 31, 34, 35, 37, 41, 42, 69, 70], "direct": [64, 70], "direction_axi": [22, 25], "directli": [48, 66, 70], "discret": [6, 9, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 39, 68, 70], "discriminant_analysi": 59, "discuss": [62, 70], "disentangl": [45, 46, 70], "dishie2498": 63, "disord": 70, "dispar": 44, "distanc": 53, "distinguish": 70, "distribut": [12, 26, 31, 34, 35, 37, 38, 41, 42, 68, 69, 70], "dit": 68, "diverg": 26, "divid": [31, 53, 70], "do": [46, 47, 48, 53, 62], "document": [53, 65, 66, 68], "doe": 70, "doesn": [56, 67], "doi": 70, "domain": 68, "domin": [45, 60, 70], "dominik": 70, "done": [40, 53, 60, 70], "dopaminerg": 70, "dot": [37, 53], "doubl": [48, 70], "download": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60], "draft": 62, "draw": 51, "drawn": 70, "dry": [53, 67], "dtc": [19, 23, 70], "dual": [15, 19, 23], "due": 70, "dufour": 70, "dynam": [67, 68, 70], "e": [36, 37, 38, 42, 45, 46, 48, 60, 62, 64, 67, 68, 70], "e1008289": 70, "e21090869": 70, "each": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 37, 38, 40, 44, 45, 46, 53, 56, 59, 60, 62, 64, 67, 70], "eas": 65, "easiest": 66, "ebrain": 65, "ecolog": 64, "ecologi": 64, "econom": 70, "edg": [31, 51, 65], "edge_fc": 51, "edge_fc_cmap": 51, "editor": 62, "effect": [60, 64, 70], "effici": [53, 68], "eilon": 70, "either": [5, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 31, 36, 46, 59], "elad": 70, "electrophysiolog": 70, "elegantli": 70, "element": [5, 15, 20, 26, 37, 38, 40, 45, 53, 60, 64, 70], "elif": [38, 40, 59], "ellison": 70, "els": [38, 40], "elwood": 70, "emerg": [47, 60, 70], "emmanuel": 70, "empti": 56, "en": [53, 66], "enabl": [44, 70], "encod": [15, 16, 19, 23, 26, 30, 34, 43, 49, 59, 64, 68, 69], "end": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62], "endr": 70, "eneuro": 70, "engag": 60, "engin": [64, 65], "enrico": 70, "ensur": 62, "ent": 38, "ent_theor": 38, "entropi": [6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 33, 39, 40, 41, 44, 45, 51, 62, 64, 68, 69], "entropy_analyt": 42, "entropy_bin": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "entropy_gauss": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "entropy_gc": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "entropy_hist": 12, "entropy_kernel": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "entropy_knn": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "enumer": [36, 37, 38, 39, 40, 45, 47, 59], "environ": 67, "equal": [29, 31, 37], "equiv": [20, 46, 48], "equival": [26, 39, 53], "eran": 70, "error": [36, 39, 64], "especi": 68, "essenc": 64, "estim": [8, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 33, 34, 35, 41, 42, 44, 60, 68, 69, 70], "et": [11, 16, 17, 19, 20, 22, 23, 25, 40, 44, 45, 70], "etc": [67, 68], "etiennecmb": 63, "eu": 65, "euler": [36, 37], "evalu": 70, "even": [45, 70], "eventu": 48, "evolut": [22, 25, 70], "evolv": 60, "exact": 56, "exampl": [18, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 59, 60, 61, 62, 65, 67, 68, 69], "exceed": 20, "except": [45, 53, 56, 60], "excess": 70, "exclud": 70, "exclus": 44, "execut": [41, 49, 52, 53, 54, 57, 61, 65, 69], "exogen": [23, 70], "expect": [42, 46, 47, 64], "experimentalist": 70, "explain": 64, "explan": 70, "explor": 70, "expon": 53, "extend": 70, "extens": [15, 26, 70], "extern": [60, 64, 70], "extract": [38, 39, 40, 42, 51], "extrins": 64, "ey": [38, 40], "f": [36, 37, 38, 39, 40, 53, 56, 59, 60, 70], "fact": [67, 70], "fae": 70, "failur": 64, "fall": 64, "fals": [5, 28, 29, 31, 38, 39, 40, 44, 46, 48, 56, 59, 60, 67, 70], "familiar": 65, "fascin": 70, "fast": [56, 67], "faster": [67, 68], "fault": 64, "favorit": 62, "fcn": [12, 13, 36, 37, 38, 39, 40, 53], "featur": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 46, 47, 48, 59], "federico": 70, "fernando": 70, "ferraz": 70, "fetch": 62, "fi": 70, "field": [67, 70], "fig": [37, 38, 40, 59], "figsiz": [37, 38, 40, 59], "figur": [37, 38, 40], "file": [41, 49, 52, 54, 57, 61, 62, 69], "file1": 62, "file2": 62, "fill": 5, "fill_between": [36, 37, 38, 39, 40, 56], "fill_valu": 5, "final": [37, 45, 53, 60, 62, 67, 70], "find": [45, 48, 68], "finoia": 70, "first": [16, 29, 45, 46, 47, 48, 51, 53, 56, 60, 67], "fit": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67, 68], "fix": 56, "flake8": 62, "flecker": 70, "float": [6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 32, 53, 59], "focu": 70, "focus": [45, 70], "foldiak": 70, "follow": [22, 36, 44, 47, 48, 60, 62, 67, 68, 70], "font_size_nod": 51, "fontweight": [36, 37, 38, 39, 40, 45, 56, 59, 60, 67], "fork": 62, "formal": 70, "formisano": 70, "formula": [42, 70], "found": [44, 45, 64, 68], "foundat": [65, 70], "frac": [36, 37, 38, 39, 40, 42], "framework": [47, 48, 64, 65, 70], "franceschiello": 70, "fraser": 70, "freder": 70, "frequenc": [31, 70], "frequentist": 70, "friendli": 53, "from": [31, 37, 38, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 59, 60, 61, 62, 64, 66, 67, 68, 69], "fryer": 70, "full": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62], "fulli": [59, 64], "function": [2, 4, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 34, 36, 37, 38, 39, 40, 42, 51, 59, 60, 62, 65, 68, 70], "functool": [39, 53], "fundament": [42, 64, 70], "further": [44, 45, 46, 48, 53, 56, 59, 68], "futur": [25, 47, 64, 70], "fx": [38, 39, 40], "g": [47, 68, 70], "gabert": 70, "gabriel": 70, "gal": 70, "galleri": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 69], "gastpar": 70, "gather": 70, "gauss": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37], "gaussian": [7, 8, 10, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 36, 37, 38, 39, 40, 42, 60, 67, 68, 70], "gaussian_kd": 10, "gbauer": 70, "gc": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 42, 44, 45, 51, 56, 60, 67, 68], "gca": 56, "gcmi": [38, 40], "gener": [28, 34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 64, 67, 70], "genet": 70, "geomspac": [36, 37, 38, 39, 40], "georg": 70, "get": [5, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 36, 37, 38, 39, 40, 45, 56, 67, 68], "get_combin": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 47], "get_covari": 37, "get_entropi": [36, 37, 38, 42, 67], "get_mi": [39, 40, 42], "get_nbest_mult": [44, 45, 46, 47, 48, 51, 56, 68], "ggplot": [36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67], "ginestra": 70, "giordano": 70, "giovanni": 70, "git": [62, 66], "github": [62, 66], "giulia": 70, "give": 45, "given": [39, 40, 44, 45, 64, 70], "globerson": 70, "glossari": 68, "go": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 65, 67, 68, 70], "goaillard": 70, "goodman": 70, "googl": 65, "gpu": [53, 65, 66], "grabowski": 70, "gradient": [16, 45, 48, 59], "gradientoinfo": [45, 59, 60, 68, 70], "grant": 65, "graphic": 70, "grassberg": 70, "greater": [60, 64, 70], "griffith": 70, "gross": 70, "group": [48, 64, 70], "grow": [67, 70], "gui": 70, "guid": [42, 70], "guilherm": 70, "guillaum": 70, "h": [15, 19, 23, 26, 36, 37, 38, 42, 44, 45, 51, 70], "h_": [17, 44], "h_idx": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "h_max": 60, "h_theoric": [36, 37], "h_x": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37], "ha": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 44, 53, 65, 70], "half": 70, "hallmark": 60, "han": [45, 59, 60, 70], "handl": 70, "hann": 59, "harald": 70, "harri": 70, "have": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37, 38, 40, 42, 45, 53, 66, 67, 68, 70], "height": 31, "henc": 70, "henrik": 70, "here": [45, 46, 47, 48, 51, 56, 59, 60, 66, 68], "hgx": 68, "high": [12, 13, 28, 34, 35, 41, 47, 69, 70], "higher": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 33, 34, 37, 42, 44, 46, 48, 50, 52, 53, 59, 64, 69], "highest": [44, 46, 47, 48, 51, 56], "highli": 68, "highlight": [44, 70], "hinteract": 65, "hist": 27, "hist_kwarg": 27, "histogram": [12, 27, 31, 36, 37, 38, 39, 40, 70], "hoi": [33, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 53, 56, 58, 60, 61, 64, 66, 67, 68, 69, 70], "hoi_m": 56, "hoi_order_3": 51, "hoi_r": 48, "hoi_syn": 48, "hold": 44, "holland": 70, "horizon": 65, "horizont": 37, "how": [16, 19, 28, 31, 34, 44, 45, 46, 47, 48, 51, 53, 56, 58, 59, 61, 64, 68, 69, 70], "howev": [44, 46, 48, 56, 59, 67, 70], "html": [53, 66], "http": [44, 53, 62, 66, 70], "huge": 67, "hull": 51, "human": 70, "hx": [6, 7, 8, 9, 10, 11], "hypergraph": 51, "hypothesi": 70, "i": [5, 6, 9, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 53, 56, 59, 60, 62, 64, 65, 66, 67, 68, 70], "i_": [17, 44], "iacopini": 70, "iacopo": 70, "ibm": 70, "idea": 45, "ident": 70, "identifi": [44, 70], "idtxl": 68, "ieee": 70, "ignor": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "igor": 70, "ik": [16, 45], "il": 70, "illustr": [34, 45, 46, 47, 48, 51, 56], "imagin": 53, "implement": [44, 51, 53, 62, 68, 70], "import": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67, 68, 70], "improv": [62, 64], "imshow": 47, "in_ax": [53, 67], "inc": 70, "incept": 70, "includ": [28, 37, 56, 62, 65], "increas": [37, 67], "independ": [42, 47, 70], "index": [20, 21, 24, 27, 30, 34, 43, 44, 45, 47, 48, 49, 51, 56, 64, 69], "indic": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 70], "individu": [20, 45, 60, 64, 70], "inf": 70, "infer": [44, 68, 70], "inflat": 47, "influenc": 45, "info": [16, 19, 23, 45, 56], "inform": [11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 33, 38, 40, 41, 43, 46, 48, 49, 51, 58, 60, 61, 64, 65, 67, 68, 69], "infotheori": 68, "infotopo": [44, 51, 68, 70], "initi": 56, "inject": [45, 47, 51, 60], "innov": 65, "input": [6, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 37, 42, 53], "insid": [46, 48, 62], "insight": 70, "inspect": [17, 27, 30, 34, 46, 47, 48, 50, 52, 69, 70], "inspir": 40, "instal": [30, 65, 67], "instanc": 70, "instead": [47, 48, 70], "int": [5, 6, 9, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 36, 37, 38, 39, 40, 59, 67], "integr": [22, 25, 30, 34, 43, 49, 68, 69], "intens": 56, "interact": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 33, 34, 37, 45, 46, 48, 50, 52, 56, 59, 60, 64, 69], "interdepend": [47, 70], "interdisciplinari": 70, "interest": 70, "intern": 70, "interpol": 47, "interpret": [46, 47, 48, 70], "interv": [19, 27, 30, 34, 36, 37, 38, 39, 40, 42, 55, 57, 68, 69, 70], "intric": 70, "intrins": [15, 45, 64], "introduc": [44, 45, 46, 48, 53, 59, 70], "introduct": [12, 13, 34, 35, 41, 50, 52, 68, 69, 70], "intuit": [45, 60], "invalu": 70, "investig": [59, 67, 70], "involv": 70, "io": [44, 53, 66], "ipynb": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60], "isol": 45, "israel": 70, "issu": [62, 67], "item": [36, 37, 38, 39, 40], "iter": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "its": [15, 16, 19, 23, 26, 30, 34, 36, 43, 48, 49, 56, 64, 68, 69, 70], "j": [15, 19, 23, 26, 45, 70], "jame": [23, 70], "jax": [5, 10, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 34, 50, 52, 65, 66, 68, 69, 70], "jax_eucl": 53, "jean": 70, "jensen": 70, "jirina": 70, "jnp": [5, 53, 67], "joachim": 70, "john": 70, "joint": [26, 38, 39, 40, 70], "joseph": 70, "journal": 70, "judith": 70, "julia": 70, "jupyt": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60], "just": 45, "k": [5, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 44, 45, 59, 67, 70], "kayser": 70, "kazuto": 70, "kbinsdiscret": 29, "keep": 56, "kei": [36, 37, 38, 39, 40], "kernel": [10, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 47, 70], "kind": [27, 44, 46, 48, 51, 53, 56, 70], "knn": [11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 70], "know": [46, 48, 60, 70], "knowledg": [62, 64], "known": [44, 53, 59, 70], "kobayashi": 70, "koch": 70, "kraskov": [11, 70], "kullback": 26, "kwarg": [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 39], "l": 70, "label": [36, 37, 38, 39, 40, 45, 59, 67], "lack": 70, "lall": 70, "lambda": 36, "lambda_": 36, "landcap": 31, "landscap": [27, 44, 56, 68], "lapish": 70, "larg": 26, "larger": 67, "largest": [45, 51], "lasserr": 70, "last": 70, "latest": [53, 66], "latora": 70, "launch": [46, 47, 48], "lax": 53, "layout": 51, "ldot": 70, "lead": [36, 53, 67], "learn": [16, 34, 56, 58, 61, 65, 66, 69, 70], "least": [53, 56, 70], "left": [42, 70], "legend": [36, 37, 38, 39, 40, 45, 59, 67], "len": [36, 37, 38, 39, 40], "length": [22, 25], "less": 70, "let": [36, 37, 38, 39, 42, 44, 45, 46, 47, 48, 53, 56, 59, 60, 67], "letter": 70, "leverag": 48, "li": 56, "librari": [53, 67, 68, 70], "liebler": 26, "light": 70, "like": [53, 68], "limit": [48, 56, 68, 70], "linalg": [37, 38, 40, 42], "line": [37, 56, 68, 70], "linear": [53, 68, 70], "lineardiscriminantanalysi": 59, "linearli": 67, "linestyl": [36, 37, 38, 39, 40], "link": [39, 40, 45, 70], "linspac": 67, "lint": 62, "list": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 36, 37, 38, 39, 40, 56, 65, 66, 68, 70], "literatur": 70, "lizier": 70, "locat": 62, "log": [36, 37, 42], "log2": [36, 38, 39, 40], "log_": [36, 38, 39, 40, 70], "logarithm": [6, 9], "look": [46, 47, 48, 68], "lost": 70, "lot": 70, "low": 70, "lower": [36, 37, 38, 39, 40, 44, 56, 70], "lowest": [46, 47, 48, 51], "luca": 70, "luppi": [25, 70], "lw": [36, 37, 38, 39, 40, 56, 59], "m": [36, 45, 47, 56, 62, 70], "machin": [16, 34, 58, 61, 69, 70], "mai": 37, "main": [34, 62, 67, 70], "mainli": [56, 70], "maintain": 62, "make": [37, 62, 70], "make_spd_matrix": 37, "mani": 70, "manipul": 68, "manon": 70, "map": 70, "marc": 70, "margin": 26, "marinazzo": 70, "marker": 37, "marqu": 70, "marseil": 65, "martial": 70, "marx": 70, "mass": 70, "math": [26, 45], "mathcal": [36, 38, 39, 40], "mathemat": [44, 45, 64, 70], "matplotlib": [36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60, 62, 67], "matrix": [37, 38, 39, 40, 42, 47, 60], "matrix_to_plot": 47, "mattehub": 63, "max": [25, 47, 53, 60, 70], "max_": [48, 70], "maxim": [20, 70], "maximum": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 32, 68], "maxsiz": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 45, 46, 47, 48, 51, 59, 60, 67, 68], "mb": [41, 49, 52, 54, 57, 61, 69], "mdpi": 70, "mean": [36, 37, 38, 39, 40, 42, 46, 48, 53, 56, 59, 60, 67], "measur": [26, 33, 45, 46, 47, 48, 60, 64, 68], "mechan": 70, "mechanist": 70, "mediano": [22, 70], "mem": [41, 49, 52, 54, 57, 61, 69], "menon": 70, "mention": 70, "messag": [62, 64], "method": [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 42, 44, 45, 51, 56, 60, 67, 68, 70], "metric": [12, 13, 27, 30, 33, 35, 36, 37, 38, 39, 40, 41, 44, 45, 46, 47, 48, 49, 51, 56, 59, 60, 64, 65, 67, 68, 69, 70], "metric_nam": [36, 37, 38, 39, 40], "mi": [8, 13, 18, 20, 21, 22, 24, 25, 34, 35, 38, 41, 42, 64, 69], "mi_bin": 39, "mi_binning_fcn": 39, "mi_theor": [39, 40], "michael": 70, "mid": 56, "midbrain": 70, "midex": 65, "milan": 70, "min": [22, 47, 53, 60, 70], "min_": [48, 70], "minimum": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 32, 47, 48, 68, 70], "minmax": 53, "minmax_2d": 53, "minmax_3d": 53, "minmax_3d_jit": 53, "minmaxscal": 51, "minsiz": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67, 68], "minu": [16, 19, 23, 45], "minut": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60], "miscellan": [52, 69], "miss": 5, "mitig": 68, "mmi": [21, 22, 24, 25, 27, 30, 34, 43, 47, 49, 69], "mode": [38, 40, 62], "model": [27, 30, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67, 68, 70], "model_r": 48, "model_select": 59, "model_syn": 48, "modifi": [62, 67], "modul": [60, 64, 67, 70], "monica": 70, "monoton": 70, "moon": 70, "more": [12, 44, 46, 48, 56, 60, 64, 65, 70], "moreno": 70, "most": [42, 46, 47, 48, 65, 70], "move": [46, 48], "mu": [36, 38, 40], "mu_": [39, 40], "mu_i": 39, "mu_x": 39, "much": [47, 56, 70], "mult_order_3": 51, "mult_siz": 31, "multi_s": 31, "multiinform": 70, "multipl": [60, 64, 65, 67], "multiplet": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 45, 46, 47, 48, 56, 68, 70], "multivari": [12, 17, 34, 35, 38, 40, 41, 42, 59, 60, 68, 69, 70], "multivariate_norm": [37, 38, 39, 40], "musician": 68, "must": 67, "mutual": [11, 13, 15, 17, 18, 21, 22, 24, 25, 26, 29, 33, 38, 40, 41, 44, 47, 48, 51, 64, 68, 69], "n": [5, 15, 16, 18, 19, 20, 23, 26, 30, 36, 37, 38, 39, 40, 45, 46, 48, 53, 54, 59, 67, 68, 70], "n_": [36, 37, 38, 39, 40, 67, 70], "n_b": 56, "n_best": [30, 45, 46, 47, 48, 51], "n_bin": [9, 29, 31, 39, 40], "n_boot": 56, "n_combin": 5, "n_dim": [38, 40], "n_f": 67, "n_featur": [6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 42, 47, 67], "n_hoi": 31, "n_m": [36, 37, 38, 39, 40, 45], "n_mult": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "n_multiplet": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "n_node": [56, 60], "n_r": [36, 37, 38, 39, 40, 59], "n_repeat": [36, 37, 38, 39, 40], "n_sampl": [6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 36, 37, 38, 39, 40, 42, 56, 59, 60, 67, 68], "n_time": 59, "n_v": 67, "n_variabl": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 67], "n_x": 59, "n_y": 59, "naftali": 70, "name": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 53, 62], "nathaniel": 70, "nation": 70, "natur": [59, 60, 70], "ndarrai": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28], "ndata": [36, 39], "nearest": [11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 70], "necessari": 70, "need": [39, 60], "neg": [20, 28, 44, 45, 46, 51, 59, 60, 64, 70], "negin": 70, "neglect": 70, "neighbor": [11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 70], "nelken": 70, "nelsontang": 53, "neq": [16, 45], "network": [15, 16, 19, 23, 26, 30, 34, 43, 44, 49, 56, 64, 67, 68, 69], "networkx": 68, "neural": 70, "neurip": 40, "neuroimag": 70, "neuron": 70, "neurosci": [68, 70], "neurotransmitt": 70, "nevertheless": 37, "new": [67, 70], "next": 67, "nh": [23, 45, 70], "nica": 70, "nice": 53, "nichola": 70, "niko": 70, "node": [44, 45, 51, 56, 60, 67, 68], "node_label": 51, "node_s": 51, "nois": 47, "non": [56, 64], "none": [5, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 37, 38, 40, 47], "nonlinear": 70, "nonneg": 70, "normal": [8, 12, 31, 34, 35, 38, 40, 41, 42, 45, 68, 69, 70], "notabl": 44, "note": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 39, 70], "notebook": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67, 68], "notic": [48, 53], "now": [37, 42, 44, 45, 46, 47, 48, 53, 56, 59, 60], "np": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67], "nthe": [38, 40], "nuanc": [64, 70], "number": [5, 9, 15, 26, 28, 29, 30, 31, 36, 37, 38, 39, 40, 53, 56, 59, 67, 70], "numpi": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 56, 59, 60, 66, 67], "numpy_eucl": 53, "numpydoc": 62, "nuzzi": 70, "o": [15, 16, 19, 23, 26, 28, 30, 34, 37, 43, 48, 49, 64, 67, 68, 69], "object": 51, "observ": [31, 46, 47, 48, 70], "obtain": [60, 64], "occur": 64, "occurr": 70, "off": [38, 40], "offer": 70, "offici": 53, "often": [64, 70], "oinfo": [16, 44, 45, 56, 59, 60, 67, 68, 70], "oldest": [26, 70], "omega": [16, 19, 23, 45, 70], "omega_": 59, "onc": [62, 68, 70], "one": [37, 45, 56, 60, 64, 67, 70], "onli": [28, 38, 40, 44, 46, 47, 48, 51, 56, 59, 62, 64, 66, 70], "open": 62, "oper": [39, 47, 53, 67, 70], "optim": 37, "option": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 53, 66], "orchestra": 68, "order": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 33, 34, 37, 42, 43, 45, 46, 47, 48, 49, 50, 52, 59, 64, 69], "org": 70, "organ": 70, "origin": [11, 44, 62, 68], "other": [15, 42, 45, 46, 48, 60, 64, 70], "otherwis": 68, "our": [44, 51, 53, 62, 68, 70], "out": 39, "output": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 51], "over": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 53, 56, 60], "owen": 70, "own": [47, 70], "p": [26, 70], "p_high": 56, "p_low": 56, "packag": [51, 62, 65, 68], "page": [62, 68, 70], "pair": [38, 40, 59, 70], "pairwis": [18, 47, 64, 65, 68], "panda": [30, 31, 51, 62, 66], "paola": 70, "paramet": [5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 59, 60], "parametr": [56, 70], "part": [15, 48, 51, 59, 60, 64, 67, 70], "partial": [39, 53, 59, 64, 70], "partial_": [16, 45, 70], "particular": [36, 39, 40, 53, 70], "particularli": 70, "partit": 70, "pass": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 62], "past": [47, 67], "patania": 70, "path_to_test_fil": 62, "pathwai": 70, "pattern": [60, 70], "paul": 70, "paw": 70, "pcolormesh": 27, "pedro": [22, 70], "pep8": 62, "per": [31, 38, 40], "percent": 31, "percentil": [36, 37, 38, 39, 40, 56], "perform": [29, 53, 68, 70], "permut": 59, "perspect": 70, "peter": 70, "petri": 70, "phenomena": 70, "phenotyp": 70, "phiid": [22, 25], "philipp": 70, "philosoph": 70, "phy": 11, "physic": 70, "physrev": 70, "pi": [36, 37, 38, 42], "pickard": 70, "pid": [64, 70], "pierr": 70, "pinpoint": 44, "pip": [62, 66, 67, 68], "pitmonticon": 63, "plai": 70, "pleas": [39, 62, 65, 66, 68], "plethora": 70, "plo": 70, "plot": [17, 30, 33, 34, 36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 50, 52, 59, 60, 67, 68, 69, 70], "plot_bootstrap": [56, 57, 69], "plot_decod": 59, "plot_entropi": [36, 41, 69], "plot_entropies_mvar": [37, 41, 69], "plot_entropy_high_dimension": [38, 41, 69], "plot_infotopo": [44, 49, 69], "plot_inspect_result": [51, 52, 69], "plot_landscap": [44, 46, 48, 51, 56, 68], "plot_mi": [39, 41, 69], "plot_mi_high_dimension": [40, 41, 69], "plot_ml_vs_it": [59, 61, 69], "plot_oinfo": [45, 49, 69], "plot_rsi": [46, 49, 69], "plot_sim_red_syn": [60, 61, 69], "plot_syn_phiid": [47, 49, 69], "plot_syn_red_mmi": [48, 49, 69], "plot_xi": 59, "plt": [27, 36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67], "plt_kwarg": [27, 44, 46, 48, 56], "plu": [45, 47, 70], "po": 51, "point": [11, 44, 45, 53, 59, 67, 70], "popul": 29, "pose": 67, "posit": [20, 28, 37, 44, 45, 46, 47, 48, 51, 53, 59, 60, 70], "possess": 44, "possibl": [5, 46, 48, 60, 67, 70], "post": 33, "potenti": 68, "pouei": 70, "pre": 33, "precis": 60, "predict": 47, "predictor": 64, "prepar": 14, "preprint": 70, "preprocess": [29, 51], "presenc": [47, 48, 64, 70], "present": [44, 60, 70], "preserv": 70, "pretti": 68, "prevail": 70, "previou": [45, 60], "principl": 70, "print": [42, 44, 45, 46, 47, 48, 51, 53, 56, 60, 68], "probabl": [12, 31, 70], "problem": [67, 70], "procedur": 70, "proceed": 70, "process": [9, 33, 37, 64, 70], "produc": [60, 64, 70], "product": [26, 53], "program": 67, "programm": 65, "project": 65, "promin": 70, "properti": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 47, 70], "proport": 31, "propos": [62, 70], "proven": 70, "provid": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 59, 64, 65, 68, 70], "proxi": 70, "psycholog": 70, "publish": 70, "pure": 53, "purport": 20, "pursuit": 70, "push": 62, "py": [36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 56, 57, 59, 60, 61, 62, 69], "pyphi": 68, "pyplot": [36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67], "pytest": 62, "python": [11, 34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 65, 66, 67, 68, 70], "quadruplet": [44, 56], "quantif": 64, "quantifi": [17, 45, 64, 65, 68, 70], "quantil": 29, "quantiti": 45, "question": [45, 59, 62, 70], "quick": [34, 50, 52, 69], "quickli": 70, "r": [56, 59, 70], "rajagopalan": 70, "rand": [42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67], "randal": 70, "random": [17, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 64, 67, 70], "random_st": 56, "randomli": 56, "rang": [36, 37, 38, 39, 40, 47, 56, 59, 70], "rate": 36, "ravel": 59, "re": [44, 60, 65], "read": 45, "readthedoc": [44, 53, 66], "real": [67, 70], "realli": 56, "rebas": 62, "receiv": [46, 47, 48, 59, 60], "recent": [67, 70], "recommand": 56, "recommend": [45, 67], "reconcil": 70, "record": 70, "recoveri": 64, "red": [22, 47, 48, 59, 70], "red_result": 47, "redmmi": 48, "redphiidmmi": 47, "reduc": 70, "reduct": [64, 70], "redund": [15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 34, 43, 49, 51, 58, 59, 61, 64, 68, 69], "redundancymmi": [48, 70], "redundancyphiid": [47, 70], "refer": [11, 15, 16, 17, 19, 20, 22, 23, 25, 26, 28, 51, 64, 66, 70], "reflect": [46, 70], "regard": 56, "region": 70, "rel": [53, 68], "rel_strength": 59, "rel_typ": 59, "relat": [15, 16, 19, 23, 26, 39, 45, 47, 59, 70], "relationship": [59, 60, 64, 68, 70], "relev": 70, "reli": [67, 68], "reliabl": 64, "rememb": 48, "remind": [44, 56], "remot": 62, "remov": 45, "repeat": [53, 56], "repetit": [36, 37, 38, 39, 40], "repo": 62, "report": 70, "repositori": 62, "repres": [5, 31, 45, 56, 60, 64, 70], "represent": 27, "requir": [30, 39, 64, 66, 67], "resampl": 56, "research": [65, 67, 70], "reshap": [36, 53, 59, 60], "resourc": 53, "respect": [28, 45, 47, 48, 59, 64, 68, 70], "result": [36, 38, 39, 40, 46, 47, 48, 56, 60, 67, 70], "retriev": [45, 46, 48, 51, 59, 68], "return": [5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 37, 38, 39, 40, 51, 53, 59, 60, 67], "rev": 11, "reveal": 70, "review": 70, "rf": 59, "right": [42, 70], "rightarrow": [16, 17, 19, 20], "robin": 70, "robust": [47, 68, 70], "role": 70, "rosa": [19, 45, 70], "rotat": 56, "rousselet": 70, "row": 70, "rowvar": 42, "royal": 70, "rsi": [18, 46, 48, 64], "rule": 70, "run": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 65, 67, 68], "ryan": 70, "s_": 48, "sai": [53, 56, 60], "said": 45, "same": [29, 44, 46, 47, 48, 53, 56, 60, 64, 65, 68, 70], "sampl": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 37, 38, 42, 44, 45, 46, 47, 48, 56, 59, 60, 67], "satisfi": 62, "satosi": 70, "sca": [37, 59], "scagliarini": [16, 70], "scale": 67, "scan": 53, "scatter": [27, 44, 46, 48, 51, 56], "scenario": 70, "schneidman": 70, "schyn": 70, "scienc": 70, "scientif": 70, "scientist": 70, "scikit": [56, 65, 66], "scipi": [10, 53, 66], "script": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 68], "sebastiano": 70, "second": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67, 70], "section": [45, 68, 70], "see": [10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 36, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 68, 70], "seed": [51, 60], "seen": 70, "segreg": 44, "select": [46, 47, 48, 67], "self": 70, "semi": 37, "semin": 70, "sen": 60, "send": [45, 46, 48], "sens": 70, "sensit": [15, 26, 70], "sent": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "separ": [47, 64, 70], "septemb": 70, "seri": [68, 70], "serv": 70, "set": [5, 15, 18, 20, 28, 42, 53, 60, 62, 64, 67, 70], "set_text": [38, 40], "set_xlabel": [38, 40], "set_xticklabel": 56, "set_ylabel": [38, 40], "seth": 70, "sever": [36, 37, 39], "shade": 56, "shannon": [39, 64, 70], "shape": [5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 31, 37, 38, 40, 42, 46, 48, 53, 56, 59], "share": [15, 26, 45, 47, 64, 70], "sharei": 59, "sharex": 59, "shed": 70, "short": [44, 53], "should": [6, 8, 9, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 44, 62, 70], "show": [31, 36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60], "showcas": [45, 51], "shown": 70, "sigma": [36, 37, 38, 40, 42], "sigma_": [39, 40], "sigma_i": 39, "sigma_x": 39, "sign": 70, "signal": [60, 62], "sim": [36, 39, 40], "simeq": 67, "similar": 40, "similarli": 60, "simmetr": 47, "simon": 70, "simpl": [46, 47, 48, 56, 60, 70], "simpli": [64, 70], "simul": [16, 19, 33, 34, 36, 37, 38, 39, 40, 56, 58, 61, 69, 70], "simulate_data": 59, "simulate_hoi_gauss": [60, 68], "sinc": [42, 70], "sinfo": [45, 70], "singl": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37, 46, 48, 62, 70], "situat": 70, "six": 48, "size": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 36, 37, 42, 46, 47, 48, 67, 68, 70], "sklearn": [29, 37, 51, 56, 59], "sl": 59, "slice": 59, "slow": 53, "small": [44, 70], "smallest": [45, 51], "smooth": 70, "so": [42, 59, 62, 70], "social": [64, 68], "societi": 70, "softwar": [62, 66], "some": [36, 45, 47, 53, 56, 60, 67, 70], "sonia": 70, "sourc": [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 70], "space": 70, "spars": [38, 40], "spatial": 56, "special": 39, "specif": [36, 44, 60, 62, 65], "specifi": [5, 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 38, 40, 53, 59], "spectral_r": [44, 51, 56], "sphinx": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62], "sphinx_gallery_thumbnail_numb": [51, 56], "sphinxcontrib": 62, "spread": [46, 51, 68], "springer": 70, "sqrt": [37, 53], "squeez": [56, 59, 60], "st": 70, "stack": 56, "stamataki": 70, "stand": [44, 46, 48], "standard": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 39, 70], "stark": 70, "start": [42, 44, 46, 47, 48, 59, 67], "stat": [10, 31], "state": [47, 64, 70], "static": [60, 70], "static_argnum": 53, "statist": [17, 31, 56, 57, 59, 65, 69, 70], "step": [56, 62], "still": 70, "stochast": 70, "storag": 64, "store": 47, "str": [10, 45, 56], "stramaglia": 70, "strang": 70, "strategi": 29, "strength": [45, 59, 70], "stronger": 47, "strongest": 68, "strongli": 68, "structur": [67, 68, 70], "studen": 70, "studi": [47, 64, 67, 68, 70], "style": [36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60, 65, 67], "subgroup": 48, "subplot": [37, 59], "subselect": 56, "subset": [17, 44, 45, 46, 48, 70], "subtl": [46, 48], "subtract": 45, "suffer": 68, "suggest": [53, 62, 70], "sum": [23, 31, 45, 47, 53, 64, 70], "sum_": [15, 16, 17, 19, 20, 23, 26, 44, 45, 46, 70], "summari": 68, "summer": 65, "sun": [15, 70], "superflu": 44, "support": 65, "suptitl": [38, 40], "sure": 62, "surround": 56, "susann": 70, "swinnei": 70, "switch": 60, "symmetr": [37, 70], "syn": [25, 47, 48, 59, 70], "syn_result": 47, "sync": 62, "synergi": [15, 16, 17, 19, 20, 21, 24, 25, 27, 28, 30, 34, 43, 44, 45, 49, 51, 58, 59, 61, 64, 68, 69], "synergist": [20, 46, 47, 48, 51, 56, 59, 64, 68, 70], "synergy_phiid": 47, "synergymmi": [48, 70], "synergyphiid": [47, 70], "synmmi": 48, "synphiidmmi": 47, "synsum": 20, "system": [45, 60, 64, 67, 68, 70], "t": [22, 25, 37, 38, 39, 40, 44, 47, 56, 59, 67, 70], "t1": 53, "t2": 53, "t_end": 59, "t_start": 59, "tabl": [44, 45, 46, 47, 48, 51, 56, 68], "take": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37, 42, 45, 46, 47, 48, 53, 60, 67, 70], "taken": [53, 67], "tapia": [17, 70], "target": [5, 16, 28, 48, 59, 60, 64, 70], "task": [15, 16, 19, 23, 26], "tau": [22, 25, 47, 70], "taxonomi": 70, "tc": [19, 23, 70], "tdmi": 70, "te": [15, 70], "technic": 70, "techniqu": 64, "tempor": [60, 70], "tend": [45, 68], "term": [45, 60, 68, 70], "termin": 68, "test": [53, 62, 70], "tests_entropi": 62, "text": [56, 60], "th": [11, 36, 37, 38, 39, 40, 70], "tha": 60, "than": [46, 60, 64, 67, 70], "thei": 70, "them": [42, 47, 59, 70], "theme": 62, "theoret": [0, 12, 13, 16, 33, 34, 35, 36, 37, 38, 39, 40, 41, 58, 61, 65, 67, 68, 69], "theori": [42, 44, 64, 68, 70], "therefor": [45, 53, 56, 60], "thi": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 64, 65, 67, 68, 70], "thick": 56, "thing": [44, 53], "third": 44, "thoma": 70, "thomasrobiglio": 63, "those": [44, 68], "though": 70, "three": [60, 64, 67, 68, 70], "threshold": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], "through": [37, 42, 70], "ti": 70, "tight_layout": [38, 40], "tim": 70, "time": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67, 68, 70], "timeit": 53, "timings_cpu": 67, "timings_gpu": 67, "timm": [20, 70], "tishbi": 70, "titl": [36, 37, 38, 39, 40, 45, 56, 59, 60, 67], "to_max": 32, "to_min": 32, "togeth": [60, 64, 68], "toi": [67, 68], "toler": 64, "tolist": 51, "toma": 70, "too": 70, "tool": [67, 70], "toolbox": [67, 70], "top": [62, 65, 68], "topolog": [17, 19, 27, 30, 34, 43, 49, 56, 68, 69], "toponetx": 68, "total": [5, 15, 18, 19, 20, 23, 26, 31, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 59, 60, 61, 69], "toward": [36, 38, 39, 40, 70], "tpu": [65, 67], "tqdm": 66, "tr": 70, "tradit": 64, "tradition": 68, "transact": 70, "transmit": 64, "trend": 70, "trial": 56, "trial_block": 59, "trick": 60, "triplet": [28, 44, 45, 46, 48, 51, 56, 60], "triplet_charact": [28, 60, 68], "true": [5, 8, 27, 28, 29, 38, 40, 42, 51, 59, 60], "try": 59, "tup": 47, "turbo": [46, 48], "tuto_cor": [41, 42, 69], "tuto_jax": [52, 53, 69], "tutori": [36, 39, 40, 42, 53, 60, 61, 69, 70], "twice": 53, "two": [39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 59, 60, 64, 70], "type": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 44, 45, 62, 68, 70], "u": [36, 37, 39, 59, 66, 68], "u_x": 59, "unavail": 70, "uncertainti": [64, 70], "under": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 47, 65, 70], "underli": 70, "undersampl": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 44, 46, 48], "understand": [64, 70], "understood": [15, 64], "undirect": [64, 70], "uniform": [42, 47, 70], "uniqu": [31, 53, 59, 64], "unit": [42, 65, 70], "univari": 59, "univers": 65, "unveil": 70, "up": [51, 65, 67], "updat": [53, 68], "upmanu": 70, "upper": [36, 37, 38, 39, 40, 70], "upstream": 62, "url": 70, "us": [5, 6, 9, 10, 11, 18, 31, 36, 37, 38, 39, 40, 42, 46, 47, 48, 51, 60, 64, 65, 66, 67, 68, 70], "usabl": 68, "use_sklearn": 29, "user": 68, "usual": 68, "util": [33, 39, 44, 45, 46, 47, 48, 51, 56, 68], "v": [16, 34, 58, 61, 62, 69, 70], "vaadia": 70, "vajda": 70, "valu": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 60, 70], "vari": [36, 38, 39, 40, 60], "variabl": [12, 13, 15, 16, 17, 18, 20, 22, 25, 26, 28, 29, 30, 37, 38, 39, 40, 42, 45, 46, 47, 48, 59, 60, 64, 67, 68, 70], "varianc": [38, 40, 42, 70], "variat": 70, "variou": [12, 34, 35, 37, 38, 39, 40, 41, 68, 69, 70], "varlei": 70, "vast": 70, "ve": 53, "vec": [38, 40], "vejnarov": 70, "verbos": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 56, 59, 67], "veri": [42, 46, 47, 48], "version": [64, 66], "via": 70, "virgil": 70, "visit": 70, "visual": [51, 68], "vito": 70, "vmap": 67, "vogt": 70, "vulner": 70, "wa": [44, 48, 64], "wai": [46, 47, 48, 60, 64, 66, 70], "want": [45, 53, 60, 62, 65, 68], "watab": 26, "watanab": 70, "we": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 65, 67, 68, 70], "web": [62, 70], "well": [64, 68, 70], "weslei": 70, "what": [31, 45, 60, 64], "when": [20, 28, 36, 37, 38, 39, 40, 44, 45, 47, 48, 56, 59, 60, 64, 67, 70], "where": [37, 42, 56, 62, 70], "whether": [8, 28, 31, 45, 46, 59, 60, 68, 70], "which": [22, 25, 29, 42, 44, 45, 48, 59, 60, 64, 70], "while": [42, 44, 45, 46, 47, 51, 67, 70], "whole": [45, 47, 64, 70], "wholeminussum": 20, "why": 45, "width": 31, "william": 70, "win": [45, 60], "window": [45, 60], "within": 70, "without": [16, 28, 45], "word": 64, "work": [60, 64, 66, 70], "workspac": 70, "would": 64, "wrap": 53, "write": 53, "written": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 53, 70], "www": [53, 70], "x": [6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 32, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 60, 67, 70], "x_": [15, 16, 17, 18, 19, 20, 22, 23, 25, 26, 38, 44, 45, 46, 47, 48, 59, 70], "x_1": [38, 70], "x_2": [38, 70], "x_axi": 56, "x_bin": 29, "x_high": [36, 37, 38, 39, 40], "x_i": [38, 70], "x_j": [15, 45, 70], "x_jax": 53, "x_low": [36, 37, 38, 39, 40], "x_m": 59, "x_n": [38, 70], "x_np": 53, "x_red": 59, "x_ref": 60, "x_syn": 59, "x_t": [22, 25, 47, 70], "xarrai": [31, 62, 66], "xgi": [51, 68], "xi": [38, 40], "xla": 67, "xlabel": [36, 37, 39, 45, 56, 60, 67], "xlim": 60, "xn": 32, "xtick": 56, "xy": 39, "y": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 38, 39, 40, 42, 45, 46, 47, 48, 60, 70], "y_": [22, 25, 47, 59, 70], "y_jax": 53, "y_norm": 59, "y_np": 53, "y_red": 59, "y_syn": 59, "y_t": [22, 25, 47, 70], "yamir": 70, "year": 70, "yi": 40, "yield": 44, "ylabel": [36, 37, 39, 45, 56, 59, 60, 67], "ylim": 60, "you": [42, 44, 46, 47, 48, 51, 53, 62, 65, 66, 68], "young": 70, "your": [53, 62, 67, 68], "your_usernam": 62, "yuri": 70, "z": 70, "ze": 70, "zero": [31, 36, 37, 38, 39, 40, 42, 47, 59], "zini": 70, "zip": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67], "\u00e1": 70, "\u00e8": 70, "\u00e9": 70, "\u00f3": 70, "\u00f6": 70, "\u0142": 70, "\u017c": 70, "\u03c3": 36}, "titles": ["<code class=\"docutils literal notranslate\"><span class=\"pre\">hoi.core</span></code>", "<code class=\"docutils literal notranslate\"><span class=\"pre\">hoi.metrics</span></code>", "<code class=\"docutils literal notranslate\"><span class=\"pre\">hoi.plot</span></code>", "<code class=\"docutils literal notranslate\"><span class=\"pre\">hoi.simulation</span></code>", "<code class=\"docutils literal notranslate\"><span class=\"pre\">hoi.utils</span></code>", "hoi.core.combinations", "hoi.core.entropy_bin", "hoi.core.entropy_gauss", "hoi.core.entropy_gc", "hoi.core.entropy_hist", "hoi.core.entropy_kernel", "hoi.core.entropy_knn", "hoi.core.get_entropy", "hoi.core.get_mi", "hoi.core.prepare_for_it", "hoi.metrics.DTC", "hoi.metrics.GradientOinfo", "hoi.metrics.InfoTopo", "hoi.metrics.InfoTot", "hoi.metrics.Oinfo", "hoi.metrics.RSI", "hoi.metrics.RedundancyMMI", "hoi.metrics.RedundancyphiID", "hoi.metrics.Sinfo", "hoi.metrics.SynergyMMI", "hoi.metrics.SynergyphiID", "hoi.metrics.TC", "hoi.plot.plot_landscape", "hoi.simulation.simulate_hoi_gauss", "hoi.utils.digitize", "hoi.utils.get_nbest_mult", "hoi.utils.landscape", "hoi.utils.normalize", "List of classes and functions", "Examples", "Entropy and mutual information", "Comparison of entropy estimators for various distributions", "Comparison of entropy estimators for a multivariate normal", "Comparison of entropy estimators with high-dimensional data", "Comparison of mutual-information estimators", "Comparison of MI estimators with high-dimensional data", "Computation times", "Introduction to core information theoretical metrics", "Metrics of HOI", "Topological Information : conditioning on orders", "O-information and its derivatives for network behavior and encoding", "Redundancy-Synergy Index", "Integrated Information Decomposition", "Redundancy and Synergy MMI", "Computation times", "Miscellaneous", "Inspect and plot Higher-Order Interactions", "Computation times", "Quick introduction to jax", "Computation times", "Statistics : bootstrapping and permutations", "Bootstrapping and confidence interval", "Computation times", "Tutorials", "Machine-learning vs. Information theoretic approaches for HOI", "How to simulate redundancy and synergy", "Computation times", "Developer Documentation", "List of contributors", "Glossary", "HOI : High-Performance Estimation of Higher-Order Interactions", "Installation", "Jax: linear algebra backend", "Quickstart", "Computation times", "Theoretical background"], "titleterms": {"": [45, 70], "For": 53, "algebra": 67, "an": 36, "analysi": 68, "approach": [56, 59], "arrai": 67, "backend": 67, "background": 70, "behavior": [1, 45, 60, 70], "bibliographi": 70, "bootstrap": [34, 55, 56], "class": 33, "code": [45, 62], "combin": [5, 45, 46, 47, 48], "combinator": 0, "comparison": [36, 37, 38, 39, 40, 67], "compil": 53, "comput": [41, 49, 52, 54, 56, 57, 61, 67, 68, 69], "condit": 44, "confid": 56, "contribut": 62, "contributor": 63, "copi": 60, "core": [0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 42, 70], "correl": [45, 70], "cpu": 67, "data": [36, 38, 39, 40, 45, 51, 59, 68], "decod": 59, "decomposit": [47, 70], "definit": [36, 37, 38, 39, 40, 46, 47, 48], "depend": 66, "deriv": 45, "develop": 62, "digit": 29, "dimension": [38, 40, 67], "distribut": [36, 39, 40], "document": 62, "dtc": [15, 45], "dual": [45, 70], "dynam": [45, 60], "encod": [1, 45, 60, 70], "entropi": [0, 34, 35, 36, 37, 38, 42, 67, 70], "entropy_bin": 6, "entropy_gauss": 7, "entropy_gc": 8, "entropy_hist": 9, "entropy_kernel": 10, "entropy_knn": 11, "estim": [36, 37, 38, 39, 40, 51, 56, 65], "exampl": [12, 13, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 34], "exponenti": 36, "from": [36, 39, 40, 70], "function": [33, 53], "fund": 65, "get": [51, 65], "get_entropi": 12, "get_mi": 13, "get_nbest_mult": 30, "glossari": 64, "gpu": 67, "gradient": 70, "gradientoinfo": 16, "high": [38, 40, 65], "higher": [51, 56, 65, 67, 68, 70], "hoi": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 43, 51, 59, 62, 65], "how": 60, "index": [46, 70], "individu": 51, "inform": [0, 34, 35, 39, 42, 44, 45, 47, 56, 59, 70], "infotopo": 17, "infotot": 18, "inspect": [51, 68], "instal": [62, 66, 68], "integr": [47, 70], "interact": [44, 51, 65, 67, 68, 70], "interv": 56, "introduct": [42, 53], "involv": 65, "isol": 44, "its": 45, "jax": [53, 67], "jit": 53, "landscap": [31, 51], "larg": 67, "learn": 59, "licens": 65, "linear": 67, "list": [33, 63], "loop": 53, "machin": 59, "measur": [0, 70], "metric": [1, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 34, 42, 43], "mi": [39, 40, 70], "miscellan": [34, 50], "mmi": [48, 70], "modul": 53, "multi": 67, "multinorm": 40, "multiplet": [44, 51, 67], "multivari": [37, 45, 46, 48], "mutual": [0, 34, 35, 39, 42, 70], "network": [1, 45, 60, 70], "normal": [32, 36, 37, 39], "numpi": 53, "o": [44, 45, 56, 70], "oinfo": 19, "oper": 60, "order": [44, 51, 56, 65, 67, 68, 70], "other": 68, "pairwis": 70, "perform": [65, 67], "permut": [34, 55], "plot": [2, 27, 51, 56], "plot_landscap": 27, "postprocess": 4, "practic": 68, "prepare_for_it": 14, "preprocess": 4, "problem": 44, "pull": 62, "quick": 53, "quickstart": 68, "recommend": 68, "redund": [44, 45, 46, 47, 48, 56, 60, 70], "redundancymmi": 21, "redundancyphiid": 22, "request": 62, "result": [51, 68], "rsi": [20, 70], "sampl": [36, 39, 40], "simul": [3, 28, 44, 45, 46, 47, 48, 51, 59, 60, 68], "simulate_hoi_gauss": 28, "sinfo": 23, "softwar": 68, "spatial": 44, "split": 40, "spread": [44, 56], "statist": [34, 55], "sum": 60, "summari": 51, "synergi": [46, 47, 48, 56, 60, 70], "synergist": [44, 45, 60], "synergymmi": 24, "synergyphiid": 25, "target": 45, "tc": [26, 45], "theoret": [42, 59, 70], "time": [41, 49, 52, 54, 57, 61, 69], "topolog": [44, 70], "total": [45, 70], "tutori": [34, 58], "uniform": 36, "univari": [46, 48], "us": [12, 13, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 44, 45, 53, 56, 59, 62], "user": 66, "util": [4, 29, 30, 31, 32], "v": [59, 67], "variou": 36, "vector": 53, "vmap": 53, "x": 59, "y": 59}})
\ No newline at end of file
+Search.setIndex({"alltitles": {"Bibliography": [[70, "bibliography"]], "Bootstrapping and confidence interval": [[56, null]], "CPU vs. GPU : Performance comparison": [[67, "cpu-vs-gpu-performance-comparison"]], "Combinatorics": [[0, "combinatorics"]], "Combining redundancy and synergy": [[46, "combining-redundancy-and-synergy"], [47, "combining-redundancy-and-synergy"], [48, "combining-redundancy-and-synergy"]], "Combining redundant and synergistic codings using a multivariate target": [[45, "combining-redundant-and-synergistic-codings-using-a-multivariate-target"]], "Comparison of MI estimators with high-dimensional data": [[40, null]], "Comparison of entropy estimators for a multivariate normal": [[37, null]], "Comparison of entropy estimators for various distributions": [[36, null]], "Comparison of entropy estimators with high-dimensional data": [[38, null]], "Comparison of estimators": [[37, "comparison-of-estimators"]], "Comparison of mutual-information estimators": [[39, null]], "Compiling functions using jit": [[53, "compiling-functions-using-jit"]], "Computation times": [[41, null], [49, null], [52, null], [54, null], [57, null], [61, null], [69, null]], "Compute Higher-Order Interactions": [[68, "compute-higher-order-interactions"]], "Compute bootstrap": [[56, "compute-bootstrap"]], "Computing Higher-Order Interactions on large multiplets": [[67, "computing-higher-order-interactions-on-large-multiplets"]], "Computing entropy on large multi-dimensional arrays": [[67, "computing-entropy-on-large-multi-dimensional-arrays"]], "Contributing code using pull requests": [[62, "contributing-code-using-pull-requests"]], "Contributing to HOI": [[62, "contributing-to-hoi"]], "Core information theoretic measures": [[70, "core-information-theoretic-measures"]], "Data simulation": [[45, "data-simulation"], [59, "data-simulation"]], "Decoding Y using X": [[59, "decoding-y-using-x"]], "Definition": [[46, "definition"], [47, "definition"], [48, "definition"]], "Definition of MI estimators": [[39, "definition-of-mi-estimators"], [40, "definition-of-mi-estimators"]], "Definition of entropy estimators": [[38, "definition-of-entropy-estimators"]], "Definition of estimators of entropy": [[36, "definition-of-estimators-of-entropy"], [37, "definition-of-estimators-of-entropy"]], "Dependencies": [[66, "dependencies"]], "Developer Documentation": [[62, null]], "Dual Total Correlation (DTC)": [[45, "dual-total-correlation-dtc"]], "Dual Total correlation": [[70, "dual-total-correlation"]], "Dynamic redundant and synergistic codings": [[45, "dynamic-redundant-and-synergistic-codings"]], "Entropy": [[42, "entropy"]], "Entropy and mutual information": [[34, "entropy-and-mutual-information"], [35, null]], "Entropy of data sampled from a uniform distribution": [[36, "entropy-of-data-sampled-from-a-uniform-distribution"]], "Entropy of data sampled from an exponential distribution": [[36, "entropy-of-data-sampled-from-an-exponential-distribution"]], "Entropy of data sampled from normal distribution": [[36, "entropy-of-data-sampled-from-normal-distribution"]], "Estimate HOI": [[51, "estimate-hoi"]], "Estimation of the confidence interval using a bootstrapping approach": [[56, "estimation-of-the-confidence-interval-using-a-bootstrapping-approach"]], "Examples": [[34, null]], "Examples using hoi.core.get_entropy": [[12, "examples-using-hoi-core-get-entropy"]], "Examples using hoi.core.get_mi": [[13, "examples-using-hoi-core-get-mi"]], "Examples using hoi.metrics.DTC": [[15, "examples-using-hoi-metrics-dtc"]], "Examples using hoi.metrics.GradientOinfo": [[16, "examples-using-hoi-metrics-gradientoinfo"]], "Examples using hoi.metrics.InfoTopo": [[17, "examples-using-hoi-metrics-infotopo"]], "Examples using hoi.metrics.Oinfo": [[19, "examples-using-hoi-metrics-oinfo"]], "Examples using hoi.metrics.RSI": [[20, "examples-using-hoi-metrics-rsi"]], "Examples using hoi.metrics.RedundancyMMI": [[21, "examples-using-hoi-metrics-redundancymmi"]], "Examples using hoi.metrics.RedundancyphiID": [[22, "examples-using-hoi-metrics-redundancyphiid"]], "Examples using hoi.metrics.Sinfo": [[23, "examples-using-hoi-metrics-sinfo"]], "Examples using hoi.metrics.SynergyMMI": [[24, "examples-using-hoi-metrics-synergymmi"]], "Examples using hoi.metrics.SynergyphiID": [[25, "examples-using-hoi-metrics-synergyphiid"]], "Examples using hoi.metrics.TC": [[26, "examples-using-hoi-metrics-tc"]], "Examples using hoi.plot.plot_landscape": [[27, "examples-using-hoi-plot-plot-landscape"]], "Examples using hoi.simulation.simulate_hoi_gauss": [[28, "examples-using-hoi-simulation-simulate-hoi-gauss"]], "Examples using hoi.utils.digitize": [[29, "examples-using-hoi-utils-digitize"]], "Examples using hoi.utils.get_nbest_mult": [[30, "examples-using-hoi-utils-get-nbest-mult"]], "For loops with jax": [[53, "for-loops-with-jax"]], "From pairwise to higher-order interactions": [[70, "from-pairwise-to-higher-order-interactions"]], "Funding": [[65, "funding"]], "Get a summary of the results": [[51, "get-a-summary-of-the-results"]], "Get involved": [[65, "get-involved"]], "Glossary": [[64, null]], "Gradient of O-information": [[70, "gradient-of-o-information"]], "HOI : High-Performance Estimation of Higher-Order Interactions": [[65, null]], "How to simulate redundancy and synergy": [[60, null]], "Inspect and plot Higher-Order Interactions": [[51, null]], "Inspect the results": [[68, "inspect-the-results"]], "Installation": [[66, null], [68, "installation"]], "Installation for developers": [[62, "installation-for-developers"]], "Integrated Information Decomposition": [[47, null]], "Introduction to core information theoretical metrics": [[42, null]], "Jax.numpy module": [[53, "jax-numpy-module"]], "Jax: linear algebra backend": [[67, null]], "Landscape plot": [[51, "landscape-plot"]], "License": [[65, "license"]], "List of classes and functions": [[33, null]], "List of contributors": [[63, null]], "MI of data sampled from normal distribution": [[39, "mi-of-data-sampled-from-normal-distribution"]], "MI of data sampled from splitted multinormal distribution": [[40, "mi-of-data-sampled-from-splitted-multinormal-distribution"]], "Machine-learning vs. Information theoretic approaches for HOI": [[59, null]], "Measures of Entropy": [[0, "measures-of-entropy"]], "Measures of Mutual Information": [[0, "measures-of-mutual-information"]], "Measuring Entropy": [[70, "measuring-entropy"]], "Measuring Mutual Information (MI)": [[70, "measuring-mutual-information-mi"]], "Metrics of HOI": [[34, "metrics-of-hoi"], [43, null]], "Miscellaneous": [[34, "miscellaneous"], [50, null]], "Multiplet isolation using the Topological Information": [[44, "multiplet-isolation-using-the-topological-information"]], "Mutual information": [[42, "mutual-information"]], "Network behavior": [[1, "network-behavior"], [70, "network-behavior"]], "Network encoding": [[1, "network-encoding"], [70, "network-encoding"]], "O-information": [[45, "o-information"], [70, "o-information"]], "O-information : Redundancy and synergy spread to higher orders": [[56, "o-information-redundancy-and-synergy-spread-to-higher-orders"]], "O-information and its derivatives for network behavior and encoding": [[45, null]], "O-information for network behavior": [[45, "o-information-for-network-behavior"]], "O-information for network encoding": [[45, "o-information-for-network-encoding"]], "Other softwares for the analysis of higher-order interactions": [[68, "other-softwares-for-the-analysis-of-higher-order-interactions"]], "Plot the O-information with the confidence interval": [[56, "plot-the-o-information-with-the-confidence-interval"]], "Plotting individual multiplets": [[51, "plotting-individual-multiplets"]], "Postprocessing": [[4, "postprocessing"]], "Practical recommendations": [[68, "practical-recommendations"]], "Preprocessing": [[4, "preprocessing"]], "Quick introduction to jax": [[53, null]], "Quickstart": [[68, null]], "Redundancy and Synergy MMI": [[48, null]], "Redundancy-Synergy Index": [[46, null]], "Redundancy-Synergy index (RSI)": [[70, "redundancy-synergy-index-rsi"]], "Redundant and synergistic network behavior": [[60, "redundant-and-synergistic-network-behavior"]], "Redundant and synergistic network encoding": [[60, "redundant-and-synergistic-network-encoding"]], "S information": [[70, "s-information"]], "S-information": [[45, "s-information"]], "Simulate data": [[51, "simulate-data"], [68, "simulate-data"]], "Simulate multivariate redundancy": [[46, "simulate-multivariate-redundancy"], [48, "simulate-multivariate-redundancy"]], "Simulate redundancy": [[47, "simulate-redundancy"]], "Simulate redundant and synergistic interactions": [[44, "simulate-redundant-and-synergistic-interactions"]], "Simulate synergy": [[47, "simulate-synergy"]], "Simulate univariate and multivariate synergy": [[46, "simulate-univariate-and-multivariate-synergy"], [48, "simulate-univariate-and-multivariate-synergy"]], "Simulate univariate redundancy": [[46, "simulate-univariate-redundancy"], [48, "simulate-univariate-redundancy"]], "Simulating dynamic redundancy and synergy": [[60, "simulating-dynamic-redundancy-and-synergy"]], "Simulating dynamic redundant and synergistic encoding": [[60, "simulating-dynamic-redundant-and-synergistic-encoding"]], "Simulating redundant behavior": [[60, "simulating-redundant-behavior"]], "Simulating redundant behavior by copy operator": [[60, "simulating-redundant-behavior-by-copy-operator"]], "Simulating redundant encoding": [[45, "simulating-redundant-encoding"], [60, "simulating-redundant-encoding"]], "Simulating redundant encoding by copy operation": [[60, "simulating-redundant-encoding-by-copy-operation"]], "Simulating synergistic behavior": [[60, "simulating-synergistic-behavior"]], "Simulating synergistic behavior by sum operation": [[60, "simulating-synergistic-behavior-by-sum-operation"]], "Simulating synergistic encoding": [[45, "simulating-synergistic-encoding"], [60, "simulating-synergistic-encoding"]], "Simulating synergistic encoding by sum operation": [[60, "simulating-synergistic-encoding-by-sum-operation"]], "Spatial spreading : the problem with the O-information": [[44, "spatial-spreading-the-problem-with-the-o-information"]], "Statistics : bootstrapping and permutations": [[34, "statistics-bootstrapping-and-permutations"], [55, null]], "Synergy and redundancy (MMI)": [[70, "synergy-and-redundancy-mmi"]], "Synergy and redundancy integrated Information Decomposition (MMI)": [[70, "synergy-and-redundancy-integrated-information-decomposition-mmi"]], "Theoretical background": [[70, null]], "Topological Information : conditioning on orders": [[44, null]], "Topological information": [[70, "topological-information"]], "Total Correlation (TC)": [[45, "total-correlation-tc"]], "Total correlation": [[70, "total-correlation"]], "Tutorials": [[34, "tutorials"], [58, null]], "User installation": [[66, "user-installation"]], "Using information-theoretic approaches": [[59, "using-information-theoretic-approaches"]], "hoi.core": [[0, null]], "hoi.core.combinations": [[5, null]], "hoi.core.entropy_bin": [[6, null]], "hoi.core.entropy_gauss": [[7, null]], "hoi.core.entropy_gc": [[8, null]], "hoi.core.entropy_hist": [[9, null]], "hoi.core.entropy_kernel": [[10, null]], "hoi.core.entropy_knn": [[11, null]], "hoi.core.get_entropy": [[12, null]], "hoi.core.get_mi": [[13, null]], "hoi.core.prepare_for_it": [[14, null]], "hoi.metrics": [[1, null]], "hoi.metrics.DTC": [[15, null]], "hoi.metrics.GradientOinfo": [[16, null]], "hoi.metrics.InfoTopo": [[17, null]], "hoi.metrics.InfoTot": [[18, null]], "hoi.metrics.Oinfo": [[19, null]], "hoi.metrics.RSI": [[20, null]], "hoi.metrics.RedundancyMMI": [[21, null]], "hoi.metrics.RedundancyphiID": [[22, null]], "hoi.metrics.Sinfo": [[23, null]], "hoi.metrics.SynergyMMI": [[24, null]], "hoi.metrics.SynergyphiID": [[25, null]], "hoi.metrics.TC": [[26, null]], "hoi.plot": [[2, null]], "hoi.plot.plot_landscape": [[27, null]], "hoi.simulation": [[3, null]], "hoi.simulation.simulate_hoi_gauss": [[28, null]], "hoi.utils": [[4, null]], "hoi.utils.digitize": [[29, null]], "hoi.utils.get_nbest_mult": [[30, null]], "hoi.utils.landscape": [[31, null]], "hoi.utils.normalize": [[32, null]], "vmap : vectorize a function": [[53, "vmap-vectorize-a-function"]]}, "docnames": ["api/api_core", "api/api_metrics", "api/api_plot", "api/api_sim", "api/api_utils", "api/generated/hoi.core.combinations", "api/generated/hoi.core.entropy_bin", "api/generated/hoi.core.entropy_gauss", "api/generated/hoi.core.entropy_gc", "api/generated/hoi.core.entropy_hist", "api/generated/hoi.core.entropy_kernel", "api/generated/hoi.core.entropy_knn", "api/generated/hoi.core.get_entropy", "api/generated/hoi.core.get_mi", "api/generated/hoi.core.prepare_for_it", "api/generated/hoi.metrics.DTC", "api/generated/hoi.metrics.GradientOinfo", "api/generated/hoi.metrics.InfoTopo", "api/generated/hoi.metrics.InfoTot", "api/generated/hoi.metrics.Oinfo", "api/generated/hoi.metrics.RSI", "api/generated/hoi.metrics.RedundancyMMI", "api/generated/hoi.metrics.RedundancyphiID", "api/generated/hoi.metrics.Sinfo", "api/generated/hoi.metrics.SynergyMMI", "api/generated/hoi.metrics.SynergyphiID", "api/generated/hoi.metrics.TC", "api/generated/hoi.plot.plot_landscape", "api/generated/hoi.simulation.simulate_hoi_gauss", "api/generated/hoi.utils.digitize", "api/generated/hoi.utils.get_nbest_mult", "api/generated/hoi.utils.landscape", "api/generated/hoi.utils.normalize", "api/modules", "auto_examples/index", "auto_examples/it/index", "auto_examples/it/plot_entropies", "auto_examples/it/plot_entropies_mvar", "auto_examples/it/plot_entropy_high_dimensional", "auto_examples/it/plot_mi", "auto_examples/it/plot_mi_high_dimensional", "auto_examples/it/sg_execution_times", "auto_examples/it/tuto_core", "auto_examples/metrics/index", "auto_examples/metrics/plot_infotopo", "auto_examples/metrics/plot_oinfo", "auto_examples/metrics/plot_rsi", "auto_examples/metrics/plot_syn_phiID", "auto_examples/metrics/plot_syn_red_mmi", "auto_examples/metrics/sg_execution_times", "auto_examples/miscellaneous/index", "auto_examples/miscellaneous/plot_inspect_results", "auto_examples/miscellaneous/sg_execution_times", "auto_examples/miscellaneous/tuto_jax", "auto_examples/sg_execution_times", "auto_examples/statistics/index", "auto_examples/statistics/plot_bootstrapping", "auto_examples/statistics/sg_execution_times", "auto_examples/tutorials/index", "auto_examples/tutorials/plot_ml_vs_it", "auto_examples/tutorials/plot_sim_red_syn", "auto_examples/tutorials/sg_execution_times", "contributor_guide", "contributors", "glossary", "index", "install", "jax", "quickstart", "sg_execution_times", "theory"], "envversion": {"sphinx": 62, "sphinx.domains.c": 3, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 9, "sphinx.domains.index": 1, "sphinx.domains.javascript": 3, "sphinx.domains.math": 2, "sphinx.domains.python": 4, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx.ext.todo": 2, "sphinx.ext.viewcode": 1, "sphinxcontrib.bibtex": 9}, "filenames": ["api/api_core.rst", "api/api_metrics.rst", "api/api_plot.rst", "api/api_sim.rst", "api/api_utils.rst", "api/generated/hoi.core.combinations.rst", "api/generated/hoi.core.entropy_bin.rst", "api/generated/hoi.core.entropy_gauss.rst", "api/generated/hoi.core.entropy_gc.rst", "api/generated/hoi.core.entropy_hist.rst", "api/generated/hoi.core.entropy_kernel.rst", "api/generated/hoi.core.entropy_knn.rst", "api/generated/hoi.core.get_entropy.rst", "api/generated/hoi.core.get_mi.rst", "api/generated/hoi.core.prepare_for_it.rst", "api/generated/hoi.metrics.DTC.rst", "api/generated/hoi.metrics.GradientOinfo.rst", "api/generated/hoi.metrics.InfoTopo.rst", "api/generated/hoi.metrics.InfoTot.rst", "api/generated/hoi.metrics.Oinfo.rst", "api/generated/hoi.metrics.RSI.rst", "api/generated/hoi.metrics.RedundancyMMI.rst", "api/generated/hoi.metrics.RedundancyphiID.rst", "api/generated/hoi.metrics.Sinfo.rst", "api/generated/hoi.metrics.SynergyMMI.rst", "api/generated/hoi.metrics.SynergyphiID.rst", "api/generated/hoi.metrics.TC.rst", "api/generated/hoi.plot.plot_landscape.rst", "api/generated/hoi.simulation.simulate_hoi_gauss.rst", "api/generated/hoi.utils.digitize.rst", "api/generated/hoi.utils.get_nbest_mult.rst", "api/generated/hoi.utils.landscape.rst", "api/generated/hoi.utils.normalize.rst", "api/modules.rst", "auto_examples/index.rst", "auto_examples/it/index.rst", "auto_examples/it/plot_entropies.rst", "auto_examples/it/plot_entropies_mvar.rst", "auto_examples/it/plot_entropy_high_dimensional.rst", "auto_examples/it/plot_mi.rst", "auto_examples/it/plot_mi_high_dimensional.rst", "auto_examples/it/sg_execution_times.rst", "auto_examples/it/tuto_core.rst", "auto_examples/metrics/index.rst", "auto_examples/metrics/plot_infotopo.rst", "auto_examples/metrics/plot_oinfo.rst", "auto_examples/metrics/plot_rsi.rst", "auto_examples/metrics/plot_syn_phiID.rst", "auto_examples/metrics/plot_syn_red_mmi.rst", "auto_examples/metrics/sg_execution_times.rst", "auto_examples/miscellaneous/index.rst", "auto_examples/miscellaneous/plot_inspect_results.rst", "auto_examples/miscellaneous/sg_execution_times.rst", "auto_examples/miscellaneous/tuto_jax.rst", "auto_examples/sg_execution_times.rst", "auto_examples/statistics/index.rst", "auto_examples/statistics/plot_bootstrapping.rst", "auto_examples/statistics/sg_execution_times.rst", "auto_examples/tutorials/index.rst", "auto_examples/tutorials/plot_ml_vs_it.rst", "auto_examples/tutorials/plot_sim_red_syn.rst", "auto_examples/tutorials/sg_execution_times.rst", "contributor_guide.rst", "contributors.rst", "glossary.rst", "index.rst", "install.rst", "jax.rst", "quickstart.rst", "sg_execution_times.rst", "theory.rst"], "indexentries": {"__iter__() (hoi.metrics.dtc method)": [[15, "hoi.metrics.DTC.__iter__", false]], "__iter__() (hoi.metrics.gradientoinfo method)": [[16, "hoi.metrics.GradientOinfo.__iter__", false]], "__iter__() (hoi.metrics.infotopo method)": [[17, "hoi.metrics.InfoTopo.__iter__", false]], "__iter__() (hoi.metrics.infotot method)": [[18, "hoi.metrics.InfoTot.__iter__", false]], "__iter__() (hoi.metrics.oinfo method)": [[19, "hoi.metrics.Oinfo.__iter__", false]], "__iter__() (hoi.metrics.redundancymmi method)": [[21, "hoi.metrics.RedundancyMMI.__iter__", false]], "__iter__() (hoi.metrics.redundancyphiid method)": [[22, "hoi.metrics.RedundancyphiID.__iter__", false]], "__iter__() (hoi.metrics.rsi method)": [[20, "hoi.metrics.RSI.__iter__", false]], "__iter__() (hoi.metrics.sinfo method)": [[23, "hoi.metrics.Sinfo.__iter__", false]], "__iter__() (hoi.metrics.synergymmi method)": [[24, "hoi.metrics.SynergyMMI.__iter__", false]], "__iter__() (hoi.metrics.synergyphiid method)": [[25, "hoi.metrics.SynergyphiID.__iter__", false]], "__iter__() (hoi.metrics.tc method)": [[26, "hoi.metrics.TC.__iter__", false]], "combinations() (in module hoi.core)": [[5, "hoi.core.combinations", false]], "compute_entropies() (hoi.metrics.dtc method)": [[15, "hoi.metrics.DTC.compute_entropies", false]], "compute_entropies() (hoi.metrics.gradientoinfo method)": [[16, "hoi.metrics.GradientOinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.infotopo method)": [[17, "hoi.metrics.InfoTopo.compute_entropies", false]], "compute_entropies() (hoi.metrics.infotot method)": [[18, "hoi.metrics.InfoTot.compute_entropies", false]], "compute_entropies() (hoi.metrics.oinfo method)": [[19, "hoi.metrics.Oinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.redundancymmi method)": [[21, "hoi.metrics.RedundancyMMI.compute_entropies", false]], "compute_entropies() (hoi.metrics.redundancyphiid method)": [[22, "hoi.metrics.RedundancyphiID.compute_entropies", false]], "compute_entropies() (hoi.metrics.rsi method)": [[20, "hoi.metrics.RSI.compute_entropies", false]], "compute_entropies() (hoi.metrics.sinfo method)": [[23, "hoi.metrics.Sinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.synergymmi method)": [[24, "hoi.metrics.SynergyMMI.compute_entropies", false]], "compute_entropies() (hoi.metrics.synergyphiid method)": [[25, "hoi.metrics.SynergyphiID.compute_entropies", false]], "compute_entropies() (hoi.metrics.tc method)": [[26, "hoi.metrics.TC.compute_entropies", false]], "digitize() (in module hoi.utils)": [[29, "hoi.utils.digitize", false]], "dtc (class in hoi.metrics)": [[15, "hoi.metrics.DTC", false]], "entropies (hoi.metrics.dtc property)": [[15, "hoi.metrics.DTC.entropies", false]], "entropies (hoi.metrics.gradientoinfo property)": [[16, "hoi.metrics.GradientOinfo.entropies", false]], "entropies (hoi.metrics.infotopo property)": [[17, "hoi.metrics.InfoTopo.entropies", false]], "entropies (hoi.metrics.infotot property)": [[18, "hoi.metrics.InfoTot.entropies", false]], "entropies (hoi.metrics.oinfo property)": [[19, "hoi.metrics.Oinfo.entropies", false]], "entropies (hoi.metrics.redundancymmi property)": [[21, "hoi.metrics.RedundancyMMI.entropies", false]], "entropies (hoi.metrics.redundancyphiid property)": [[22, "hoi.metrics.RedundancyphiID.entropies", false]], "entropies (hoi.metrics.rsi property)": [[20, "hoi.metrics.RSI.entropies", false]], "entropies (hoi.metrics.sinfo property)": [[23, "hoi.metrics.Sinfo.entropies", false]], "entropies (hoi.metrics.synergymmi property)": [[24, "hoi.metrics.SynergyMMI.entropies", false]], "entropies (hoi.metrics.synergyphiid property)": [[25, "hoi.metrics.SynergyphiID.entropies", false]], "entropies (hoi.metrics.tc property)": [[26, "hoi.metrics.TC.entropies", false]], "entropy": [[64, "term-Entropy", true]], "entropy_bin() (in module hoi.core)": [[6, "hoi.core.entropy_bin", false]], "entropy_gauss() (in module hoi.core)": [[7, "hoi.core.entropy_gauss", false]], "entropy_gc() (in module hoi.core)": [[8, "hoi.core.entropy_gc", false]], "entropy_hist() (in module hoi.core)": [[9, "hoi.core.entropy_hist", false]], "entropy_kernel() (in module hoi.core)": [[10, "hoi.core.entropy_kernel", false]], "entropy_knn() (in module hoi.core)": [[11, "hoi.core.entropy_knn", false]], "fit() (hoi.metrics.dtc method)": [[15, "hoi.metrics.DTC.fit", false]], "fit() (hoi.metrics.gradientoinfo method)": [[16, "hoi.metrics.GradientOinfo.fit", false]], "fit() (hoi.metrics.infotopo method)": [[17, "hoi.metrics.InfoTopo.fit", false]], "fit() (hoi.metrics.infotot method)": [[18, "hoi.metrics.InfoTot.fit", false]], "fit() (hoi.metrics.oinfo method)": [[19, "hoi.metrics.Oinfo.fit", false]], "fit() (hoi.metrics.redundancymmi method)": [[21, "hoi.metrics.RedundancyMMI.fit", false]], "fit() (hoi.metrics.redundancyphiid method)": [[22, "hoi.metrics.RedundancyphiID.fit", false]], "fit() (hoi.metrics.rsi method)": [[20, "hoi.metrics.RSI.fit", false]], "fit() (hoi.metrics.sinfo method)": [[23, "hoi.metrics.Sinfo.fit", false]], "fit() (hoi.metrics.synergymmi method)": [[24, "hoi.metrics.SynergyMMI.fit", false]], "fit() (hoi.metrics.synergyphiid method)": [[25, "hoi.metrics.SynergyphiID.fit", false]], "fit() (hoi.metrics.tc method)": [[26, "hoi.metrics.TC.fit", false]], "get_combinations() (hoi.metrics.dtc method)": [[15, "hoi.metrics.DTC.get_combinations", false]], "get_combinations() (hoi.metrics.gradientoinfo method)": [[16, "hoi.metrics.GradientOinfo.get_combinations", false]], "get_combinations() (hoi.metrics.infotopo method)": [[17, "hoi.metrics.InfoTopo.get_combinations", false]], "get_combinations() (hoi.metrics.infotot method)": [[18, "hoi.metrics.InfoTot.get_combinations", false]], "get_combinations() (hoi.metrics.oinfo method)": [[19, "hoi.metrics.Oinfo.get_combinations", false]], "get_combinations() (hoi.metrics.redundancymmi method)": [[21, "hoi.metrics.RedundancyMMI.get_combinations", false]], "get_combinations() (hoi.metrics.redundancyphiid method)": [[22, "hoi.metrics.RedundancyphiID.get_combinations", false]], "get_combinations() (hoi.metrics.rsi method)": [[20, "hoi.metrics.RSI.get_combinations", false]], "get_combinations() (hoi.metrics.sinfo method)": [[23, "hoi.metrics.Sinfo.get_combinations", false]], "get_combinations() (hoi.metrics.synergymmi method)": [[24, "hoi.metrics.SynergyMMI.get_combinations", false]], "get_combinations() (hoi.metrics.synergyphiid method)": [[25, "hoi.metrics.SynergyphiID.get_combinations", false]], "get_combinations() (hoi.metrics.tc method)": [[26, "hoi.metrics.TC.get_combinations", false]], "get_entropy() (in module hoi.core)": [[12, "hoi.core.get_entropy", false]], "get_mi() (in module hoi.core)": [[13, "hoi.core.get_mi", false]], "get_nbest_mult() (in module hoi.utils)": [[30, "hoi.utils.get_nbest_mult", false]], "gradientoinfo (class in hoi.metrics)": [[16, "hoi.metrics.GradientOinfo", false]], "higher order interactions": [[64, "term-Higher-Order-Interactions", true]], "hoi.metrics": [[1, "module-hoi.metrics", false]], "information theory": [[64, "term-Information-Theory", true]], "infotopo (class in hoi.metrics)": [[17, "hoi.metrics.InfoTopo", false]], "infotot (class in hoi.metrics)": [[18, "hoi.metrics.InfoTot", false]], "landscape() (in module hoi.utils)": [[31, "hoi.utils.landscape", false]], "module": [[1, "module-hoi.metrics", false]], "multiplets (hoi.metrics.dtc property)": [[15, "hoi.metrics.DTC.multiplets", false]], "multiplets (hoi.metrics.gradientoinfo property)": [[16, "hoi.metrics.GradientOinfo.multiplets", false]], "multiplets (hoi.metrics.infotopo property)": [[17, "hoi.metrics.InfoTopo.multiplets", false]], "multiplets (hoi.metrics.infotot property)": [[18, "hoi.metrics.InfoTot.multiplets", false]], "multiplets (hoi.metrics.oinfo property)": [[19, "hoi.metrics.Oinfo.multiplets", false]], "multiplets (hoi.metrics.redundancymmi property)": [[21, "hoi.metrics.RedundancyMMI.multiplets", false]], "multiplets (hoi.metrics.redundancyphiid property)": [[22, "hoi.metrics.RedundancyphiID.multiplets", false]], "multiplets (hoi.metrics.rsi property)": [[20, "hoi.metrics.RSI.multiplets", false]], "multiplets (hoi.metrics.sinfo property)": [[23, "hoi.metrics.Sinfo.multiplets", false]], "multiplets (hoi.metrics.synergymmi property)": [[24, "hoi.metrics.SynergyMMI.multiplets", false]], "multiplets (hoi.metrics.synergyphiid property)": [[25, "hoi.metrics.SynergyphiID.multiplets", false]], "multiplets (hoi.metrics.tc property)": [[26, "hoi.metrics.TC.multiplets", false]], "mutual information": [[64, "term-Mutual-Information", true]], "network behavior": [[64, "term-Network-behavior", true]], "network encoding": [[64, "term-Network-encoding", true]], "normalize() (in module hoi.utils)": [[32, "hoi.utils.normalize", false]], "oinfo (class in hoi.metrics)": [[19, "hoi.metrics.Oinfo", false]], "order (hoi.metrics.dtc property)": [[15, "hoi.metrics.DTC.order", false]], "order (hoi.metrics.gradientoinfo property)": [[16, "hoi.metrics.GradientOinfo.order", false]], "order (hoi.metrics.infotopo property)": [[17, "hoi.metrics.InfoTopo.order", false]], "order (hoi.metrics.infotot property)": [[18, "hoi.metrics.InfoTot.order", false]], "order (hoi.metrics.oinfo property)": [[19, "hoi.metrics.Oinfo.order", false]], "order (hoi.metrics.redundancymmi property)": [[21, "hoi.metrics.RedundancyMMI.order", false]], "order (hoi.metrics.redundancyphiid property)": [[22, "hoi.metrics.RedundancyphiID.order", false]], "order (hoi.metrics.rsi property)": [[20, "hoi.metrics.RSI.order", false]], "order (hoi.metrics.sinfo property)": [[23, "hoi.metrics.Sinfo.order", false]], "order (hoi.metrics.synergymmi property)": [[24, "hoi.metrics.SynergyMMI.order", false]], "order (hoi.metrics.synergyphiid property)": [[25, "hoi.metrics.SynergyphiID.order", false]], "order (hoi.metrics.tc property)": [[26, "hoi.metrics.TC.order", false]], "partial information decomposition": [[64, "term-Partial-Information-Decomposition", true]], "plot_landscape() (in module hoi.plot)": [[27, "hoi.plot.plot_landscape", false]], "prepare_for_it() (in module hoi.core)": [[14, "hoi.core.prepare_for_it", false]], "redundancy": [[64, "term-Redundancy", true]], "redundancymmi (class in hoi.metrics)": [[21, "hoi.metrics.RedundancyMMI", false]], "redundancyphiid (class in hoi.metrics)": [[22, "hoi.metrics.RedundancyphiID", false]], "rsi (class in hoi.metrics)": [[20, "hoi.metrics.RSI", false]], "simulate_hoi_gauss() (in module hoi.simulation)": [[28, "hoi.simulation.simulate_hoi_gauss", false]], "sinfo (class in hoi.metrics)": [[23, "hoi.metrics.Sinfo", false]], "synergy": [[64, "term-Synergy", true]], "synergymmi (class in hoi.metrics)": [[24, "hoi.metrics.SynergyMMI", false]], "synergyphiid (class in hoi.metrics)": [[25, "hoi.metrics.SynergyphiID", false]], "tc (class in hoi.metrics)": [[26, "hoi.metrics.TC", false]], "undersampling (hoi.metrics.dtc property)": [[15, "hoi.metrics.DTC.undersampling", false]], "undersampling (hoi.metrics.gradientoinfo property)": [[16, "hoi.metrics.GradientOinfo.undersampling", false]], "undersampling (hoi.metrics.infotopo property)": [[17, "hoi.metrics.InfoTopo.undersampling", false]], "undersampling (hoi.metrics.infotot property)": [[18, "hoi.metrics.InfoTot.undersampling", false]], "undersampling (hoi.metrics.oinfo property)": [[19, "hoi.metrics.Oinfo.undersampling", false]], "undersampling (hoi.metrics.redundancymmi property)": [[21, "hoi.metrics.RedundancyMMI.undersampling", false]], "undersampling (hoi.metrics.redundancyphiid property)": [[22, "hoi.metrics.RedundancyphiID.undersampling", false]], "undersampling (hoi.metrics.rsi property)": [[20, "hoi.metrics.RSI.undersampling", false]], "undersampling (hoi.metrics.sinfo property)": [[23, "hoi.metrics.Sinfo.undersampling", false]], "undersampling (hoi.metrics.synergymmi property)": [[24, "hoi.metrics.SynergyMMI.undersampling", false]], "undersampling (hoi.metrics.synergyphiid property)": [[25, "hoi.metrics.SynergyphiID.undersampling", false]], "undersampling (hoi.metrics.tc property)": [[26, "hoi.metrics.TC.undersampling", false]]}, "objects": {"hoi": [[1, 1, 0, "-", "metrics"]], "hoi.core": [[5, 0, 1, "", "combinations"], [6, 0, 1, "", "entropy_bin"], [7, 0, 1, "", "entropy_gauss"], [8, 0, 1, "", "entropy_gc"], [9, 0, 1, "", "entropy_hist"], [10, 0, 1, "", "entropy_kernel"], [11, 0, 1, "", "entropy_knn"], [12, 0, 1, "", "get_entropy"], [13, 0, 1, "", "get_mi"], [14, 0, 1, "", "prepare_for_it"]], "hoi.metrics": [[15, 2, 1, "", "DTC"], [16, 2, 1, "", "GradientOinfo"], [17, 2, 1, "", "InfoTopo"], [18, 2, 1, "", "InfoTot"], [19, 2, 1, "", "Oinfo"], [20, 2, 1, "", "RSI"], [21, 2, 1, "", "RedundancyMMI"], [22, 2, 1, "", "RedundancyphiID"], [23, 2, 1, "", "Sinfo"], [24, 2, 1, "", "SynergyMMI"], [25, 2, 1, "", "SynergyphiID"], [26, 2, 1, "", "TC"]], "hoi.metrics.DTC": [[15, 3, 1, "", "__iter__"], [15, 3, 1, "", "compute_entropies"], [15, 4, 1, "", "entropies"], [15, 3, 1, "", "fit"], [15, 3, 1, "", "get_combinations"], [15, 4, 1, "", "multiplets"], [15, 4, 1, "", "order"], [15, 4, 1, "", "undersampling"]], "hoi.metrics.GradientOinfo": [[16, 3, 1, "", "__iter__"], [16, 3, 1, "", "compute_entropies"], [16, 4, 1, "", "entropies"], [16, 3, 1, "", "fit"], [16, 3, 1, "", "get_combinations"], [16, 4, 1, "", "multiplets"], [16, 4, 1, "", "order"], [16, 4, 1, "", "undersampling"]], "hoi.metrics.InfoTopo": [[17, 3, 1, "", "__iter__"], [17, 3, 1, "", "compute_entropies"], [17, 4, 1, "", "entropies"], [17, 3, 1, "", "fit"], [17, 3, 1, "", "get_combinations"], [17, 4, 1, "", "multiplets"], [17, 4, 1, "", "order"], [17, 4, 1, "", "undersampling"]], "hoi.metrics.InfoTot": [[18, 3, 1, "", "__iter__"], [18, 3, 1, "", "compute_entropies"], [18, 4, 1, "", "entropies"], [18, 3, 1, "", "fit"], [18, 3, 1, "", "get_combinations"], [18, 4, 1, "", "multiplets"], [18, 4, 1, "", "order"], [18, 4, 1, "", "undersampling"]], "hoi.metrics.Oinfo": [[19, 3, 1, "", "__iter__"], [19, 3, 1, "", "compute_entropies"], [19, 4, 1, "", "entropies"], [19, 3, 1, "", "fit"], [19, 3, 1, "", "get_combinations"], [19, 4, 1, "", "multiplets"], [19, 4, 1, "", "order"], [19, 4, 1, "", "undersampling"]], "hoi.metrics.RSI": [[20, 3, 1, "", "__iter__"], [20, 3, 1, "", "compute_entropies"], [20, 4, 1, "", "entropies"], [20, 3, 1, "", "fit"], [20, 3, 1, "", "get_combinations"], [20, 4, 1, "", "multiplets"], [20, 4, 1, "", "order"], [20, 4, 1, "", "undersampling"]], "hoi.metrics.RedundancyMMI": [[21, 3, 1, "", "__iter__"], [21, 3, 1, "", "compute_entropies"], [21, 4, 1, "", "entropies"], [21, 3, 1, "", "fit"], [21, 3, 1, "", "get_combinations"], [21, 4, 1, "", "multiplets"], [21, 4, 1, "", "order"], [21, 4, 1, "", "undersampling"]], "hoi.metrics.RedundancyphiID": [[22, 3, 1, "", "__iter__"], [22, 3, 1, "", "compute_entropies"], [22, 4, 1, "", "entropies"], [22, 3, 1, "", "fit"], [22, 3, 1, "", "get_combinations"], [22, 4, 1, "", "multiplets"], [22, 4, 1, "", "order"], [22, 4, 1, "", "undersampling"]], "hoi.metrics.Sinfo": [[23, 3, 1, "", "__iter__"], [23, 3, 1, "", "compute_entropies"], [23, 4, 1, "", "entropies"], [23, 3, 1, "", "fit"], [23, 3, 1, "", "get_combinations"], [23, 4, 1, "", "multiplets"], [23, 4, 1, "", "order"], [23, 4, 1, "", "undersampling"]], "hoi.metrics.SynergyMMI": [[24, 3, 1, "", "__iter__"], [24, 3, 1, "", "compute_entropies"], [24, 4, 1, "", "entropies"], [24, 3, 1, "", "fit"], [24, 3, 1, "", "get_combinations"], [24, 4, 1, "", "multiplets"], [24, 4, 1, "", "order"], [24, 4, 1, "", "undersampling"]], "hoi.metrics.SynergyphiID": [[25, 3, 1, "", "__iter__"], [25, 3, 1, "", "compute_entropies"], [25, 4, 1, "", "entropies"], [25, 3, 1, "", "fit"], [25, 3, 1, "", "get_combinations"], [25, 4, 1, "", "multiplets"], [25, 4, 1, "", "order"], [25, 4, 1, "", "undersampling"]], "hoi.metrics.TC": [[26, 3, 1, "", "__iter__"], [26, 3, 1, "", "compute_entropies"], [26, 4, 1, "", "entropies"], [26, 3, 1, "", "fit"], [26, 3, 1, "", "get_combinations"], [26, 4, 1, "", "multiplets"], [26, 4, 1, "", "order"], [26, 4, 1, "", "undersampling"]], "hoi.plot": [[27, 0, 1, "", "plot_landscape"]], "hoi.simulation": [[28, 0, 1, "", "simulate_hoi_gauss"]], "hoi.utils": [[29, 0, 1, "", "digitize"], [30, 0, 1, "", "get_nbest_mult"], [31, 0, 1, "", "landscape"], [32, 0, 1, "", "normalize"]]}, "objnames": {"0": ["py", "function", "Python function"], "1": ["py", "module", "Python module"], "2": ["py", "class", "Python class"], "3": ["py", "method", "Python method"], "4": ["py", "property", "Python property"]}, "objtypes": {"0": "py:function", "1": "py:module", "2": "py:class", "3": "py:method", "4": "py:property"}, "terms": {"": [18, 20, 23, 36, 37, 38, 39, 40, 42, 44, 46, 47, 48, 51, 53, 56, 59, 60, 62, 65, 66, 67], "0": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 32, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 59, 60, 61, 62, 65, 67, 69, 70], "00": [41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 54, 57, 60, 61, 69], "000": 54, "000008": 45, "000013": 45, "000068": 45, "000292": 45, "000440": 56, "000526": 56, "000540": 45, "000792": 56, "000795": 44, "000867": 48, "000945": 44, "000955": 44, "001132": 51, "001188": 45, "001248": 46, "001291": 44, "001332": 44, "001399": 51, "001460": 45, "001482": 46, "001514": 45, "001530": 45, "001593": 51, "001624": 46, "001628": 45, "001651": 46, "001666": 45, "001671": 51, "001762": 51, "002230": 48, "002443": 48, "002511": 51, "002614": 45, "002717": 45, "002729": 45, "002837": 47, "004202": 51, "004351": 51, "008568": 46, "009": [40, 41, 69], "009364": 46, "009812": 48, "01": [44, 49, 52, 69], "010098": 46, "013025": 70, "014264": 47, "01it": 45, "02": [41, 48, 69], "03": [48, 49, 52, 69], "030847": 47, "032305": 70, "04": [61, 69], "042": 52, "046": [48, 49, 69], "04it": 60, "05": 47, "052802": 70, "055869": 44, "05it": 44, "066138": 70, "06it": [44, 46], "07": 41, "070711": 44, "071": 65, "07140": 70, "08": 48, "087830": 44, "09": [61, 69], "090282": 45, "090620": 44, "092037": 45, "1": [5, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 32, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 57, 59, 60, 62, 66, 67, 70], "10": [20, 36, 37, 38, 39, 40, 46, 47, 48, 51, 53, 56, 63, 67, 70], "100": [31, 44, 45, 46, 47, 48, 51, 59, 60, 67, 70], "1000": [28, 36, 37, 38, 39, 40, 42, 44, 45, 53, 56, 60, 67, 68], "100000": 53, "1004": 70, "101147319": 65, "106": 70, "107": 36, "1093": 70, "1098": 70, "1099": 70, "10e2": 67, "11": [45, 46, 51, 56, 67, 70], "1103": 70, "1134": 70, "119": 70, "12": [20, 42, 46, 48, 53, 56, 59, 70], "12482": 70, "13": [45, 51, 56, 61, 67, 70], "1315": 70, "13186": 70, "1321": 70, "133": 70, "134994": 47, "13637": 70, "14": [23, 37, 44, 45, 46, 48, 51, 56, 63, 70], "140": 70, "146471": 56, "148361": 56, "14it": 46, "15": [36, 38, 40, 46, 48, 49, 56, 57, 67, 69, 70], "152": 70, "1541": 70, "156": 70, "1573": 70, "159": 70, "16": [45, 46, 56, 69, 70], "16243": 51, "16it": 51, "17": [25, 46, 51, 56, 70], "17019176483154297": 60, "177": 70, "177947": 45, "179842": 45, "18": [46, 48, 53, 56, 64, 70], "180913": 45, "189541": 46, "19": [22, 45, 48, 51, 56, 70], "190": [47, 70], "192637": 48, "193685": 46, "1940": 64, "1948": 70, "196": 69, "1960": [26, 70], "196290": 51, "1963": 70, "1975": 70, "197775": 46, "1978": [15, 70], "1986": 70, "199325": 45, "1995": 70, "1998": 70, "1999": 70, "2": [6, 9, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 52, 53, 56, 59, 60, 61, 63, 65, 67, 70], "20": [36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 53, 56, 60, 69, 70], "200": [46, 47, 48, 51, 56], "2001": [20, 70], "2003": 70, "2004": [11, 70], "2005": 70, "2009": 70, "2010": 70, "2011": [23, 70], "2014": [20, 70], "2015": 70, "2017": 70, "2018": [17, 70], "2019": [17, 19, 44, 45, 70], "2020": [65, 70], "2021": [22, 70], "20210246": 70, "2022": [25, 70], "2023": [16, 40, 65, 70], "2024": 70, "203173": 44, "203503": 44, "203644": 44, "203772": 44, "203808": 44, "205925": 44, "20th": 70, "21": [48, 70], "2109": 70, "211186": 46, "213": [38, 41, 69], "214246": 45, "214289": 45, "216": 53, "21it": 46, "22": [64, 65, 66, 70], "22015380859375": 60, "22138118743896484": 60, "222631": 51, "2227": 70, "223212242126465": 60, "225347": 46, "22it": [45, 51, 60], "23": [46, 70], "2304": 70, "2318": 70, "232": [41, 42, 69], "232792": 46, "233146": 46, "236016e": 48, "238701": 70, "24": [38, 41, 51, 69, 70], "2404": 70, "241095": 45, "241659": 45, "24it": [44, 45], "25": [19, 44, 45, 46, 53, 70], "2515": 70, "26": [16, 44, 46, 48, 70], "261": 70, "26it": 60, "27": [20, 46, 48, 51, 53, 70], "273": [59, 61, 69], "273890": 46, "274": [52, 53, 69], "27it": 60, "28": [64, 70], "282138118999967": 53, "28618431091308594": 60, "288": 63, "28it": [45, 60], "29": [44, 70], "29493": 44, "297": 70, "29it": 44, "2d": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 53], "2f": 42, "2\u03c0e": 37, "2\u03c0e\u03c3": 36, "3": [11, 28, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 64, 65, 66, 67, 68, 70], "30": [40, 41, 45, 48, 51, 53, 60, 69, 70], "300": 59, "305800": 46, "31": [17, 36, 44, 46, 70], "312485": 46, "313": [37, 41, 69], "314976": 46, "315670": 46, "31it": 46, "32": [15, 37, 41, 44, 46, 69, 70], "329931": 48, "33": [20, 44, 46, 48, 51, 53, 70], "337": 70, "3390": 70, "33it": [48, 60], "34": [64, 70], "34401702880859375": 60, "347109": 45, "3490": 70, "3495": 70, "34it": 46, "35": [44, 64, 70], "35it": [44, 60], "36": [44, 53, 70], "365911e": 48, "36it": [46, 47], "37": [26, 70], "371283": 45, "3766": 70, "3779": 70, "379": 70, "379484": 46, "38": [64, 70], "380": 70, "381920": 46, "387095": 45, "390869": 44, "392": [36, 41, 69], "392231": 44, "392336": 48, "392670": 44, "392677": 44, "392874": 44, "397405": 45, "39it": [45, 46, 60], "3d": 53, "4": [17, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 67, 68, 70], "40": [44, 59], "402": [44, 49, 69], "42": [51, 60], "420686": 48, "423": 70, "43": 44, "4300": 70, "439481e": 48, "444745": 48, "45": [56, 70], "450861": 48, "45it": 44, "46": 63, "46it": 48, "470587": 45, "476": 70, "477": 70, "47it": 44, "483097": 48, "484223": 45, "484230": 45, "485553": 45, "485621": 45, "485729": 45, "486022": 45, "498634": 46, "49it": [47, 60], "5": [20, 30, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 51, 56, 59, 60, 67, 70], "50": [45, 51, 59, 60], "50it": 51, "51": 70, "52": 70, "533365": 48, "54": 53, "545935": 47, "559214": 46, "55it": 51, "56": 69, "569149": 46, "57": 44, "5714287757873535": 53, "573858": 46, "57it": [44, 46], "581": [47, 49, 69], "5857170439999777": 53, "58it": 44, "597383": 47, "6": [37, 38, 40, 41, 42, 44, 45, 46, 47, 48, 51, 53, 56, 60, 67, 70], "60": [44, 59], "600548": 48, "603431": 47, "61it": [48, 51], "62it": 46, "63it": [48, 60], "646320": 45, "64it": 48, "654": [56, 57, 60, 61, 69], "66": 70, "67": [46, 48, 51], "68": 70, "688": [39, 41, 69], "68it": 48, "69": [44, 70], "698441": 47, "698491": 45, "7": [15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 44, 45, 46, 47, 48, 51, 56, 59, 63, 67, 70], "70": 44, "705744e": 48, "71": 44, "72": 44, "726": 49, "729": 53, "72it": 60, "73": 44, "730": [45, 49, 69], "749583": 45, "74it": 46, "767": [51, 52, 69], "76it": [44, 48, 51, 60], "77": 63, "771": 70, "77it": [45, 47], "782": 70, "78it": 46, "8": [9, 15, 16, 18, 19, 20, 21, 23, 24, 26, 28, 37, 44, 45, 46, 48, 51, 53, 56, 59, 62, 66, 70], "80": [44, 45, 60], "80it": [44, 46, 48], "81": 53, "82": 70, "824267": 45, "82it": [44, 46, 48], "83": 51, "84": 44, "848": 41, "84it": 47, "8529834747314453": 60, "85it": 45, "86": 44, "869": 70, "86it": 45, "874": 70, "87it": 45, "88it": [45, 48], "89": 44, "89it": 45, "9": [15, 16, 18, 19, 20, 21, 23, 24, 26, 44, 45, 51, 53, 56, 59, 66, 70], "90": [44, 59], "91": 70, "92": 70, "927": 61, "92it": 45, "9361505508422852": 60, "948908": 45, "94it": [46, 48], "95": [36, 37, 38, 39, 40, 44, 56], "968": [46, 49, 69], "968453": 45, "971174": 45, "971751": 45, "98it": [44, 46, 51], "99": 44, "A": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 46, 47, 48, 54, 60, 65, 68, 70], "As": [44, 45, 51, 53, 56, 59, 60, 68, 70], "Be": 60, "But": 45, "By": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29], "For": [12, 25, 29, 36, 37, 42, 44, 45, 46, 47, 48, 51, 56, 59, 62, 68, 70], "IT": [64, 70], "If": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 62, 65, 66, 68, 70], "In": [28, 36, 38, 39, 40, 42, 44, 46, 48, 51, 53, 56, 60, 64, 67, 68, 70], "It": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 37, 47, 48, 64, 70], "Its": 70, "No": 65, "On": 67, "One": [46, 48, 53, 67, 70], "That": [45, 46, 48, 60], "The": [6, 9, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 37, 42, 44, 45, 46, 47, 51, 53, 56, 59, 62, 64, 65, 67, 70], "Their": 47, "Then": [37, 44, 45, 53, 60, 62, 70], "There": 44, "These": [42, 64, 70], "To": [45, 51, 56, 59, 60, 62, 66, 67, 68, 70], "_": [16, 45, 59], "__iter__": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "_autosummari": 53, "_hoi": 56, "_trial": 59, "aa": 70, "ab": [60, 65], "abil": 64, "abl": [44, 48], "about": [20, 25, 28, 44, 45, 46, 47, 48, 56, 59, 60, 64, 70], "abov": [45, 46, 48, 56, 60, 70], "academi": 70, "accur": [68, 70], "accuraci": 59, "achiev": [46, 47, 48, 56, 70], "acknowledg": 65, "across": [51, 56, 68], "activ": [60, 70], "acuiti": 68, "ad": 70, "adam": 70, "adapt": 70, "add": [27, 45, 46, 48, 51, 62], "add_edges_from": 51, "add_nodes_from": 51, "add_subplot": [38, 40], "addit": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 56, 62, 68], "address": [64, 70], "adopt": 65, "adrian": 70, "advanc": [64, 70], "advantag": 70, "advis": 70, "after": 70, "again": [44, 45, 46, 47, 48], "aggreg": 31, "agreement": 65, "aim": [64, 70], "aix": 65, "al": [11, 16, 17, 19, 20, 22, 23, 25, 40, 44, 45, 70], "alain": 70, "alexand": 70, "alford": 70, "algebra": [53, 68], "alic": 70, "all": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 34, 38, 40, 44, 45, 48, 56, 59, 60, 62, 67, 69, 70], "allanson": 70, "allow": [45, 53, 64, 65, 68, 70], "along": [29, 53], "alpha": [36, 37, 38, 39, 40, 51, 56], "alreadi": [6, 9, 66, 70], "also": [11, 20, 23, 37, 44, 45, 46, 47, 48, 56, 64, 65, 66, 68, 70], "altern": 51, "although": 68, "alwai": 70, "am": [22, 70], "american": 70, "amico": 70, "amir": 70, "ammount": 48, "among": [64, 70], "amount": [45, 47, 64, 70], "amx": 65, "an": [5, 15, 26, 31, 37, 42, 45, 48, 51, 53, 56, 60, 62, 64, 67, 68, 70], "analys": 51, "analysi": 70, "analyt": [42, 64], "analyz": 68, "anatomi": 70, "anderson": 70, "andrea": 70, "andrew": 70, "ani": [15, 44, 51, 56, 67, 70], "anil": 70, "annal": 70, "anoth": [15, 42, 64, 70], "answer": 59, "antonacci": 70, "anywher": 65, "aopi": 63, "ap": 70, "apart": 70, "api": [65, 68], "append": [56, 67], "appli": [8, 53, 70], "applic": 70, "approach": [16, 25, 34, 39, 48, 58, 61, 68, 69, 70], "approxim": [47, 48, 70], "ar": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 48, 51, 53, 56, 59, 60, 62, 64, 67, 68, 70], "arang": [51, 56, 59, 67], "arbitrari": [15, 26, 70], "architectur": 70, "area": [31, 56, 68], "areg": 60, "argument": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 53], "around": [31, 56, 59], "arrai": [5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 42, 53, 59], "array_lik": [6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 59], "array_split": 59, "arruda": 70, "arxiv": 70, "asarrai": [53, 67], "ask": 45, "aspect": [47, 70], "assert": 59, "associ": [27, 30, 31, 47, 64, 70], "assum": 62, "assumpt": 68, "astyp": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 67], "atric": 70, "attent": 70, "attractor": 70, "attribut": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "auditori": 70, "auto": 47, "auto_exampl": [41, 49, 52, 54, 57, 61], "auto_examples_jupyt": 34, "auto_examples_python": 34, "autocorrel": 47, "automat": 53, "avail": [42, 70], "averag": 56, "avoid": [44, 70], "ax": [27, 37, 38, 40, 51, 53, 56, 59], "axhlin": [36, 37, 38, 39, 40], "axi": [22, 25, 27, 29, 31, 36, 37, 38, 39, 40, 53, 56], "b": [36, 60, 62, 70], "backend": [65, 68], "background": 68, "balaji": 70, "bandwidth": 10, "bar": 31, "barrat": 70, "barrett": 70, "base": [6, 9, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 42, 44, 48, 62, 70], "base_model": 16, "basic": [53, 62], "battiston": 70, "baudot": [17, 44, 70], "bayesian": 70, "becam": 70, "becaus": [39, 45, 60], "becom": 70, "been": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 65, 70], "beer": 70, "beerenwinkel": 70, "befor": [14, 60], "begg": 70, "behavior": [15, 16, 19, 23, 26, 30, 34, 43, 49, 64, 68, 69], "behaviour": 70, "behind": [45, 70], "being": 44, "bell": 70, "bellow": 68, "below": [37, 44, 51], "benchmark": 68, "benedetta": 70, "benjamin": 70, "bennequin": 70, "berri": 70, "besid": 70, "best": [30, 46, 47, 48], "better": 56, "between": [15, 16, 17, 18, 19, 23, 26, 32, 36, 37, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 64, 65, 68, 70], "beyond": [64, 65, 68, 70], "bia": 8, "bialek": 70, "bianconi": 70, "biascorrect": [8, 38, 39, 40], "bibtex": 62, "big": 70, "bin": [6, 9, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 39, 70], "binar": [9, 70], "binari": 39, "bind": 70, "binom": 67, "biolog": 64, "biologi": [64, 70], "biorxiv": 70, "bit": [6, 7, 8, 9, 10, 11, 36, 37, 38, 39, 40, 42, 45, 46, 48, 56, 59, 60, 70], "bivari": [45, 46, 48], "black": [37, 62], "blakeaw": 11, "block": 70, "blog": 53, "bodi": 70, "bold": [36, 37, 38, 39, 40, 45, 56, 59, 60, 67], "book": 62, "bool": [5, 8, 27, 28, 29, 31], "boostrap": 56, "bootstrap": [19, 27, 30, 57, 68, 69, 70], "bor": 70, "both": [15, 44, 45, 60, 67, 68, 70], "bound": [36, 37, 38, 39, 40, 70], "boundari": 36, "brain": [68, 70], "brainet": [62, 66], "branch": 62, "branch_nam": 62, "brien": 70, "bring": 56, "broad": 70, "brovelli": 63, "browser": 62, "bruno": 70, "bsd": 65, "bug": 62, "build": [31, 42, 62, 70], "built": [65, 68], "bump": 59, "button": 62, "bw_method": 10, "c": [36, 37, 38, 39, 40, 42, 59, 60, 68], "c0": 59, "c_": [46, 48], "calcul": 37, "call": [23, 42, 53, 68, 70], "callabl": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 42], "can": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 37, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 64, 66, 67, 68, 70], "cancel": 39, "cannot": [64, 70], "capabl": [44, 45, 46], "capac": 64, "captur": 68, "card": [17, 44, 70], "care": [60, 70], "carhart": 70, "carri": [20, 45, 46, 47, 48, 56, 59, 60, 64, 70], "case": [28, 31, 39, 42, 48, 59, 64, 70], "categori": [64, 70], "causal": 70, "cbar": 27, "cd": 62, "cell": 67, "cencetti": 70, "center": 31, "central": 31, "centuri": 70, "certain": [37, 70], "challeng": 70, "chang": [53, 62], "channel": 64, "chao": 70, "charact": [28, 45], "character": [45, 70], "characteris": 70, "characterist": [44, 70], "chechik": [20, 70], "check": [31, 44, 48, 62], "checkout": [44, 45, 46, 48, 56, 59, 62, 65, 68], "chichek": 70, "choic": 70, "choos": 28, "chrisferreyra13": 63, "christin": 70, "christof": 70, "christoph": 70, "circular": 51, "circular_layout": 51, "claim": 68, "class": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 65, 68], "claud": [64, 70], "claus": 65, "clear": 70, "clf": 59, "click": 62, "clone": 62, "close": 42, "closest": 11, "cmap": [44, 46, 48, 56], "code": [11, 34, 36, 37, 38, 39, 40, 42, 44, 46, 47, 48, 51, 53, 56, 59, 60, 65, 67, 70], "codecov": 62, "cognit": 70, "colab": 67, "collect": [45, 51, 70], "color": [36, 37, 38, 39, 40, 59], "colorbar": [27, 47], "column": [45, 46, 48], "com": [53, 62, 66, 70], "comb": 5, "combin": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 64, 68], "combinatori": 33, "come": 70, "command": [62, 68], "commit": 62, "common": 70, "commun": [64, 70], "compar": [36, 37, 38, 39, 40, 59, 67, 70], "comparison": [12, 13, 29, 34, 35, 41, 42, 56, 68, 69, 70], "compil": 67, "complet": 70, "complex": [64, 67, 68, 70], "complic": 70, "compon": [64, 70], "compos": 68, "compress": 64, "comput": [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 31, 36, 37, 38, 39, 40, 42, 44, 45, 47, 48, 60, 62, 65, 70], "computation": 56, "compute_entropi": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37], "compute_hoi_beh": 60, "compute_hoi_enc": 60, "compute_tim": 67, "compute_true_entropi": 38, "compute_true_mi": 40, "concept": [64, 70], "concern": 45, "concis": 70, "conclud": 56, "concret": 70, "condit": [17, 19, 27, 30, 34, 43, 45, 49, 56, 69, 70], "confid": [19, 27, 30, 34, 55, 57, 68, 69, 70], "connect": 70, "conscious": 70, "consequ": 45, "consid": [9, 22, 25, 47, 48, 64, 67, 70], "consist": [60, 70], "constant": [36, 37], "constraint": [45, 70], "contain": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 31, 37, 44, 45, 70], "content": 70, "context": [60, 70], "continu": [29, 39, 70], "contrast": 44, "contribut": [60, 63, 64, 65, 68, 70], "control": 70, "convei": [28, 70], "convent": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "converg": [36, 38, 39, 40], "convers": 44, "cooper": 64, "coordin": 70, "copi": [45, 46, 47, 48, 59, 64, 70], "copnorm": 8, "copula": [8, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 42, 67, 68, 70], "core": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 33, 34, 35, 36, 37, 38, 39, 40, 41, 62, 67, 69], "correct": [8, 39, 64, 70], "correctli": 44, "correl": [15, 19, 23, 26], "correspond": 44, "cost": [67, 70], "could": 45, "count": 31, "coupl": [25, 47, 70], "cov": [37, 38, 40, 42, 62], "cov_matrix": [38, 39, 40], "covari": [37, 38, 39, 40, 42, 60], "cpu": [53, 65, 66], "craig": 70, "creat": [37, 38, 39, 40, 47, 51, 56, 59, 60, 62, 67], "create_cov_matrix": [38, 40], "creation": 68, "cross_val_scor": 59, "crucial": 70, "crutchfield": 70, "cryptographi": 64, "current": 27, "custom": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "cut": 65, "cv": 59, "czy": 70, "czyz": 40, "d": [37, 42, 70], "da": 59, "da_": 59, "daniel": 70, "darbellai": 70, "data": [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 31, 34, 35, 37, 41, 42, 56, 60, 64, 67, 69, 70], "data_s": 67, "dataarrai": 31, "datafram": [30, 31, 51], "dataset": 37, "date": 65, "david": 70, "de": 70, "deal": [67, 70], "deciph": 70, "decode_i": 59, "decompos": [64, 70], "decomposit": [22, 25, 30, 34, 43, 49, 64, 69], "def": [36, 37, 38, 39, 40, 53, 59, 60, 67], "default": [5, 6, 9, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30], "default_devic": 67, "defin": [15, 16, 17, 19, 20, 22, 23, 25, 26, 36, 37, 38, 39, 40, 42, 45, 46, 47, 48, 51, 53, 56, 60, 67, 68, 70], "definit": [44, 45, 68, 70], "degre": 70, "delai": [22, 25, 70], "delv": 70, "demonstr": 37, "dens": [38, 40], "densiti": [10, 31, 70], "depend": [17, 31, 59, 65, 68, 70], "depict": 56, "deriv": [15, 16, 19, 23, 26, 30, 34, 43, 49, 69, 70], "describ": [37, 64, 68, 70], "descript": 70, "descriptor": 70, "design": [20, 70], "despit": 44, "det": [37, 38, 40, 42], "det_cov": 38, "det_i": 40, "det_x": 40, "det_xi": 40, "detail": [12, 68, 70], "detect": 64, "determin": 37, "develop": [64, 65, 67, 68, 70], "deviat": 36, "devic": 67, "df": [46, 47, 48], "df_best": 30, "diag": 37, "diag_indic": [38, 40], "diagon": [37, 38, 40], "dict": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 44, 46, 48, 56], "did": 44, "differ": [15, 16, 19, 39, 42, 44, 45, 53, 56, 59, 60, 64, 67, 70], "differenti": [12, 39], "differnt": [38, 40], "digit": 39, "dim": 38, "dimens": [37, 38, 40, 53, 56], "dimension": [12, 13, 31, 34, 35, 37, 41, 42, 69, 70], "direct": [64, 70], "direction_axi": [22, 25], "directli": [48, 66, 70], "discret": [6, 9, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 39, 68, 70], "discriminant_analysi": 59, "discuss": [62, 70], "disentangl": [45, 46, 70], "dishie2498": 63, "disord": 70, "dispar": 44, "distanc": 53, "distinguish": 70, "distribut": [12, 26, 31, 34, 35, 37, 38, 41, 42, 68, 69, 70], "dit": 68, "diverg": 26, "divid": [31, 53, 70], "do": [46, 47, 48, 53, 62], "document": [53, 65, 66, 68], "doe": 70, "doesn": [56, 67], "doi": 70, "domain": 68, "domin": [45, 60, 70], "dominik": 70, "done": [40, 53, 60, 70], "dopaminerg": 70, "dot": [37, 53], "doubl": [48, 70], "download": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60], "draft": 62, "draw": 51, "drawn": 70, "dry": [53, 67], "dtc": [19, 23, 70], "dual": [15, 19, 23], "due": 70, "dufour": 70, "dynam": [67, 68, 70], "e": [36, 37, 38, 42, 45, 46, 48, 60, 62, 64, 67, 68, 70], "e1008289": 70, "e21090869": 70, "each": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 37, 38, 40, 44, 45, 46, 53, 56, 59, 60, 62, 64, 67, 70], "eas": 65, "easiest": 66, "ebrain": 65, "ecolog": 64, "ecologi": 64, "econom": 70, "edg": [31, 51, 65], "edge_fc": 51, "edge_fc_cmap": 51, "editor": 62, "effect": [60, 64, 70], "effici": [53, 68], "eilon": 70, "either": [5, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 31, 36, 46, 59], "elad": 70, "electrophysiolog": 70, "elegantli": 70, "element": [5, 15, 20, 26, 37, 38, 40, 45, 53, 60, 64, 70], "elif": [38, 40, 59], "ellison": 70, "els": [38, 40], "elwood": 70, "emerg": [47, 60, 70], "emmanuel": 70, "empti": 56, "en": [53, 66], "enabl": [44, 70], "encod": [15, 16, 19, 23, 26, 30, 34, 43, 49, 59, 64, 68, 69], "end": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62], "endr": 70, "eneuro": 70, "engag": 60, "engin": [64, 65], "enrico": 70, "ensur": 62, "ent": 38, "ent_theor": 38, "entropi": [6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 33, 39, 40, 41, 44, 45, 51, 62, 64, 68, 69], "entropy_analyt": 42, "entropy_bin": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "entropy_gauss": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "entropy_gc": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "entropy_hist": 12, "entropy_kernel": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "entropy_knn": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "enumer": [36, 37, 38, 39, 40, 45, 47, 59], "environ": 67, "equal": [29, 31, 37], "equiv": [20, 46, 48], "equival": [26, 39, 53], "eran": 70, "error": [36, 39, 64], "especi": 68, "essenc": 64, "estim": [8, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 33, 34, 35, 41, 42, 44, 60, 68, 69, 70], "et": [11, 16, 17, 19, 20, 22, 23, 25, 40, 44, 45, 70], "etc": [67, 68], "etiennecmb": 63, "eu": 65, "euler": [36, 37], "evalu": 70, "even": [45, 70], "eventu": 48, "evolut": [22, 25, 70], "evolv": 60, "exact": 56, "exampl": [18, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 59, 60, 61, 62, 65, 67, 68, 69], "exceed": 20, "except": [45, 53, 56, 60], "excess": 70, "exclud": 70, "exclus": 44, "execut": [41, 49, 52, 53, 54, 57, 61, 65, 69], "exogen": [23, 70], "expect": [42, 46, 47, 64], "experimentalist": 70, "explain": 64, "explan": 70, "explor": 70, "expon": 53, "extend": 70, "extens": [15, 26, 70], "extern": [60, 64, 70], "extract": [38, 39, 40, 42, 51], "extrins": 64, "ey": [38, 40], "f": [36, 37, 38, 39, 40, 53, 56, 59, 60, 70], "fact": [67, 70], "fae": 70, "failur": 64, "fall": 64, "fals": [5, 28, 29, 31, 38, 39, 40, 44, 46, 48, 56, 59, 60, 67, 70], "familiar": 65, "fascin": 70, "fast": [56, 67], "faster": [67, 68], "fault": 64, "favorit": 62, "fcn": [12, 13, 36, 37, 38, 39, 40, 53], "featur": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 46, 47, 48, 59], "federico": 70, "fernando": 70, "ferraz": 70, "fetch": 62, "fi": 70, "field": [67, 70], "fig": [37, 38, 40, 59], "figsiz": [37, 38, 40, 59], "figur": [37, 38, 40], "file": [41, 49, 52, 54, 57, 61, 62, 69], "file1": 62, "file2": 62, "fill": 5, "fill_between": [36, 37, 38, 39, 40, 56], "fill_valu": 5, "final": [37, 45, 53, 60, 62, 67, 70], "find": [45, 48, 68], "finoia": 70, "first": [16, 29, 45, 46, 47, 48, 51, 53, 56, 60, 67], "fit": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67, 68], "fix": 56, "flake8": 62, "flecker": 70, "float": [6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 32, 53, 59], "focu": 70, "focus": [45, 70], "foldiak": 70, "follow": [22, 36, 44, 47, 48, 60, 62, 67, 68, 70], "font_size_nod": 51, "fontweight": [36, 37, 38, 39, 40, 45, 56, 59, 60, 67], "fork": 62, "formal": 70, "formisano": 70, "formula": [42, 70], "found": [44, 45, 64, 68], "foundat": [65, 70], "frac": [36, 37, 38, 39, 40, 42], "framework": [47, 48, 64, 65, 70], "franceschiello": 70, "fraser": 70, "freder": 70, "frequenc": [31, 70], "frequentist": 70, "friendli": 53, "from": [31, 37, 38, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 59, 60, 61, 62, 64, 66, 67, 68, 69], "fryer": 70, "full": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62], "fulli": [59, 64], "function": [2, 4, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 34, 36, 37, 38, 39, 40, 42, 51, 59, 60, 62, 65, 68, 70], "functool": [39, 53], "fundament": [42, 64, 70], "further": [44, 45, 46, 48, 53, 56, 59, 68], "futur": [25, 47, 64, 70], "fx": [38, 39, 40], "g": [47, 68, 70], "gabert": 70, "gabriel": 70, "gal": 70, "galleri": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 69], "gastpar": 70, "gather": 70, "gauss": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37], "gaussian": [7, 8, 10, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 36, 37, 38, 39, 40, 42, 60, 67, 68, 70], "gaussian_kd": 10, "gbauer": 70, "gc": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 42, 44, 45, 51, 56, 60, 67, 68], "gca": 56, "gcmi": [38, 40], "gener": [28, 34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 64, 67, 70], "genet": 70, "geomspac": [36, 37, 38, 39, 40], "georg": 70, "get": [5, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 36, 37, 38, 39, 40, 45, 56, 67, 68], "get_combin": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 47], "get_covari": 37, "get_entropi": [36, 37, 38, 42, 67], "get_mi": [39, 40, 42], "get_nbest_mult": [44, 45, 46, 47, 48, 51, 56, 68], "ggplot": [36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67], "ginestra": 70, "giordano": 70, "giovanni": 70, "git": [62, 66], "github": [62, 66], "giulia": 70, "give": 45, "given": [39, 40, 44, 45, 64, 70], "globerson": 70, "glossari": 68, "go": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 65, 67, 68, 70], "goaillard": 70, "goodman": 70, "googl": 65, "gpu": [53, 65, 66], "grabowski": 70, "gradient": [16, 45, 48, 59], "gradientoinfo": [45, 59, 60, 68, 70], "grant": 65, "graphic": 70, "grassberg": 70, "greater": [60, 64, 70], "griffith": 70, "gross": 70, "group": [48, 64, 70], "grow": [67, 70], "gui": 70, "guid": [42, 70], "guilherm": 70, "guillaum": 70, "h": [15, 19, 23, 26, 36, 37, 38, 42, 44, 45, 51, 70], "h_": [17, 44], "h_idx": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "h_max": 60, "h_theoric": [36, 37], "h_x": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37], "ha": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 44, 53, 65, 70], "half": 70, "hallmark": 60, "han": [45, 59, 60, 70], "handl": 70, "hann": 59, "harald": 70, "harri": 70, "have": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37, 38, 40, 42, 45, 53, 66, 67, 68, 70], "height": 31, "henc": 70, "henrik": 70, "here": [45, 46, 47, 48, 51, 56, 59, 60, 66, 68], "hgx": 68, "high": [12, 13, 28, 34, 35, 41, 47, 69, 70], "higher": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 33, 34, 37, 42, 44, 46, 48, 50, 52, 53, 59, 64, 69], "highest": [44, 46, 47, 48, 51, 56], "highli": 68, "highlight": [44, 70], "hinteract": 65, "hist": 27, "hist_kwarg": 27, "histogram": [12, 27, 31, 36, 37, 38, 39, 40, 70], "hoi": [33, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 53, 56, 58, 60, 61, 64, 66, 67, 68, 69, 70], "hoi_m": 56, "hoi_order_3": 51, "hoi_r": 48, "hoi_syn": 48, "hold": 44, "holland": 70, "horizon": 65, "horizont": 37, "how": [16, 19, 28, 31, 34, 44, 45, 46, 47, 48, 51, 53, 56, 58, 59, 61, 64, 68, 69, 70], "howev": [44, 46, 48, 56, 59, 67, 70], "html": [53, 66], "http": [44, 53, 62, 66, 70], "huge": 67, "hull": 51, "human": 70, "hx": [6, 7, 8, 9, 10, 11], "hypergraph": 51, "hypothesi": 70, "i": [5, 6, 9, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 53, 56, 59, 60, 62, 64, 65, 66, 67, 68, 70], "i_": [17, 44], "iacopini": 70, "iacopo": 70, "ibm": 70, "idea": 45, "ident": 70, "identifi": [44, 70], "idtxl": 68, "ieee": 70, "ignor": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "igor": 70, "ik": [16, 45], "il": 70, "illustr": [34, 45, 46, 47, 48, 51, 56], "imagin": 53, "implement": [44, 51, 53, 62, 68, 70], "import": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67, 68, 70], "improv": [62, 64], "imshow": 47, "in_ax": [53, 67], "inc": 70, "incept": 70, "includ": [28, 37, 56, 62, 65], "increas": [37, 67], "independ": [42, 47, 70], "index": [20, 21, 24, 27, 30, 34, 43, 44, 45, 47, 48, 49, 51, 56, 64, 69], "indic": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 70], "individu": [20, 45, 60, 64, 70], "inf": 70, "infer": [44, 68, 70], "inflat": 47, "influenc": 45, "info": [16, 19, 23, 45, 56], "inform": [11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 33, 38, 40, 41, 43, 46, 48, 49, 51, 58, 60, 61, 64, 65, 67, 68, 69], "infotheori": 68, "infotopo": [44, 51, 68, 70], "initi": 56, "inject": [45, 47, 51, 60], "innov": 65, "input": [6, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 37, 42, 53], "insid": [46, 48, 62], "insight": 70, "inspect": [17, 27, 30, 34, 46, 47, 48, 50, 52, 69, 70], "inspir": 40, "instal": [30, 65, 67], "instanc": 70, "instead": [47, 48, 70], "int": [5, 6, 9, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 36, 37, 38, 39, 40, 59, 67], "integr": [22, 25, 30, 34, 43, 49, 68, 69], "intens": 56, "interact": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 33, 34, 37, 45, 46, 48, 50, 52, 56, 59, 60, 64, 69], "interdepend": [47, 70], "interdisciplinari": 70, "interest": 70, "intern": 70, "interpol": 47, "interpret": [46, 47, 48, 70], "interv": [19, 27, 30, 34, 36, 37, 38, 39, 40, 42, 55, 57, 68, 69, 70], "intric": 70, "intrins": [15, 45, 64], "introduc": [44, 45, 46, 48, 53, 59, 70], "introduct": [12, 13, 34, 35, 41, 50, 52, 68, 69, 70], "intuit": [45, 60], "invalu": 70, "investig": [59, 67, 70], "involv": 70, "io": [44, 53, 66], "ipynb": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60], "isol": 45, "israel": 70, "issu": [62, 67], "item": [36, 37, 38, 39, 40], "iter": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "its": [15, 16, 19, 23, 26, 30, 34, 36, 43, 48, 49, 56, 64, 68, 69, 70], "j": [15, 19, 23, 26, 45, 70], "jame": [23, 70], "jax": [5, 10, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 34, 50, 52, 65, 66, 68, 69, 70], "jax_eucl": 53, "jean": 70, "jensen": 70, "jirina": 70, "jnp": [5, 53, 67], "joachim": 70, "john": 70, "joint": [26, 38, 39, 40, 70], "joseph": 70, "journal": 70, "judith": 70, "julia": 70, "jupyt": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60], "just": 45, "k": [5, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 44, 45, 59, 67, 70], "kayser": 70, "kazuto": 70, "kbinsdiscret": 29, "keep": 56, "kei": [36, 37, 38, 39, 40], "kernel": [10, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 47, 70], "kind": [27, 44, 46, 48, 51, 53, 56, 70], "knn": [11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 70], "know": [46, 48, 60, 70], "knowledg": [62, 64], "known": [44, 53, 59, 70], "kobayashi": 70, "koch": 70, "kraskov": [11, 70], "kullback": 26, "kwarg": [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 39], "l": 70, "label": [36, 37, 38, 39, 40, 45, 59, 67], "lack": 70, "lall": 70, "lambda": 36, "lambda_": 36, "landcap": 31, "landscap": [27, 44, 56, 68], "lapish": 70, "larg": 26, "larger": 67, "largest": [45, 51], "lasserr": 70, "last": 70, "latest": [53, 66], "latora": 70, "launch": [46, 47, 48], "lax": 53, "layout": 51, "ldot": 70, "lead": [36, 53, 67], "learn": [16, 34, 56, 58, 61, 65, 66, 69, 70], "least": [53, 56, 70], "left": [42, 70], "legend": [36, 37, 38, 39, 40, 45, 59, 67], "len": [36, 37, 38, 39, 40], "length": [22, 25], "less": 70, "let": [36, 37, 38, 39, 42, 44, 45, 46, 47, 48, 53, 56, 59, 60, 67], "letter": 70, "leverag": 48, "li": 56, "librari": [53, 67, 68, 70], "liebler": 26, "light": 70, "like": [53, 68], "limit": [48, 56, 68, 70], "linalg": [37, 38, 40, 42], "line": [37, 56, 68, 70], "linear": [53, 68, 70], "lineardiscriminantanalysi": 59, "linearli": 67, "linestyl": [36, 37, 38, 39, 40], "link": [39, 40, 45, 70], "linspac": 67, "lint": 62, "list": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 36, 37, 38, 39, 40, 56, 65, 66, 68, 70], "literatur": 70, "lizier": 70, "locat": 62, "log": [36, 37, 42], "log2": [36, 38, 39, 40], "log_": [36, 38, 39, 40, 70], "logarithm": [6, 9], "look": [46, 47, 48, 68], "lost": 70, "lot": 70, "low": 70, "lower": [36, 37, 38, 39, 40, 44, 56, 70], "lowest": [46, 47, 48, 51], "luca": 70, "luppi": [25, 70], "lw": [36, 37, 38, 39, 40, 56, 59], "m": [36, 45, 47, 56, 62, 70], "machin": [16, 34, 58, 61, 69, 70], "mai": 37, "main": [34, 62, 67, 70], "mainli": [56, 70], "maintain": 62, "make": [37, 62, 70], "make_spd_matrix": 37, "mani": 70, "manipul": 68, "manon": 70, "map": 70, "marc": 70, "margin": 26, "marinazzo": 70, "marker": 37, "marqu": 70, "marseil": 65, "martial": 70, "marx": 70, "mass": 70, "math": [26, 45], "mathcal": [36, 38, 39, 40], "mathemat": [44, 45, 64, 70], "matplotlib": [36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60, 62, 67], "matrix": [37, 38, 39, 40, 42, 47, 60], "matrix_to_plot": 47, "mattehub": 63, "max": [25, 47, 53, 60, 70], "max_": [48, 70], "maxim": [20, 70], "maximum": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 32, 68], "maxsiz": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 45, 46, 47, 48, 51, 59, 60, 67, 68], "mb": [41, 49, 52, 54, 57, 61, 69], "mdpi": 70, "mean": [36, 37, 38, 39, 40, 42, 46, 48, 53, 56, 59, 60, 67], "measur": [26, 33, 45, 46, 47, 48, 60, 64, 68], "mechan": 70, "mechanist": 70, "mediano": [22, 70], "mem": [41, 49, 52, 54, 57, 61, 69], "menon": 70, "mention": 70, "messag": [62, 64], "method": [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 42, 44, 45, 51, 56, 60, 67, 68, 70], "metric": [12, 13, 27, 30, 33, 35, 36, 37, 38, 39, 40, 41, 44, 45, 46, 47, 48, 49, 51, 56, 59, 60, 64, 65, 67, 68, 69, 70], "metric_nam": [36, 37, 38, 39, 40], "mi": [8, 13, 18, 20, 21, 22, 24, 25, 34, 35, 38, 41, 42, 64, 69], "mi_bin": 39, "mi_binning_fcn": 39, "mi_theor": [39, 40], "michael": 70, "mid": 56, "midbrain": 70, "midex": 65, "milan": 70, "min": [22, 47, 53, 60, 70], "min_": [48, 70], "minimum": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 32, 47, 48, 68, 70], "minmax": 53, "minmax_2d": 53, "minmax_3d": 53, "minmax_3d_jit": 53, "minmaxscal": 51, "minsiz": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67, 68], "minu": [16, 19, 23, 45], "minut": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60], "miscellan": [52, 69], "miss": 5, "mitig": 68, "mmi": [21, 22, 24, 25, 27, 30, 34, 43, 47, 49, 69], "mode": [38, 40, 62], "model": [27, 30, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67, 68, 70], "model_r": 48, "model_select": 59, "model_syn": 48, "modifi": [62, 67], "modul": [60, 64, 67, 70], "monica": 70, "monoton": 70, "moon": 70, "more": [12, 44, 46, 48, 56, 60, 64, 65, 70], "moreno": 70, "most": [42, 46, 47, 48, 65, 70], "move": [46, 48], "mu": [36, 38, 40], "mu_": [39, 40], "mu_i": 39, "mu_x": 39, "much": [47, 56, 70], "mult_order_3": 51, "mult_siz": 31, "multi_s": 31, "multiinform": 70, "multipl": [60, 64, 65, 67], "multiplet": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 45, 46, 47, 48, 56, 68, 70], "multivari": [12, 17, 34, 35, 38, 40, 41, 42, 59, 60, 68, 69, 70], "multivariate_norm": [37, 38, 39, 40], "musician": 68, "must": 67, "mutual": [11, 13, 15, 17, 18, 21, 22, 24, 25, 26, 29, 33, 38, 40, 41, 44, 47, 48, 51, 64, 68, 69], "n": [5, 15, 16, 18, 19, 20, 23, 26, 30, 36, 37, 38, 39, 40, 45, 46, 48, 53, 54, 59, 67, 68, 70], "n_": [36, 37, 38, 39, 40, 67, 70], "n_b": 56, "n_best": [30, 45, 46, 47, 48, 51], "n_bin": [9, 29, 31, 39, 40], "n_boot": 56, "n_combin": 5, "n_dim": [38, 40], "n_f": 67, "n_featur": [6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 42, 47, 67], "n_hoi": 31, "n_m": [36, 37, 38, 39, 40, 45], "n_mult": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "n_multiplet": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "n_node": [56, 60], "n_r": [36, 37, 38, 39, 40, 59], "n_repeat": [36, 37, 38, 39, 40], "n_sampl": [6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 36, 37, 38, 39, 40, 42, 56, 59, 60, 67, 68], "n_time": 59, "n_v": 67, "n_variabl": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 67], "n_x": 59, "n_y": 59, "naftali": 70, "name": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 53, 62], "nathaniel": 70, "nation": 70, "natur": [59, 60, 70], "ndarrai": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28], "ndata": [36, 39], "nearest": [11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 70], "necessari": 70, "need": [39, 60], "neg": [20, 28, 44, 45, 46, 51, 59, 60, 64, 70], "negin": 70, "neglect": 70, "neighbor": [11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 70], "nelken": 70, "nelsontang": 53, "neq": [16, 45], "network": [15, 16, 19, 23, 26, 30, 34, 43, 44, 49, 56, 64, 67, 68, 69], "networkx": 68, "neural": 70, "neurip": 40, "neuroimag": 70, "neuron": 70, "neurosci": [68, 70], "neurotransmitt": 70, "nevertheless": 37, "new": [67, 70], "next": 67, "nh": [23, 45, 70], "nica": 70, "nice": 53, "nichola": 70, "niko": 70, "node": [44, 45, 51, 56, 60, 67, 68], "node_label": 51, "node_s": 51, "nois": 47, "non": [56, 64], "none": [5, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 37, 38, 40, 47], "nonlinear": 70, "nonneg": 70, "normal": [8, 12, 31, 34, 35, 38, 40, 41, 42, 45, 68, 69, 70], "notabl": 44, "note": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 39, 70], "notebook": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67, 68], "notic": [48, 53], "now": [37, 42, 44, 45, 46, 47, 48, 53, 56, 59, 60], "np": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67], "nthe": [38, 40], "nuanc": [64, 70], "number": [5, 9, 15, 26, 28, 29, 30, 31, 36, 37, 38, 39, 40, 53, 56, 59, 67, 70], "numpi": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 56, 59, 60, 66, 67], "numpy_eucl": 53, "numpydoc": 62, "nuzzi": 70, "o": [15, 16, 19, 23, 26, 28, 30, 34, 37, 43, 48, 49, 64, 67, 68, 69], "object": 51, "observ": [31, 46, 47, 48, 70], "obtain": [60, 64], "occur": 64, "occurr": 70, "off": [38, 40], "offer": 70, "offici": 53, "often": [64, 70], "oinfo": [16, 44, 45, 56, 59, 60, 67, 68, 70], "oldest": [26, 70], "omega": [16, 19, 23, 45, 70], "omega_": 59, "onc": [62, 68, 70], "one": [37, 45, 56, 60, 64, 67, 70], "onli": [28, 38, 40, 44, 46, 47, 48, 51, 56, 59, 62, 64, 66, 70], "open": 62, "oper": [39, 47, 53, 67, 70], "optim": 37, "option": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 53, 66], "orchestra": 68, "order": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 33, 34, 37, 42, 43, 45, 46, 47, 48, 49, 50, 52, 59, 64, 69], "org": 70, "organ": 70, "origin": [11, 44, 62, 68], "other": [15, 42, 45, 46, 48, 60, 64, 70], "otherwis": 68, "our": [44, 51, 53, 62, 68, 70], "out": 39, "output": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 51], "over": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 53, 56, 60], "owen": 70, "own": [47, 70], "p": [26, 70], "p_high": 56, "p_low": 56, "packag": [51, 62, 65, 68], "page": [62, 68, 70], "pair": [38, 40, 59, 70], "pairwis": [18, 47, 64, 65, 68], "panda": [30, 31, 51, 62, 66], "paola": 70, "paramet": [5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 59, 60], "parametr": [56, 70], "part": [15, 48, 51, 59, 60, 64, 67, 70], "partial": [39, 53, 59, 64, 70], "partial_": [16, 45, 70], "particular": [36, 39, 40, 53, 70], "particularli": 70, "partit": 70, "pass": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 62], "past": [47, 67], "patania": 70, "path_to_test_fil": 62, "pathwai": 70, "pattern": [60, 70], "paul": 70, "paw": 70, "pcolormesh": 27, "pedro": [22, 70], "pep8": 62, "per": [31, 38, 40], "percent": 31, "percentil": [36, 37, 38, 39, 40, 56], "perform": [29, 53, 68, 70], "permut": 59, "perspect": 70, "peter": 70, "petri": 70, "phenomena": 70, "phenotyp": 70, "phiid": [22, 25], "philipp": 70, "philosoph": 70, "phy": 11, "physic": 70, "physrev": 70, "pi": [36, 37, 38, 42], "pickard": 70, "pid": [64, 70], "pierr": 70, "pinpoint": 44, "pip": [62, 66, 67, 68], "pitmonticon": 63, "plai": 70, "pleas": [39, 62, 65, 66, 68], "plethora": 70, "plo": 70, "plot": [17, 30, 33, 34, 36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 50, 52, 59, 60, 67, 68, 69, 70], "plot_bootstrap": [56, 57, 69], "plot_decod": 59, "plot_entropi": [36, 41, 69], "plot_entropies_mvar": [37, 41, 69], "plot_entropy_high_dimension": [38, 41, 69], "plot_infotopo": [44, 49, 69], "plot_inspect_result": [51, 52, 69], "plot_landscap": [44, 46, 48, 51, 56, 68], "plot_mi": [39, 41, 69], "plot_mi_high_dimension": [40, 41, 69], "plot_ml_vs_it": [59, 61, 69], "plot_oinfo": [45, 49, 69], "plot_rsi": [46, 49, 69], "plot_sim_red_syn": [60, 61, 69], "plot_syn_phiid": [47, 49, 69], "plot_syn_red_mmi": [48, 49, 69], "plot_xi": 59, "plt": [27, 36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67], "plt_kwarg": [27, 44, 46, 48, 56], "plu": [45, 47, 70], "po": 51, "point": [11, 44, 45, 53, 59, 67, 70], "popul": 29, "pose": 67, "posit": [20, 28, 37, 44, 45, 46, 47, 48, 51, 53, 59, 60, 70], "possess": 44, "possibl": [5, 46, 48, 60, 67, 70], "post": 33, "potenti": 68, "pouei": 70, "pre": 33, "precis": 60, "predict": 47, "predictor": 64, "prepar": 14, "preprint": 70, "preprocess": [29, 51], "presenc": [47, 48, 64, 70], "present": [44, 60, 70], "preserv": 70, "pretti": 68, "prevail": 70, "previou": [45, 60], "principl": 70, "print": [42, 44, 45, 46, 47, 48, 51, 53, 56, 60, 68], "probabl": [12, 31, 70], "problem": [67, 70], "procedur": 70, "proceed": 70, "process": [9, 33, 37, 64, 70], "produc": [60, 64, 70], "product": [26, 53], "program": 67, "programm": 65, "project": 65, "promin": 70, "properti": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 47, 70], "proport": 31, "propos": [62, 70], "proven": 70, "provid": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 59, 64, 65, 68, 70], "proxi": 70, "psycholog": 70, "publish": 70, "pure": 53, "purport": 20, "pursuit": 70, "push": 62, "py": [36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 56, 57, 59, 60, 61, 62, 69], "pyphi": 68, "pyplot": [36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60, 67], "pytest": 62, "python": [11, 34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 65, 66, 67, 68, 70], "quadruplet": [44, 56], "quantif": 64, "quantifi": [17, 45, 64, 65, 68, 70], "quantil": 29, "quantiti": 45, "question": [45, 59, 62, 70], "quick": [34, 50, 52, 69], "quickli": 70, "r": [56, 59, 70], "rajagopalan": 70, "rand": [42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67], "randal": 70, "random": [17, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 64, 67, 70], "random_st": 56, "randomli": 56, "rang": [36, 37, 38, 39, 40, 47, 56, 59, 70], "rate": 36, "ravel": 59, "re": [44, 60, 65], "read": 45, "readthedoc": [44, 53, 66], "real": [67, 70], "realli": 56, "rebas": 62, "receiv": [46, 47, 48, 59, 60], "recent": [67, 70], "recommand": 56, "recommend": [45, 67], "reconcil": 70, "record": 70, "recoveri": 64, "red": [22, 47, 48, 59, 70], "red_result": 47, "redmmi": 48, "redphiidmmi": 47, "reduc": 70, "reduct": [64, 70], "redund": [15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 34, 43, 49, 51, 58, 59, 61, 64, 68, 69], "redundancymmi": [48, 70], "redundancyphiid": [47, 70], "refer": [11, 15, 16, 17, 19, 20, 22, 23, 25, 26, 28, 51, 64, 66, 70], "reflect": [46, 70], "regard": 56, "region": 70, "rel": [53, 68], "rel_strength": 59, "rel_typ": 59, "relat": [15, 16, 19, 23, 26, 39, 45, 47, 59, 70], "relationship": [59, 60, 64, 68, 70], "relev": 70, "reli": [67, 68], "reliabl": 64, "rememb": 48, "remind": [44, 56], "remot": 62, "remov": 45, "repeat": [53, 56], "repetit": [36, 37, 38, 39, 40], "repo": 62, "report": 70, "repositori": 62, "repres": [5, 31, 45, 56, 60, 64, 70], "represent": 27, "requir": [30, 39, 64, 66, 67], "resampl": 56, "research": [65, 67, 70], "reshap": [36, 53, 59, 60], "resourc": 53, "respect": [28, 45, 47, 48, 59, 64, 68, 70], "result": [36, 38, 39, 40, 46, 47, 48, 56, 60, 67, 70], "retriev": [45, 46, 48, 51, 59, 68], "return": [5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 37, 38, 39, 40, 51, 53, 59, 60, 67], "rev": 11, "reveal": 70, "review": 70, "rf": 59, "right": [42, 70], "rightarrow": [16, 17, 19, 20], "robin": 70, "robust": [47, 68, 70], "role": 70, "rosa": [19, 45, 70], "rotat": 56, "rousselet": 70, "row": 70, "rowvar": 42, "royal": 70, "rsi": [18, 46, 48, 64], "rule": 70, "run": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 65, 67, 68], "ryan": 70, "s_": 48, "sai": [53, 56, 60], "said": 45, "same": [29, 44, 46, 47, 48, 53, 56, 60, 64, 65, 68, 70], "sampl": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 37, 38, 42, 44, 45, 46, 47, 48, 56, 59, 60, 67], "satisfi": 62, "satosi": 70, "sca": [37, 59], "scagliarini": [16, 70], "scale": 67, "scan": 53, "scatter": [27, 44, 46, 48, 51, 56], "scenario": 70, "schneidman": 70, "schyn": 70, "scienc": 70, "scientif": 70, "scientist": 70, "scikit": [56, 65, 66], "scipi": [10, 53, 66], "script": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 68], "sebastiano": 70, "second": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67, 70], "section": [45, 68, 70], "see": [10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 36, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 68, 70], "seed": [51, 60], "seen": 70, "segreg": 44, "select": [46, 47, 48, 67], "self": 70, "semi": 37, "semin": 70, "sen": 60, "send": [45, 46, 48], "sens": 70, "sensit": [15, 26, 70], "sent": [12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "separ": [47, 64, 70], "septemb": 70, "seri": [68, 70], "serv": 70, "set": [5, 15, 18, 20, 28, 42, 53, 60, 62, 64, 67, 70], "set_text": [38, 40], "set_xlabel": [38, 40], "set_xticklabel": 56, "set_ylabel": [38, 40], "seth": 70, "sever": [36, 37, 39], "shade": 56, "shannon": [39, 64, 70], "shape": [5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 31, 37, 38, 40, 42, 46, 48, 53, 56, 59], "share": [15, 26, 45, 47, 64, 70], "sharei": 59, "sharex": 59, "shed": 70, "short": [44, 53], "should": [6, 8, 9, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 44, 62, 70], "show": [31, 36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60], "showcas": [45, 51], "shown": 70, "sigma": [36, 37, 38, 40, 42], "sigma_": [39, 40], "sigma_i": 39, "sigma_x": 39, "sign": 70, "signal": [60, 62], "sim": [36, 39, 40], "simeq": 67, "similar": 40, "similarli": 60, "simmetr": 47, "simon": 70, "simpl": [46, 47, 48, 56, 60, 70], "simpli": [64, 70], "simul": [16, 19, 33, 34, 36, 37, 38, 39, 40, 56, 58, 61, 69, 70], "simulate_data": 59, "simulate_hoi_gauss": [60, 68], "sinc": [42, 70], "sinfo": [45, 70], "singl": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37, 46, 48, 62, 70], "situat": 70, "six": 48, "size": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 36, 37, 42, 46, 47, 48, 67, 68, 70], "sklearn": [29, 37, 51, 56, 59], "sl": 59, "slice": 59, "slow": 53, "small": [44, 70], "smallest": [45, 51], "smooth": 70, "so": [42, 59, 62, 70], "social": [64, 68], "societi": 70, "softwar": [62, 66], "some": [36, 45, 47, 53, 56, 60, 67, 70], "sonia": 70, "sourc": [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 70], "space": 70, "spars": [38, 40], "spatial": 56, "special": 39, "specif": [36, 44, 60, 62, 65], "specifi": [5, 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 38, 40, 53, 59], "spectral_r": [44, 51, 56], "sphinx": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62], "sphinx_gallery_thumbnail_numb": [51, 56], "sphinxcontrib": 62, "spread": [46, 51, 68], "springer": 70, "sqrt": [37, 53], "squeez": [56, 59, 60], "st": 70, "stack": 56, "stamataki": 70, "stand": [44, 46, 48], "standard": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 39, 70], "stark": 70, "start": [42, 44, 46, 47, 48, 59, 67], "stat": [10, 31], "state": [47, 64, 70], "static": [60, 70], "static_argnum": 53, "statist": [17, 31, 56, 57, 59, 65, 69, 70], "step": [56, 62], "still": 70, "stochast": 70, "storag": 64, "store": 47, "str": [10, 45, 56], "stramaglia": 70, "strang": 70, "strategi": 29, "strength": [45, 59, 70], "stronger": 47, "strongest": 68, "strongli": 68, "structur": [67, 68, 70], "studen": 70, "studi": [47, 64, 67, 68, 70], "style": [36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 51, 56, 59, 60, 65, 67], "subgroup": 48, "subplot": [37, 59], "subselect": 56, "subset": [17, 44, 45, 46, 48, 70], "subtl": [46, 48], "subtract": 45, "suffer": 68, "suggest": [53, 62, 70], "sum": [23, 31, 45, 47, 53, 64, 70], "sum_": [15, 16, 17, 19, 20, 23, 26, 44, 45, 46, 70], "summari": 68, "summer": 65, "sun": [15, 70], "superflu": 44, "support": 65, "suptitl": [38, 40], "sure": 62, "surround": 56, "susann": 70, "swinnei": 70, "switch": 60, "symmetr": [37, 70], "syn": [25, 47, 48, 59, 70], "syn_result": 47, "sync": 62, "synergi": [15, 16, 17, 19, 20, 21, 24, 25, 27, 28, 30, 34, 43, 44, 45, 49, 51, 58, 59, 61, 64, 68, 69], "synergist": [20, 46, 47, 48, 51, 56, 59, 64, 68, 70], "synergy_phiid": 47, "synergymmi": [48, 70], "synergyphiid": [47, 70], "synmmi": 48, "synphiidmmi": 47, "synsum": 20, "system": [45, 60, 64, 67, 68, 70], "t": [22, 25, 37, 38, 39, 40, 44, 47, 56, 59, 67, 70], "t1": 53, "t2": 53, "t_end": 59, "t_start": 59, "tabl": [44, 45, 46, 47, 48, 51, 56, 68], "take": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37, 42, 45, 46, 47, 48, 53, 60, 67, 70], "taken": [53, 67], "tapia": [17, 70], "target": [5, 16, 28, 48, 59, 60, 64, 70], "task": [15, 16, 19, 23, 26], "tau": [22, 25, 47, 70], "taxonomi": 70, "tc": [19, 23, 70], "tdmi": 70, "te": [15, 70], "technic": 70, "techniqu": 64, "tempor": [60, 70], "tend": [45, 68], "term": [45, 60, 68, 70], "termin": 68, "test": [53, 62, 70], "tests_entropi": 62, "text": [56, 60], "th": [11, 36, 37, 38, 39, 40, 70], "tha": 60, "than": [46, 60, 64, 67, 70], "thei": 70, "them": [42, 47, 59, 70], "theme": 62, "theoret": [0, 12, 13, 16, 33, 34, 35, 36, 37, 38, 39, 40, 41, 58, 61, 65, 67, 68, 69], "theori": [42, 44, 64, 68, 70], "therefor": [45, 53, 56, 60], "thi": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 64, 65, 67, 68, 70], "thick": 56, "thing": [44, 53], "third": 44, "thoma": 70, "thomasrobiglio": 63, "those": [44, 68], "though": 70, "three": [60, 64, 67, 68, 70], "threshold": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], "through": [37, 42, 70], "ti": 70, "tight_layout": [38, 40], "tim": 70, "time": [36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67, 68, 70], "timeit": 53, "timings_cpu": 67, "timings_gpu": 67, "timm": [20, 70], "tishbi": 70, "titl": [36, 37, 38, 39, 40, 45, 56, 59, 60, 67], "to_max": 32, "to_min": 32, "togeth": [60, 64, 68], "toi": [67, 68], "toler": 64, "tolist": 51, "toma": 70, "too": 70, "tool": [67, 70], "toolbox": [67, 70], "top": [62, 65, 68], "topolog": [17, 19, 27, 30, 34, 43, 49, 56, 68, 69], "toponetx": 68, "total": [5, 15, 18, 19, 20, 23, 26, 31, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 59, 60, 61, 69], "toward": [36, 38, 39, 40, 70], "tpu": [65, 67], "tqdm": 66, "tr": 70, "tradit": 64, "tradition": 68, "transact": 70, "transmit": 64, "trend": 70, "trial": 56, "trial_block": 59, "trick": 60, "triplet": [28, 44, 45, 46, 48, 51, 56, 60], "triplet_charact": [28, 60, 68], "true": [5, 8, 27, 28, 29, 38, 40, 42, 51, 59, 60], "try": 59, "tup": 47, "turbo": [46, 48], "tuto_cor": [41, 42, 69], "tuto_jax": [52, 53, 69], "tutori": [36, 39, 40, 42, 53, 60, 61, 69, 70], "twice": 53, "two": [39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 59, 60, 64, 70], "type": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 44, 45, 62, 68, 70], "u": [36, 37, 39, 59, 66, 68], "u_x": 59, "unavail": 70, "uncertainti": [64, 70], "under": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 47, 65, 70], "underli": 70, "undersampl": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 44, 46, 48], "understand": [64, 70], "understood": [15, 64], "undirect": [64, 70], "uniform": [42, 47, 70], "uniqu": [31, 53, 59, 64], "unit": [42, 65, 70], "univari": 59, "univers": 65, "unveil": 70, "up": [51, 65, 67], "updat": [53, 68], "upmanu": 70, "upper": [36, 37, 38, 39, 40, 70], "upstream": 62, "url": 70, "us": [5, 6, 9, 10, 11, 18, 31, 36, 37, 38, 39, 40, 42, 46, 47, 48, 51, 60, 64, 65, 66, 67, 68, 70], "usabl": 68, "use_sklearn": 29, "user": 68, "usual": 68, "util": [33, 39, 44, 45, 46, 47, 48, 51, 56, 68], "v": [16, 34, 58, 61, 62, 69, 70], "vaadia": 70, "vajda": 70, "valu": [5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 60, 70], "vari": [36, 38, 39, 40, 60], "variabl": [12, 13, 15, 16, 17, 18, 20, 22, 25, 26, 28, 29, 30, 37, 38, 39, 40, 42, 45, 46, 47, 48, 59, 60, 64, 67, 68, 70], "varianc": [38, 40, 42, 70], "variat": 70, "variou": [12, 34, 35, 37, 38, 39, 40, 41, 68, 69, 70], "varlei": 70, "vast": 70, "ve": 53, "vec": [38, 40], "vejnarov": 70, "verbos": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 56, 59, 67], "veri": [42, 46, 47, 48], "version": [64, 66], "via": 70, "virgil": 70, "visit": 70, "visual": [51, 68], "vito": 70, "vmap": 67, "vogt": 70, "vulner": 70, "wa": [44, 48, 64], "wai": [46, 47, 48, 60, 64, 66, 70], "want": [45, 53, 60, 62, 65, 68], "watab": 26, "watanab": 70, "we": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 62, 65, 67, 68, 70], "web": [62, 70], "well": [64, 68, 70], "weslei": 70, "what": [31, 45, 60, 64], "when": [20, 28, 36, 37, 38, 39, 40, 44, 45, 47, 48, 56, 59, 60, 64, 67, 70], "where": [37, 42, 56, 62, 70], "whether": [8, 28, 31, 45, 46, 59, 60, 68, 70], "which": [22, 25, 29, 42, 44, 45, 48, 59, 60, 64, 70], "while": [42, 44, 45, 46, 47, 51, 67, 70], "whole": [45, 47, 64, 70], "wholeminussum": 20, "why": 45, "width": 31, "william": 70, "win": [45, 60], "window": [45, 60], "within": 70, "without": [16, 28, 45], "word": 64, "work": [60, 64, 66, 70], "workspac": 70, "would": 64, "wrap": 53, "write": 53, "written": [12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 53, 70], "www": [53, 70], "x": [6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 32, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 60, 67, 70], "x_": [15, 16, 17, 18, 19, 20, 22, 23, 25, 26, 38, 44, 45, 46, 47, 48, 59, 70], "x_1": [38, 70], "x_2": [38, 70], "x_axi": 56, "x_bin": 29, "x_high": [36, 37, 38, 39, 40], "x_i": [38, 70], "x_j": [15, 45, 70], "x_jax": 53, "x_low": [36, 37, 38, 39, 40], "x_m": 59, "x_n": [38, 70], "x_np": 53, "x_red": 59, "x_ref": 60, "x_syn": 59, "x_t": [22, 25, 47, 70], "xarrai": [31, 62, 66], "xgi": [51, 68], "xi": [38, 40], "xla": 67, "xlabel": [36, 37, 39, 45, 56, 60, 67], "xlim": 60, "xn": 32, "xtick": 56, "xy": 39, "y": [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 38, 39, 40, 42, 45, 46, 47, 48, 60, 70], "y_": [22, 25, 47, 59, 70], "y_jax": 53, "y_norm": 59, "y_np": 53, "y_red": 59, "y_syn": 59, "y_t": [22, 25, 47, 70], "yamir": 70, "year": 70, "yi": 40, "yield": 44, "ylabel": [36, 37, 39, 45, 56, 59, 60, 67], "ylim": 60, "you": [42, 44, 46, 47, 48, 51, 53, 62, 65, 66, 68], "young": 70, "your": [53, 62, 67, 68], "your_usernam": 62, "yuri": 70, "z": 70, "ze": 70, "zero": [31, 36, 37, 38, 39, 40, 42, 47, 59], "zini": 70, "zip": [34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 51, 53, 56, 59, 60, 67], "\u00e1": 70, "\u00e8": 70, "\u00e9": 70, "\u00f3": 70, "\u00f6": 70, "\u0142": 70, "\u017c": 70, "\u03c3": 36}, "titles": ["<code class=\"docutils literal notranslate\"><span class=\"pre\">hoi.core</span></code>", "<code class=\"docutils literal notranslate\"><span class=\"pre\">hoi.metrics</span></code>", "<code class=\"docutils literal notranslate\"><span class=\"pre\">hoi.plot</span></code>", "<code class=\"docutils literal notranslate\"><span class=\"pre\">hoi.simulation</span></code>", "<code class=\"docutils literal notranslate\"><span class=\"pre\">hoi.utils</span></code>", "hoi.core.combinations", "hoi.core.entropy_bin", "hoi.core.entropy_gauss", "hoi.core.entropy_gc", "hoi.core.entropy_hist", "hoi.core.entropy_kernel", "hoi.core.entropy_knn", "hoi.core.get_entropy", "hoi.core.get_mi", "hoi.core.prepare_for_it", "hoi.metrics.DTC", "hoi.metrics.GradientOinfo", "hoi.metrics.InfoTopo", "hoi.metrics.InfoTot", "hoi.metrics.Oinfo", "hoi.metrics.RSI", "hoi.metrics.RedundancyMMI", "hoi.metrics.RedundancyphiID", "hoi.metrics.Sinfo", "hoi.metrics.SynergyMMI", "hoi.metrics.SynergyphiID", "hoi.metrics.TC", "hoi.plot.plot_landscape", "hoi.simulation.simulate_hoi_gauss", "hoi.utils.digitize", "hoi.utils.get_nbest_mult", "hoi.utils.landscape", "hoi.utils.normalize", "List of classes and functions", "Examples", "Entropy and mutual information", "Comparison of entropy estimators for various distributions", "Comparison of entropy estimators for a multivariate normal", "Comparison of entropy estimators with high-dimensional data", "Comparison of mutual-information estimators", "Comparison of MI estimators with high-dimensional data", "Computation times", "Introduction to core information theoretical metrics", "Metrics of HOI", "Topological Information : conditioning on orders", "O-information and its derivatives for network behavior and encoding", "Redundancy-Synergy Index", "Integrated Information Decomposition", "Redundancy and Synergy MMI", "Computation times", "Miscellaneous", "Inspect and plot Higher-Order Interactions", "Computation times", "Quick introduction to jax", "Computation times", "Statistics : bootstrapping and permutations", "Bootstrapping and confidence interval", "Computation times", "Tutorials", "Machine-learning vs. Information theoretic approaches for HOI", "How to simulate redundancy and synergy", "Computation times", "Developer Documentation", "List of contributors", "Glossary", "HOI : High-Performance Estimation of Higher-Order Interactions", "Installation", "Jax: linear algebra backend", "Quickstart", "Computation times", "Theoretical background"], "titleterms": {"": [45, 70], "For": 53, "algebra": 67, "an": 36, "analysi": 68, "approach": [56, 59], "arrai": 67, "backend": 67, "background": 70, "behavior": [1, 45, 60, 70], "bibliographi": 70, "bootstrap": [34, 55, 56], "class": 33, "code": [45, 62], "combin": [5, 45, 46, 47, 48], "combinator": 0, "comparison": [36, 37, 38, 39, 40, 67], "compil": 53, "comput": [41, 49, 52, 54, 56, 57, 61, 67, 68, 69], "condit": 44, "confid": 56, "contribut": 62, "contributor": 63, "copi": 60, "core": [0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 42, 70], "correl": [45, 70], "cpu": 67, "data": [36, 38, 39, 40, 45, 51, 59, 68], "decod": 59, "decomposit": [47, 70], "definit": [36, 37, 38, 39, 40, 46, 47, 48], "depend": 66, "deriv": 45, "develop": 62, "digit": 29, "dimension": [38, 40, 67], "distribut": [36, 39, 40], "document": 62, "dtc": [15, 45], "dual": [45, 70], "dynam": [45, 60], "encod": [1, 45, 60, 70], "entropi": [0, 34, 35, 36, 37, 38, 42, 67, 70], "entropy_bin": 6, "entropy_gauss": 7, "entropy_gc": 8, "entropy_hist": 9, "entropy_kernel": 10, "entropy_knn": 11, "estim": [36, 37, 38, 39, 40, 51, 56, 65], "exampl": [12, 13, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 34], "exponenti": 36, "from": [36, 39, 40, 70], "function": [33, 53], "fund": 65, "get": [51, 65], "get_entropi": 12, "get_mi": 13, "get_nbest_mult": 30, "glossari": 64, "gpu": 67, "gradient": 70, "gradientoinfo": 16, "high": [38, 40, 65], "higher": [51, 56, 65, 67, 68, 70], "hoi": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 43, 51, 59, 62, 65], "how": 60, "index": [46, 70], "individu": 51, "inform": [0, 34, 35, 39, 42, 44, 45, 47, 56, 59, 70], "infotopo": 17, "infotot": 18, "inspect": [51, 68], "instal": [62, 66, 68], "integr": [47, 70], "interact": [44, 51, 65, 67, 68, 70], "interv": 56, "introduct": [42, 53], "involv": 65, "isol": 44, "its": 45, "jax": [53, 67], "jit": 53, "landscap": [31, 51], "larg": 67, "learn": 59, "licens": 65, "linear": 67, "list": [33, 63], "loop": 53, "machin": 59, "measur": [0, 70], "metric": [1, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 34, 42, 43], "mi": [39, 40, 70], "miscellan": [34, 50], "mmi": [48, 70], "modul": 53, "multi": 67, "multinorm": 40, "multiplet": [44, 51, 67], "multivari": [37, 45, 46, 48], "mutual": [0, 34, 35, 39, 42, 70], "network": [1, 45, 60, 70], "normal": [32, 36, 37, 39], "numpi": 53, "o": [44, 45, 56, 70], "oinfo": 19, "oper": 60, "order": [44, 51, 56, 65, 67, 68, 70], "other": 68, "pairwis": 70, "perform": [65, 67], "permut": [34, 55], "plot": [2, 27, 51, 56], "plot_landscap": 27, "postprocess": 4, "practic": 68, "prepare_for_it": 14, "preprocess": 4, "problem": 44, "pull": 62, "quick": 53, "quickstart": 68, "recommend": 68, "redund": [44, 45, 46, 47, 48, 56, 60, 70], "redundancymmi": 21, "redundancyphiid": 22, "request": 62, "result": [51, 68], "rsi": [20, 70], "sampl": [36, 39, 40], "simul": [3, 28, 44, 45, 46, 47, 48, 51, 59, 60, 68], "simulate_hoi_gauss": 28, "sinfo": 23, "softwar": 68, "spatial": 44, "split": 40, "spread": [44, 56], "statist": [34, 55], "sum": 60, "summari": 51, "synergi": [46, 47, 48, 56, 60, 70], "synergist": [44, 45, 60], "synergymmi": 24, "synergyphiid": 25, "target": 45, "tc": [26, 45], "theoret": [42, 59, 70], "time": [41, 49, 52, 54, 57, 61, 69], "topolog": [44, 70], "total": [45, 70], "tutori": [34, 58], "uniform": 36, "univari": [46, 48], "us": [12, 13, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 44, 45, 53, 56, 59, 62], "user": 66, "util": [4, 29, 30, 31, 32], "v": [59, 67], "variou": 36, "vector": 53, "vmap": 53, "x": 59, "y": 59}})
\ No newline at end of file
diff --git a/sg_execution_times.html b/sg_execution_times.html
index 9cf40530..75e491e8 100644
--- a/sg_execution_times.html
+++ b/sg_execution_times.html
@@ -404,7 +404,7 @@ <h1>Computation times</h1>
                   
   <section id="computation-times">
 <span id="sphx-glr-sg-execution-times"></span><h1>Computation times<a class="headerlink" href="#computation-times" title="Link to this heading">#</a></h1>
-<p><strong>02:55.695</strong> total execution time for 16 files <strong>from all galleries</strong>:</p>
+<p><strong>02:56.196</strong> total execution time for 16 files <strong>from all galleries</strong>:</p>
 <div class="docutils container">
 <style scoped>
 <link href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/5.3.0/css/bootstrap.min.css" rel="stylesheet" />
@@ -426,67 +426,67 @@ <h1>Computation times</h1>
 </thead>
 <tbody>
 <tr class="row-even"><td><p><a class="reference internal" href="auto_examples/it/plot_entropies_mvar.html#sphx-glr-auto-examples-it-plot-entropies-mvar-py"><span class="std std-ref">Comparison of entropy estimators for a multivariate normal</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/it/plot_entropies_mvar.py</span></code>)</p></td>
-<td><p>00:31.995</p></td>
+<td><p>00:32.313</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="auto_examples/it/plot_mi_high_dimensional.html#sphx-glr-auto-examples-it-plot-mi-high-dimensional-py"><span class="std std-ref">Comparison of MI estimators with high-dimensional data</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/it/plot_mi_high_dimensional.py</span></code>)</p></td>
-<td><p>00:29.919</p></td>
+<td><p>00:30.009</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="auto_examples/it/plot_entropy_high_dimensional.html#sphx-glr-auto-examples-it-plot-entropy-high-dimensional-py"><span class="std std-ref">Comparison of entropy estimators with high-dimensional data</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/it/plot_entropy_high_dimensional.py</span></code>)</p></td>
-<td><p>00:24.189</p></td>
+<td><p>00:24.213</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="auto_examples/it/plot_mi.html#sphx-glr-auto-examples-it-plot-mi-py"><span class="std std-ref">Comparison of mutual-information estimators</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/it/plot_mi.py</span></code>)</p></td>
-<td><p>00:20.547</p></td>
+<td><p>00:20.688</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="auto_examples/it/plot_entropies.html#sphx-glr-auto-examples-it-plot-entropies-py"><span class="std std-ref">Comparison of entropy estimators for various distributions</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/it/plot_entropies.py</span></code>)</p></td>
-<td><p>00:20.308</p></td>
+<td><p>00:20.392</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="auto_examples/statistics/plot_bootstrapping.html#sphx-glr-auto-examples-statistics-plot-bootstrapping-py"><span class="std std-ref">Bootstrapping and confidence interval</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/statistics/plot_bootstrapping.py</span></code>)</p></td>
-<td><p>00:15.886</p></td>
+<td><p>00:15.654</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="auto_examples/tutorials/plot_ml_vs_it.html#sphx-glr-auto-examples-tutorials-plot-ml-vs-it-py"><span class="std std-ref">Machine-learning vs. Information theoretic approaches for HOI</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/tutorials/plot_ml_vs_it.py</span></code>)</p></td>
-<td><p>00:09.287</p></td>
+<td><p>00:09.273</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="auto_examples/tutorials/plot_sim_red_syn.html#sphx-glr-auto-examples-tutorials-plot-sim-red-syn-py"><span class="std std-ref">How to simulate redundancy and synergy</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/tutorials/plot_sim_red_syn.py</span></code>)</p></td>
-<td><p>00:04.738</p></td>
+<td><p>00:04.654</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="auto_examples/metrics/plot_rsi.html#sphx-glr-auto-examples-metrics-plot-rsi-py"><span class="std std-ref">Redundancy-Synergy Index</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/metrics/plot_rsi.py</span></code>)</p></td>
-<td><p>00:03.981</p></td>
+<td><p>00:03.968</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="auto_examples/metrics/plot_oinfo.html#sphx-glr-auto-examples-metrics-plot-oinfo-py"><span class="std std-ref">O-information and its derivatives for network behavior and encoding</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/metrics/plot_oinfo.py</span></code>)</p></td>
-<td><p>00:03.764</p></td>
+<td><p>00:03.730</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="auto_examples/metrics/plot_infotopo.html#sphx-glr-auto-examples-metrics-plot-infotopo-py"><span class="std std-ref">Topological Information : conditioning on orders</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/metrics/plot_infotopo.py</span></code>)</p></td>
-<td><p>00:03.378</p></td>
+<td><p>00:03.402</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="auto_examples/metrics/plot_syn_red_mmi.html#sphx-glr-auto-examples-metrics-plot-syn-red-mmi-py"><span class="std std-ref">Redundancy and Synergy MMI</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/metrics/plot_syn_red_mmi.py</span></code>)</p></td>
-<td><p>00:03.054</p></td>
+<td><p>00:03.046</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="auto_examples/miscellaneous/plot_inspect_results.html#sphx-glr-auto-examples-miscellaneous-plot-inspect-results-py"><span class="std std-ref">Inspect and plot Higher-Order Interactions</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/miscellaneous/plot_inspect_results.py</span></code>)</p></td>
-<td><p>00:01.627</p></td>
+<td><p>00:01.767</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="auto_examples/metrics/plot_syn_phiID.html#sphx-glr-auto-examples-metrics-plot-syn-phiid-py"><span class="std std-ref">Integrated Information Decomposition</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/metrics/plot_syn_phiID.py</span></code>)</p></td>
-<td><p>00:01.541</p></td>
+<td><p>00:01.581</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="auto_examples/miscellaneous/tuto_jax.html#sphx-glr-auto-examples-miscellaneous-tuto-jax-py"><span class="std std-ref">Quick introduction to jax</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/miscellaneous/tuto_jax.py</span></code>)</p></td>
-<td><p>00:01.250</p></td>
+<td><p>00:01.274</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="auto_examples/it/tuto_core.html#sphx-glr-auto-examples-it-tuto-core-py"><span class="std std-ref">Introduction to core information theoretical metrics</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/it/tuto_core.py</span></code>)</p></td>
-<td><p>00:00.231</p></td>
+<td><p>00:00.232</p></td>
 <td><p>0.0</p></td>
 </tr>
 </tbody>