diff --git a/_downloads/071683bb9f5d321841ee9dd62eee27a4/plot_sim_red_syn.zip b/_downloads/071683bb9f5d321841ee9dd62eee27a4/plot_sim_red_syn.zip
index 33d5db45..c9bafbc7 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 4e8aeed1..da06151f 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 0921d46e..3fad1ac9 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 1a39bb93..f6215b7a 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 33d1c008..4fbe7ef1 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 96afb97e..e5d66919 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 83f93dea..d2fedfdd 100644
Binary files a/_downloads/4edd620b8310fd78193d26c454d1ca13/plot_rsi.zip and b/_downloads/4edd620b8310fd78193d26c454d1ca13/plot_rsi.zip differ
diff --git a/_downloads/58edfc8265b6af8f03b242ea4656b10f/plot_syn_phiID.zip b/_downloads/58edfc8265b6af8f03b242ea4656b10f/plot_syn_phiID.zip
index 3faa85ca..c4d20e62 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 78d37a72..e75dcb2b 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 2a61fb63..1c21243e 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 d2e4d8a6..5e441ba0 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 e4ccb216..fb3b4b11 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 80dfa9bd..657e6cdb 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/9b8182d6a0423d2c5a54190326bb52f0/plot_jax.zip b/_downloads/9b8182d6a0423d2c5a54190326bb52f0/plot_jax.zip
index 4d489eb8..3fb506b2 100644
Binary files a/_downloads/9b8182d6a0423d2c5a54190326bb52f0/plot_jax.zip and b/_downloads/9b8182d6a0423d2c5a54190326bb52f0/plot_jax.zip differ
diff --git a/_downloads/b4b212cbccfe9b262b7e665ad86bc92a/plot_tutorial_core.zip b/_downloads/b4b212cbccfe9b262b7e665ad86bc92a/plot_tutorial_core.zip
index 0c08030f..a5c037e1 100644
Binary files a/_downloads/b4b212cbccfe9b262b7e665ad86bc92a/plot_tutorial_core.zip and b/_downloads/b4b212cbccfe9b262b7e665ad86bc92a/plot_tutorial_core.zip differ
diff --git a/_downloads/cb54325e1a49091788b29a83388e5628/plot_mi.zip b/_downloads/cb54325e1a49091788b29a83388e5628/plot_mi.zip
index ba04c210..58134fbb 100644
Binary files a/_downloads/cb54325e1a49091788b29a83388e5628/plot_mi.zip and b/_downloads/cb54325e1a49091788b29a83388e5628/plot_mi.zip differ
diff --git a/_downloads/f599913a46208f71dc47a6311a232f10/plot_syn_red_mmi.zip b/_downloads/f599913a46208f71dc47a6311a232f10/plot_syn_red_mmi.zip
index 5fa74139..af8e72da 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 7b3a8a87..66e376d2 100644
Binary files a/_downloads/f97532cb8c6e95a143612bdc254c6548/plot_entropy_high_dimensional.zip and b/_downloads/f97532cb8c6e95a143612bdc254c6548/plot_entropy_high_dimensional.zip differ
diff --git a/_images/sphx_glr_plot_inspect_results_002.png b/_images/sphx_glr_plot_inspect_results_002.png
index 2c8a809d..2a80f77b 100644
Binary files a/_images/sphx_glr_plot_inspect_results_002.png and b/_images/sphx_glr_plot_inspect_results_002.png differ
diff --git a/_images/sphx_glr_plot_inspect_results_thumb.png b/_images/sphx_glr_plot_inspect_results_thumb.png
index 078bd68e..35bbff44 100644
Binary files a/_images/sphx_glr_plot_inspect_results_thumb.png and b/_images/sphx_glr_plot_inspect_results_thumb.png differ
diff --git a/auto_examples/it/plot_entropies.html b/auto_examples/it/plot_entropies.html
index 615dcdd2..753311f8 100644
--- a/auto_examples/it/plot_entropies.html
+++ b/auto_examples/it/plot_entropies.html
@@ -606,7 +606,7 @@ <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 17.244 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 17.157 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 8d0b3cee..97d2e2f6 100644
--- a/auto_examples/it/plot_entropies_mvar.html
+++ b/auto_examples/it/plot_entropies_mvar.html
@@ -581,7 +581,7 @@ <h2>Comparison of estimators<a class="headerlink" href="#comparison-of-estimator
 <span class="n">plot</span><span class="p">(</span><span class="n">h_x</span><span class="p">,</span> <span class="n">h_theoric</span><span class="p">,</span> <span class="n">n</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 24.671 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 24.547 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 4c446f13..99c94550 100644
--- a/auto_examples/it/plot_entropy_high_dimensional.html
+++ b/auto_examples/it/plot_entropy_high_dimensional.html
@@ -580,7 +580,7 @@ <h2>Entropy of data sampled from multinormal distribution<a class="headerlink" h
 <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> (22 minutes 57.337 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> (22 minutes 53.701 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 20762afc..da9017a7 100644
--- a/auto_examples/it/plot_mi.html
+++ b/auto_examples/it/plot_mi.html
@@ -564,7 +564,7 @@ <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 16.615 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 16.602 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 29b5c68c..deefe906 100644
--- a/auto_examples/it/plot_mi_high_dimensional.html
+++ b/auto_examples/it/plot_mi_high_dimensional.html
@@ -583,7 +583,7 @@ <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> (42 minutes 37.326 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> (42 minutes 39.388 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 5e95b153..a11a8e47 100644
--- a/auto_examples/it/sg_execution_times.html
+++ b/auto_examples/it/sg_execution_times.html
@@ -420,7 +420,7 @@ <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>66:33.424</strong> total execution time for 6 files <strong>from auto_examples/it</strong>:</p>
+<p><strong>66:31.624</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" />
@@ -442,23 +442,23 @@ <h1>Computation times</h1>
 </thead>
 <tbody>
 <tr class="row-even"><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>42:37.326</p></td>
+<td><p>42:39.388</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><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>22:57.337</p></td>
+<td><p>22:53.701</p></td>
 <td><p>0.0</p></td>
 </tr>
 <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>00:24.671</p></td>
+<td><p>00:24.547</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><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>00:17.244</p></td>
+<td><p>00:17.157</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><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>00:16.615</p></td>
+<td><p>00:16.602</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="plot_tutorial_core.html#sphx-glr-auto-examples-it-plot-tutorial-core-py"><span class="std std-ref">Introduction to core information theoretical metrics</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_tutorial_core.py</span></code>)</p></td>
diff --git a/auto_examples/metrics/plot_infotopo.html b/auto_examples/metrics/plot_infotopo.html
index a32a2a37..6e295d69 100644
--- a/auto_examples/metrics/plot_infotopo.html
+++ b/auto_examples/metrics/plot_infotopo.html
@@ -486,11 +486,11 @@ <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,    2.85it/s]
- 40%|████      | Oinfo (4):  2/5 [00:00&lt;00:00,    3.51it/s]
- 60%|██████    | Oinfo (5):  3/5 [00:01&lt;00:00,    2.83it/s]
- 80%|████████  | Oinfo (6):  4/5 [00:01&lt;00:00,    2.61it/s]
-100%|██████████| Oinfo (7):  5/5 [00:01&lt;00:00,    2.67it/s]
+ 20%|██        | Oinfo (3):  1/5 [00:00&lt;00:01,    2.89it/s]
+ 40%|████      | Oinfo (4):  2/5 [00:00&lt;00:00,    3.55it/s]
+ 60%|██████    | Oinfo (5):  3/5 [00:01&lt;00:00,    2.85it/s]
+ 80%|████████  | Oinfo (6):  4/5 [00:01&lt;00:00,    2.64it/s]
+100%|██████████| Oinfo (7):  5/5 [00:01&lt;00:00,    2.69it/s]
 </pre></div>
 </div>
 <p>Now we can plot the landscape. This landscape show the values of HOI for
@@ -543,17 +543,17 @@ <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,    8.47it/s]
- 29%|██▊       | Entropy H(2):  2/7 [00:00&lt;00:00,    8.27it/s]
- 43%|████▎     | Entropy H(3):  3/7 [00:00&lt;00:00,    8.27it/s]
- 57%|█████▋    | Entropy H(4):  4/7 [00:00&lt;00:00,    8.69it/s]
- 71%|███████▏  | Entropy H(5):  5/7 [00:00&lt;00:00,    8.96it/s]
- 86%|████████▌ | Entropy H(6):  6/7 [00:00&lt;00:00,    9.19it/s]
-100%|██████████| Entropy H(7):  7/7 [00:00&lt;00:00,    9.42it/s]
+ 14%|█▍        | Entropy H(1):  1/7 [00:00&lt;00:00,    8.54it/s]
+ 29%|██▊       | Entropy H(2):  2/7 [00:00&lt;00:00,    8.35it/s]
+ 43%|████▎     | Entropy H(3):  3/7 [00:00&lt;00:00,    8.42it/s]
+ 57%|█████▋    | Entropy H(4):  4/7 [00:00&lt;00:00,    8.83it/s]
+ 71%|███████▏  | Entropy H(5):  5/7 [00:00&lt;00:00,    9.11it/s]
+ 86%|████████▌ | Entropy H(6):  6/7 [00:00&lt;00:00,    9.26it/s]
+100%|██████████| Entropy H(7):  7/7 [00:00&lt;00:00,    9.50it/s]
 
 
   0%|          |  0/99 [00:00&lt;?,       ?it/s]
-100%|██████████| Mutual information:  99/99 [00:00&lt;00:00, 146778.40it/s]
+100%|██████████| Mutual information:  99/99 [00:00&lt;00:00, 152436.16it/s]
 </pre></div>
 </div>
 <p>Again, we can plot the landscape. This time, as we can see, there’s no more
@@ -587,7 +587,7 @@ <h2>Multiplet isolation using the Topological Information<a class="headerlink" h
 9     33      3 -0.098192     [3, 5, 6]
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.486 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.434 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 92a358ab..e6b766c5 100644
--- a/auto_examples/metrics/plot_oinfo.html
+++ b/auto_examples/metrics/plot_oinfo.html
@@ -512,7 +512,7 @@ <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,    4.13it/s]
+100%|██████████| TC (3):  1/1 [00:00&lt;00:00,    4.10it/s]
 
    index  order       hoi  multiplet
 0      0      3  0.914042  [0, 1, 2]
@@ -553,7 +553,7 @@ <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,    6.24it/s]
+100%|██████████| DTC (3):  1/1 [00:00&lt;00:00,    6.08it/s]
 
    index  order       hoi  multiplet
 0     19      3  0.909558  [3, 4, 5]
@@ -591,7 +591,7 @@ <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,    4.88it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.92it/s]
 
    index  order       hoi  multiplet
 0      0      3  0.195104  [0, 1, 2]
@@ -626,7 +626,7 @@ <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,    4.90it/s]
+100%|██████████| Sinfo (3):  1/1 [00:00&lt;00:00,    4.95it/s]
 
    index  order       hoi  multiplet
 0     19      3  1.644727  [3, 4, 5]
@@ -682,11 +682,11 @@ <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,    4.89it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.94it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.39it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.50it/s]
 
    index  order       hoi  multiplet
 0      0      3  0.349639  [0, 1, 2]
@@ -719,11 +719,11 @@ <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,    4.90it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.84it/s]
 
 
   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,    4.92it/s]
 
    index  order       hoi  multiplet
 0      6      3  0.001733  [0, 2, 5]
@@ -762,11 +762,11 @@ <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,    4.90it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.93it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.45it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.49it/s]
 
    index  order       hoi  multiplet
 0      0      3  0.405968  [0, 1, 2]
@@ -814,14 +814,14 @@ <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,    2.76it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    2.73it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.24it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.27it/s]
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.711 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.707 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 9eebeae7..aa76f024 100644
--- a/auto_examples/metrics/plot_rsi.html
+++ b/auto_examples/metrics/plot_rsi.html
@@ -495,9 +495,9 @@ <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,    2.25it/s]
- 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    2.92it/s]
-100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    3.13it/s]
+ 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    2.23it/s]
+ 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    2.87it/s]
+100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    3.09it/s]
 
    index  order       hoi  multiplet
 0      5      3  0.014083  [0, 2, 3]
@@ -539,8 +539,8 @@ <h2>Simulate multivariate redundancy<a class="headerlink" href="#simulate-multiv
 </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,    3.38it/s]
- 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.48it/s]
-100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.03it/s]
+ 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.49it/s]
+100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.04it/s]
 
    index  order       hoi  multiplet
 0     28      3  0.010094  [2, 4, 5]
@@ -574,9 +574,9 @@ <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,    3.98it/s]
- 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    5.22it/s]
-100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.84it/s]
+ 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    4.04it/s]
+ 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    5.29it/s]
+100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.92it/s]
 
    index  order       hoi  multiplet
 0     10      3  1.453753  [0, 3, 5]
@@ -605,9 +605,9 @@ <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,    3.64it/s]
- 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.82it/s]
-100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.40it/s]
+ 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    3.67it/s]
+ 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.86it/s]
+100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.45it/s]
 
    index  order       hoi  multiplet
 0     10      3  1.513817  [0, 3, 5]
@@ -652,9 +652,9 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 </pre></div>
 </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,    3.59it/s]
- 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.79it/s]
-100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.38it/s]
+ 33%|███▎      | RSI order 3:  1/3 [00:00&lt;00:00,    3.68it/s]
+ 67%|██████▋   | RSI order 4:  2/3 [00:00&lt;00:00,    4.87it/s]
+100%|██████████| RSI order 5:  3/3 [00:00&lt;00:00,    5.45it/s]
 
    index  order       hoi  multiplet
 0      0      3  1.488034  [0, 1, 2]
@@ -665,7 +665,7 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 5     31      3 -0.461383  [3, 4, 5]
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.920 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.908 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 54de956c..3e47cd34 100644
--- a/auto_examples/metrics/plot_syn_phiID.html
+++ b/auto_examples/metrics/plot_syn_phiID.html
@@ -502,7 +502,7 @@ <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,    2.31it/s]
+100%|██████████| SynPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    2.42it/s]
 
    index  order       hoi multiplet
 0      0      2  1.032673    [0, 1]
@@ -539,7 +539,7 @@ <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,    4.33it/s]
+100%|██████████| RedPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    4.52it/s]
 
    index  order       hoi multiplet
 0      0      2  1.926982    [0, 1]
@@ -590,7 +590,7 @@ <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,    3.81it/s]
+100%|██████████| SynPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    3.86it/s]
 
    index  order       hoi multiplet
 0      0      2  1.926982    [0, 1]
@@ -622,7 +622,7 @@ <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,    5.91it/s]
+100%|██████████| RedPhiIDMMI order 2:  1/1 [00:00&lt;00:00,    5.98it/s]
 
    index  order       hoi multiplet
 0      1      2  1.418695    [0, 2]
@@ -630,7 +630,7 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 2      0      2  0.844169    [0, 1]
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 1.574 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 1.492 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 6ca73ac1..d606f17c 100644
--- a/auto_examples/metrics/plot_syn_red_mmi.html
+++ b/auto_examples/metrics/plot_syn_red_mmi.html
@@ -501,8 +501,8 @@ <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,    7.88it/s]
-100%|██████████| RedMMI order 5:  3/3 [00:00&lt;00:00,   19.76it/s]
+ 33%|███▎      | RedMMI order 3:  1/3 [00:00&lt;00:00,    7.85it/s]
+100%|██████████| RedMMI order 5:  3/3 [00:00&lt;00:00,   19.98it/s]
 
    index  order       hoi  multiplet
 0     20      3  0.377251  [1, 3, 5]
@@ -540,7 +540,7 @@ <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,    7.48it/s]
+ 33%|███▎      | RedMMI order 3:  1/3 [00:00&lt;00:00,    7.53it/s]
 
    index  order       hoi  multiplet
 0     26      3  0.488635  [2, 3, 5]
@@ -578,9 +578,9 @@ <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,    3.90it/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,    3.95it/s]
+ 33%|███▎      | SynMMI order 3:  1/3 [00:00&lt;00:00,    3.95it/s]
+ 67%|██████▋   | SynMMI order 4:  2/3 [00:00&lt;00:00,    4.01it/s]
+100%|██████████| SynMMI order 5:  3/3 [00:00&lt;00:00,    4.03it/s]
 
    index  order       hoi  multiplet
 0     10      3  1.401695  [0, 3, 5]
@@ -606,9 +606,9 @@ <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,    3.70it/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]
+ 33%|███▎      | SynMMI order 3:  1/3 [00:00&lt;00:00,    3.73it/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,    3.65it/s]
 
    index  order       hoi  multiplet
 0     10      3  1.476156  [0, 3, 5]
@@ -651,9 +651,9 @@ <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,    3.83it/s]
- 67%|██████▋   | SynMMI order 4:  2/3 [00:00&lt;00:00,    3.70it/s]
-100%|██████████| SynMMI order 5:  3/3 [00:00&lt;00:00,    3.62it/s]
+ 33%|███▎      | SynMMI order 3:  1/3 [00:00&lt;00:00,    3.81it/s]
+ 67%|██████▋   | SynMMI order 4:  2/3 [00:00&lt;00:00,    3.71it/s]
+100%|██████████| SynMMI order 5:  3/3 [00:00&lt;00:00,    3.67it/s]
 
 
 Synergy results
@@ -664,7 +664,7 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 2      8      3  0.000437  [0, 2, 6]
 
   0%|          |  0/3 [00:00&lt;?,       ?it/s]
- 33%|███▎      | RedMMI order 3:  1/3 [00:00&lt;00:00,    7.37it/s]
+ 33%|███▎      | RedMMI order 3:  1/3 [00:00&lt;00:00,    7.46it/s]
 
 
 Redundancy results
@@ -701,7 +701,7 @@ <h2>Combining redundancy and synergy<a class="headerlink" href="#combining-redun
 <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"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>&lt;Axes: xlabel=&#39;Order&#39;, ylabel=&#39;Synergy MMI [Bits]&#39;&gt;
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 3.022 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 2.986 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 3991be89..aa651757 100644
--- a/auto_examples/metrics/sg_execution_times.html
+++ b/auto_examples/metrics/sg_execution_times.html
@@ -420,7 +420,7 @@ <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>00:15.714</strong> total execution time for 5 files <strong>from auto_examples/metrics</strong>:</p>
+<p><strong>00:15.528</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" />
@@ -442,23 +442,23 @@ <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>00:03.920</p></td>
+<td><p>00:03.908</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>00:03.711</p></td>
+<td><p>00:03.707</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>00:03.486</p></td>
+<td><p>00:03.434</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>00:03.022</p></td>
+<td><p>00:02.986</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>00:01.574</p></td>
+<td><p>00:01.492</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 cfb1c171..31e14b13 100644
--- a/auto_examples/miscellaneous/plot_inspect_results.html
+++ b/auto_examples/miscellaneous/plot_inspect_results.html
@@ -482,16 +482,16 @@ <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,    5.26it/s]
- 33%|███▎      | Entropy H(2):  2/6 [00:00&lt;00:00,    4.91it/s]
- 50%|█████     | Entropy H(3):  3/6 [00:00&lt;00:00,    5.49it/s]
- 67%|██████▋   | Entropy H(4):  4/6 [00:00&lt;00:00,    6.18it/s]
- 83%|████████▎ | Entropy H(5):  5/6 [00:00&lt;00:00,    6.58it/s]
-100%|██████████| Entropy H(6):  6/6 [00:00&lt;00:00,    6.89it/s]
+ 17%|█▋        | Entropy H(1):  1/6 [00:00&lt;00:01,    4.93it/s]
+ 33%|███▎      | Entropy H(2):  2/6 [00:00&lt;00:00,    4.70it/s]
+ 50%|█████     | Entropy H(3):  3/6 [00:00&lt;00:00,    5.26it/s]
+ 67%|██████▋   | Entropy H(4):  4/6 [00:00&lt;00:00,    5.93it/s]
+ 83%|████████▎ | Entropy H(5):  5/6 [00:00&lt;00:00,    6.33it/s]
+100%|██████████| Entropy H(6):  6/6 [00:00&lt;00:00,    6.66it/s]
 
 
   0%|          |  0/42 [00:00&lt;?,       ?it/s]
-100%|██████████| Mutual information:  42/42 [00:00&lt;00:00, 99078.05it/s]
+100%|██████████| Mutual information:  42/42 [00:00&lt;00:00, 109416.63it/s]
 </pre></div>
 </div>
 </section>
@@ -572,7 +572,7 @@ <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 1.672 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 1.725 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/plot_jax.html b/auto_examples/miscellaneous/plot_jax.html
index 889d18dd..9e6cf19c 100644
--- a/auto_examples/miscellaneous/plot_jax.html
+++ b/auto_examples/miscellaneous/plot_jax.html
@@ -537,8 +537,8 @@ <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: 0.5878607690001445 seconds
-Time taken by jitted function: 0.27657762299986643 seconds
+<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Time taken by pure NumPy function: 0.5857861679996859 seconds
+Time taken by jitted function: 0.2678242389993102 seconds
 </pre></div>
 </div>
 <p>if the function takes optional argument, you can use the <cite>static_argnums</cite>
@@ -638,7 +638,7 @@ <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 1.302 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 1.260 seconds)</p>
 <div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-miscellaneous-plot-jax-py">
 <div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
 <p><a class="reference download internal" download="" href="../../_downloads/e36c31b23961440d2ccaa0dc78d4c34e/plot_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">plot_jax.ipynb</span></code></a></p>
diff --git a/auto_examples/miscellaneous/sg_execution_times.html b/auto_examples/miscellaneous/sg_execution_times.html
index 3a9caa33..3a3e5573 100644
--- a/auto_examples/miscellaneous/sg_execution_times.html
+++ b/auto_examples/miscellaneous/sg_execution_times.html
@@ -420,7 +420,7 @@ <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>00:02.974</strong> total execution time for 2 files <strong>from auto_examples/miscellaneous</strong>:</p>
+<p><strong>00:02.985</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" />
@@ -442,11 +442,11 @@ <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>00:01.672</p></td>
+<td><p>00:01.725</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="plot_jax.html#sphx-glr-auto-examples-miscellaneous-plot-jax-py"><span class="std std-ref">Quick introduction to jax</span></a> (<code class="docutils literal notranslate"><span class="pre">plot_jax.py</span></code>)</p></td>
-<td><p>00:01.302</p></td>
+<td><p>00:01.260</p></td>
 <td><p>0.0</p></td>
 </tr>
 </tbody>
diff --git a/auto_examples/statistics/plot_bootstrapping.html b/auto_examples/statistics/plot_bootstrapping.html
index 7f168c9b..1e19a672 100644
--- a/auto_examples/statistics/plot_bootstrapping.html
+++ b/auto_examples/statistics/plot_bootstrapping.html
@@ -680,7 +680,7 @@ <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 15.385 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 15.292 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 d21ccf97..edd03999 100644
--- a/auto_examples/statistics/sg_execution_times.html
+++ b/auto_examples/statistics/sg_execution_times.html
@@ -420,7 +420,7 @@ <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>00:15.385</strong> total execution time for 1 file <strong>from auto_examples/statistics</strong>:</p>
+<p><strong>00:15.292</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" />
@@ -442,7 +442,7 @@ <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>00:15.385</p></td>
+<td><p>00:15.292</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 5ec98e48..d4c5af90 100644
--- a/auto_examples/tutorials/plot_ml_vs_it.html
+++ b/auto_examples/tutorials/plot_ml_vs_it.html
@@ -618,7 +618,7 @@ <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 9.005 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 8.897 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 9bfc0141..7d95aad8 100644
--- a/auto_examples/tutorials/plot_sim_red_syn.html
+++ b/auto_examples/tutorials/plot_sim_red_syn.html
@@ -506,7 +506,7 @@ <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,    1.58it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    1.62it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -536,7 +536,7 @@ <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,    6.24it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.18it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -568,7 +568,7 @@ <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,    6.28it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.15it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -599,7 +599,7 @@ <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,    6.20it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.21it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -647,7 +647,7 @@ <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,    2.50it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    2.52it/s]
 
 Text(0.5, 1.0, &#39;Dynamic HOI&#39;)
 </pre></div>
@@ -685,11 +685,11 @@ <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,    5.93it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.31it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.07it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.14it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -721,7 +721,7 @@ <h3>Simulating synergistic encoding<a class="headerlink" href="#simulating-syner
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.42it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.45it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -752,11 +752,11 @@ <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,    6.26it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.31it/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,    6.44it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -782,11 +782,11 @@ <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,    6.25it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.31it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.41it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    6.40it/s]
 </pre></div>
 </div>
 <p>Print HOI value</p>
@@ -836,16 +836,16 @@ <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,    4.65it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    4.66it/s]
 
 
   0%|          |  0/1 [00:00&lt;?,       ?it/s]
-100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.72it/s]
+100%|██████████| Oinfo (3):  1/1 [00:00&lt;00:00,    3.77it/s]
 
 Text(0.5, 1.0, &#39;Dynamic HOI&#39;)
 </pre></div>
 </div>
-<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 4.859 seconds)</p>
+<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 4.684 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 b794f124..c9e82710 100644
--- a/auto_examples/tutorials/sg_execution_times.html
+++ b/auto_examples/tutorials/sg_execution_times.html
@@ -420,7 +420,7 @@ <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>00:13.864</strong> total execution time for 2 files <strong>from auto_examples/tutorials</strong>:</p>
+<p><strong>00:13.582</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" />
@@ -442,11 +442,11 @@ <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>00:09.005</p></td>
+<td><p>00:08.897</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>00:04.859</p></td>
+<td><p>00:04.684</p></td>
 <td><p>0.0</p></td>
 </tr>
 </tbody>
diff --git a/searchindex.js b/searchindex.js
index a8514314..d44cd687 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"Bibliography": [[68, "bibliography"]], "Bootstrapping and confidence interval": [[55, null]], "CPU vs. GPU : Performance comparison": [[65, "cpu-vs-gpu-performance-comparison"]], "Combinatory": [[0, "combinatory"]], "Combining redundancy and synergy": [[45, "combining-redundancy-and-synergy"], [46, "combining-redundancy-and-synergy"], [47, "combining-redundancy-and-synergy"]], "Combining redundant and synergistic codings using a multivariate target": [[44, "combining-redundant-and-synergistic-codings-using-a-multivariate-target"]], "Comparison of MI estimators with high-dimensional data": [[39, null]], "Comparison of entropy estimators for a multivariate normal": [[36, null]], "Comparison of entropy estimators for various distributions": [[35, null]], "Comparison of entropy estimators with high-dimensional data": [[37, null]], "Comparison of estimators": [[36, "comparison-of-estimators"]], "Comparison of mutual-information estimators": [[38, null]], "Compiling functions using jit": [[51, "compiling-functions-using-jit"]], "Computation times": [[41, null], [48, null], [52, null], [53, null], [56, null], [60, null], [67, null]], "Compute Higher-Order Interactions": [[66, "compute-higher-order-interactions"]], "Compute bootstrap": [[55, "compute-bootstrap"]], "Computing Higher-Order Interactions on large multiplets": [[65, "computing-higher-order-interactions-on-large-multiplets"]], "Computing entropy on large multi-dimensional arrays": [[65, "computing-entropy-on-large-multi-dimensional-arrays"]], "Contributing code using pull requests": [[61, "contributing-code-using-pull-requests"]], "Contributing to HOI": [[61, "contributing-to-hoi"]], "Core information theoretic measures": [[68, "core-information-theoretic-measures"]], "Data simulation": [[44, "data-simulation"], [58, "data-simulation"]], "Decoding Y using X": [[58, "decoding-y-using-x"]], "Definition": [[45, "definition"], [46, "definition"], [47, "definition"]], "Definition of MI estimators": [[38, "definition-of-mi-estimators"], [39, "definition-of-mi-estimators"]], "Definition of entropy estimators": [[37, "definition-of-entropy-estimators"]], "Definition of estimators of entropy": [[35, "definition-of-estimators-of-entropy"], [36, "definition-of-estimators-of-entropy"]], "Dependencies": [[64, "dependencies"]], "Developer Documentation": [[61, null]], "Dual Total Correlation (DTC)": [[44, "dual-total-correlation-dtc"]], "Dual Total correlation": [[68, "dual-total-correlation"]], "Dynamic redundant and synergistic codings": [[44, "dynamic-redundant-and-synergistic-codings"]], "Entropy": [[40, "entropy"]], "Entropy and mutual information": [[33, "entropy-and-mutual-information"], [34, null]], "Entropy of data sampled from a uniform distribution": [[35, "entropy-of-data-sampled-from-a-uniform-distribution"]], "Entropy of data sampled from an exponential distribution": [[35, "entropy-of-data-sampled-from-an-exponential-distribution"]], "Entropy of data sampled from multinormal distribution": [[37, "entropy-of-data-sampled-from-multinormal-distribution"]], "Entropy of data sampled from normal distribution": [[35, "entropy-of-data-sampled-from-normal-distribution"]], "Estimate HOI": [[50, "estimate-hoi"]], "Estimation of the confidence interval using a bootstrapping approach": [[55, "estimation-of-the-confidence-interval-using-a-bootstrapping-approach"]], "Examples": [[33, null]], "Examples using hoi.core.get_entropy": [[11, "examples-using-hoi-core-get-entropy"]], "Examples using hoi.core.get_mi": [[12, "examples-using-hoi-core-get-mi"]], "Examples using hoi.metrics.DTC": [[14, "examples-using-hoi-metrics-dtc"]], "Examples using hoi.metrics.GradientOinfo": [[15, "examples-using-hoi-metrics-gradientoinfo"]], "Examples using hoi.metrics.InfoTopo": [[16, "examples-using-hoi-metrics-infotopo"]], "Examples using hoi.metrics.Oinfo": [[18, "examples-using-hoi-metrics-oinfo"]], "Examples using hoi.metrics.RSI": [[19, "examples-using-hoi-metrics-rsi"]], "Examples using hoi.metrics.RedundancyMMI": [[20, "examples-using-hoi-metrics-redundancymmi"]], "Examples using hoi.metrics.RedundancyphiID": [[21, "examples-using-hoi-metrics-redundancyphiid"]], "Examples using hoi.metrics.Sinfo": [[22, "examples-using-hoi-metrics-sinfo"]], "Examples using hoi.metrics.SynergyMMI": [[23, "examples-using-hoi-metrics-synergymmi"]], "Examples using hoi.metrics.SynergyphiID": [[24, "examples-using-hoi-metrics-synergyphiid"]], "Examples using hoi.metrics.TC": [[25, "examples-using-hoi-metrics-tc"]], "Examples using hoi.plot.plot_landscape": [[26, "examples-using-hoi-plot-plot-landscape"]], "Examples using hoi.simulation.simulate_hoi_gauss": [[27, "examples-using-hoi-simulation-simulate-hoi-gauss"]], "Examples using hoi.utils.digitize": [[28, "examples-using-hoi-utils-digitize"]], "Examples using hoi.utils.get_nbest_mult": [[29, "examples-using-hoi-utils-get-nbest-mult"]], "For loops with jax": [[51, "for-loops-with-jax"]], "From pairwise to higher-order interactions": [[68, "from-pairwise-to-higher-order-interactions"]], "Get a summary of the results": [[50, "get-a-summary-of-the-results"]], "Glossary": [[62, null]], "Gradient of O-information": [[68, "gradient-of-o-information"]], "HOI : High-Performance Estimation of Higher-Order Interactions": [[63, null]], "How to simulate redundancy and synergy": [[59, null]], "Inspect and plot Higher-Order Interactions": [[50, null]], "Inspect the results": [[66, "inspect-the-results"]], "Installation": [[64, null], [66, "installation"]], "Installation for developers": [[61, "installation-for-developers"]], "Integrated Information Decomposition": [[46, null]], "Introduction to core information theoretical metrics": [[40, null]], "Jax.numpy module": [[51, "jax-numpy-module"]], "Jax: linear algebra backend": [[65, null]], "Landscape plot": [[50, "landscape-plot"]], "List of classes and functions": [[32, null]], "MI of data sampled from normal distribution": [[38, "mi-of-data-sampled-from-normal-distribution"]], "MI of data sampled from splitted multinormal distribution": [[39, "mi-of-data-sampled-from-splitted-multinormal-distribution"]], "Machine-learning vs. Information theoretic approaches for HOI": [[58, null]], "Measures of Entropy": [[0, "measures-of-entropy"]], "Measures of Mutual Information": [[0, "measures-of-mutual-information"]], "Measuring Entropy": [[68, "measuring-entropy"]], "Measuring Mutual Information (MI)": [[68, "measuring-mutual-information-mi"]], "Metrics of HOI": [[33, "metrics-of-hoi"], [42, null]], "Miscellaneous": [[33, "miscellaneous"], [49, null]], "Multiplet isolation using the Topological Information": [[43, "multiplet-isolation-using-the-topological-information"]], "Mutual information": [[40, "mutual-information"]], "Network behavior": [[1, "network-behavior"], [68, "network-behavior"]], "Network encoding": [[1, "network-encoding"], [68, "network-encoding"]], "O-information": [[44, "o-information"], [68, "o-information"]], "O-information : Redundancy and synergy spread to higher orders": [[55, "o-information-redundancy-and-synergy-spread-to-higher-orders"]], "O-information and its derivatives for network behavior and encoding": [[44, null]], "O-information for network behavior": [[44, "o-information-for-network-behavior"]], "O-information for network encoding": [[44, "o-information-for-network-encoding"]], "Plot the O-information with the confidence interval": [[55, "plot-the-o-information-with-the-confidence-interval"]], "Plotting individual multiplets": [[50, "plotting-individual-multiplets"]], "Postprocessing": [[4, "postprocessing"]], "Practical recommendations": [[66, "practical-recommendations"]], "Preprocessing": [[4, "preprocessing"]], "Quick introduction to jax": [[51, null]], "Quickstart": [[66, null]], "Redundancy and Synergy MMI": [[47, null]], "Redundancy-Synergy Index": [[45, null]], "Redundancy-Synergy index (RSI)": [[68, "redundancy-synergy-index-rsi"]], "Redundant and synergistic behavior": [[59, "redundant-and-synergistic-behavior"]], "Redundant and synergistic encoding": [[59, "redundant-and-synergistic-encoding"]], "S information": [[68, "s-information"]], "S-information": [[44, "s-information"]], "Simulate data": [[50, "simulate-data"], [66, "simulate-data"]], "Simulate multivariate redundancy": [[45, "simulate-multivariate-redundancy"], [47, "simulate-multivariate-redundancy"]], "Simulate redundancy": [[46, "simulate-redundancy"]], "Simulate redundant and synergistic interactions": [[43, "simulate-redundant-and-synergistic-interactions"]], "Simulate synergy": [[46, "simulate-synergy"]], "Simulate univariate and multivariate synergy": [[45, "simulate-univariate-and-multivariate-synergy"], [47, "simulate-univariate-and-multivariate-synergy"]], "Simulate univariate redundancy": [[45, "simulate-univariate-redundancy"], [47, "simulate-univariate-redundancy"]], "Simulating dynamic redundancy and synergy": [[59, "simulating-dynamic-redundancy-and-synergy"]], "Simulating dynamic redundant and synergistic encoding": [[59, "simulating-dynamic-redundant-and-synergistic-encoding"]], "Simulating redundant behavior": [[59, "simulating-redundant-behavior"]], "Simulating redundant behavior by copy operator": [[59, "simulating-redundant-behavior-by-copy-operator"]], "Simulating redundant encoding": [[44, "simulating-redundant-encoding"], [59, "simulating-redundant-encoding"]], "Simulating redundant encoding by copy operation": [[59, "simulating-redundant-encoding-by-copy-operation"]], "Simulating synergistic behavior": [[59, "simulating-synergistic-behavior"]], "Simulating synergistic behavior by sum operation": [[59, "simulating-synergistic-behavior-by-sum-operation"]], "Simulating synergistic encoding": [[44, "simulating-synergistic-encoding"], [59, "simulating-synergistic-encoding"]], "Simulating synergistic encoding by sum operation": [[59, "simulating-synergistic-encoding-by-sum-operation"]], "Spatial spreading : the problem with the O-information": [[43, "spatial-spreading-the-problem-with-the-o-information"]], "Statistics : bootstrapping and permutations": [[33, "statistics-bootstrapping-and-permutations"], [54, null]], "Synergy and redundancy (MMI)": [[68, "synergy-and-redundancy-mmi"]], "Synergy and redundancy integraed Information Decomposition (MMI)": [[68, "synergy-and-redundancy-integraed-information-decomposition-mmi"]], "Theoretical background": [[68, null]], "Topological Information : conditioning on orders": [[43, null]], "Topological information": [[68, "topological-information"]], "Total Correlation (TC)": [[44, "total-correlation-tc"]], "Total correlation": [[68, "total-correlation"]], "Tutorials": [[33, "tutorials"], [57, null]], "User installation": [[64, "user-installation"]], "Using information-theoretic approaches": [[58, "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_kernel": [[9, null]], "hoi.core.entropy_knn": [[10, null]], "hoi.core.get_entropy": [[11, null]], "hoi.core.get_mi": [[12, null]], "hoi.core.prepare_for_it": [[13, null]], "hoi.metrics": [[1, null]], "hoi.metrics.DTC": [[14, null]], "hoi.metrics.GradientOinfo": [[15, null]], "hoi.metrics.InfoTopo": [[16, null]], "hoi.metrics.InfoTot": [[17, null]], "hoi.metrics.Oinfo": [[18, null]], "hoi.metrics.RSI": [[19, null]], "hoi.metrics.RedundancyMMI": [[20, null]], "hoi.metrics.RedundancyphiID": [[21, null]], "hoi.metrics.Sinfo": [[22, null]], "hoi.metrics.SynergyMMI": [[23, null]], "hoi.metrics.SynergyphiID": [[24, null]], "hoi.metrics.TC": [[25, null]], "hoi.plot": [[2, null]], "hoi.plot.plot_landscape": [[26, null]], "hoi.simulation": [[3, null]], "hoi.simulation.simulate_hoi_gauss": [[27, null]], "hoi.utils": [[4, null]], "hoi.utils.digitize": [[28, null]], "hoi.utils.get_nbest_mult": [[29, null]], "hoi.utils.landscape": [[30, null]], "hoi.utils.normalize": [[31, null]], "vmap : vectorize a function": [[51, "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_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/plot_tutorial_core", "auto_examples/it/sg_execution_times", "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/plot_jax", "auto_examples/miscellaneous/sg_execution_times", "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", "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_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/plot_tutorial_core.rst", "auto_examples/it/sg_execution_times.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/plot_jax.rst", "auto_examples/miscellaneous/sg_execution_times.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", "glossary.rst", "index.rst", "install.rst", "jax.rst", "quickstart.rst", "sg_execution_times.rst", "theory.rst"], "indexentries": {"__iter__() (hoi.metrics.dtc method)": [[14, "hoi.metrics.DTC.__iter__", false]], "__iter__() (hoi.metrics.gradientoinfo method)": [[15, "hoi.metrics.GradientOinfo.__iter__", false]], "__iter__() (hoi.metrics.infotopo method)": [[16, "hoi.metrics.InfoTopo.__iter__", false]], "__iter__() (hoi.metrics.infotot method)": [[17, "hoi.metrics.InfoTot.__iter__", false]], "__iter__() (hoi.metrics.oinfo method)": [[18, "hoi.metrics.Oinfo.__iter__", false]], "__iter__() (hoi.metrics.redundancymmi method)": [[20, "hoi.metrics.RedundancyMMI.__iter__", false]], "__iter__() (hoi.metrics.redundancyphiid method)": [[21, "hoi.metrics.RedundancyphiID.__iter__", false]], "__iter__() (hoi.metrics.rsi method)": [[19, "hoi.metrics.RSI.__iter__", false]], "__iter__() (hoi.metrics.sinfo method)": [[22, "hoi.metrics.Sinfo.__iter__", false]], "__iter__() (hoi.metrics.synergymmi method)": [[23, "hoi.metrics.SynergyMMI.__iter__", false]], "__iter__() (hoi.metrics.synergyphiid method)": [[24, "hoi.metrics.SynergyphiID.__iter__", false]], "__iter__() (hoi.metrics.tc method)": [[25, "hoi.metrics.TC.__iter__", false]], "combinations() (in module hoi.core)": [[5, "hoi.core.combinations", false]], "compute_entropies() (hoi.metrics.dtc method)": [[14, "hoi.metrics.DTC.compute_entropies", false]], "compute_entropies() (hoi.metrics.gradientoinfo method)": [[15, "hoi.metrics.GradientOinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.infotopo method)": [[16, "hoi.metrics.InfoTopo.compute_entropies", false]], "compute_entropies() (hoi.metrics.infotot method)": [[17, "hoi.metrics.InfoTot.compute_entropies", false]], "compute_entropies() (hoi.metrics.oinfo method)": [[18, "hoi.metrics.Oinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.redundancymmi method)": [[20, "hoi.metrics.RedundancyMMI.compute_entropies", false]], "compute_entropies() (hoi.metrics.redundancyphiid method)": [[21, "hoi.metrics.RedundancyphiID.compute_entropies", false]], "compute_entropies() (hoi.metrics.rsi method)": [[19, "hoi.metrics.RSI.compute_entropies", false]], "compute_entropies() (hoi.metrics.sinfo method)": [[22, "hoi.metrics.Sinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.synergymmi method)": [[23, "hoi.metrics.SynergyMMI.compute_entropies", false]], "compute_entropies() (hoi.metrics.synergyphiid method)": [[24, "hoi.metrics.SynergyphiID.compute_entropies", false]], "compute_entropies() (hoi.metrics.tc method)": [[25, "hoi.metrics.TC.compute_entropies", false]], "digitize() (in module hoi.utils)": [[28, "hoi.utils.digitize", false]], "dtc (class in hoi.metrics)": [[14, "hoi.metrics.DTC", false]], "entropies (hoi.metrics.dtc property)": [[14, "hoi.metrics.DTC.entropies", false]], "entropies (hoi.metrics.gradientoinfo property)": [[15, "hoi.metrics.GradientOinfo.entropies", false]], "entropies (hoi.metrics.infotopo property)": [[16, "hoi.metrics.InfoTopo.entropies", false]], "entropies (hoi.metrics.infotot property)": [[17, "hoi.metrics.InfoTot.entropies", false]], "entropies (hoi.metrics.oinfo property)": [[18, "hoi.metrics.Oinfo.entropies", false]], "entropies (hoi.metrics.redundancymmi property)": [[20, "hoi.metrics.RedundancyMMI.entropies", false]], "entropies (hoi.metrics.redundancyphiid property)": [[21, "hoi.metrics.RedundancyphiID.entropies", false]], "entropies (hoi.metrics.rsi property)": [[19, "hoi.metrics.RSI.entropies", false]], "entropies (hoi.metrics.sinfo property)": [[22, "hoi.metrics.Sinfo.entropies", false]], "entropies (hoi.metrics.synergymmi property)": [[23, "hoi.metrics.SynergyMMI.entropies", false]], "entropies (hoi.metrics.synergyphiid property)": [[24, "hoi.metrics.SynergyphiID.entropies", false]], "entropies (hoi.metrics.tc property)": [[25, "hoi.metrics.TC.entropies", false]], "entropy": [[62, "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_kernel() (in module hoi.core)": [[9, "hoi.core.entropy_kernel", false]], "entropy_knn() (in module hoi.core)": [[10, "hoi.core.entropy_knn", false]], "fit() (hoi.metrics.dtc method)": [[14, "hoi.metrics.DTC.fit", false]], "fit() (hoi.metrics.gradientoinfo method)": [[15, "hoi.metrics.GradientOinfo.fit", false]], "fit() (hoi.metrics.infotopo method)": [[16, "hoi.metrics.InfoTopo.fit", false]], "fit() (hoi.metrics.infotot method)": [[17, "hoi.metrics.InfoTot.fit", false]], "fit() (hoi.metrics.oinfo method)": [[18, "hoi.metrics.Oinfo.fit", false]], "fit() (hoi.metrics.redundancymmi method)": [[20, "hoi.metrics.RedundancyMMI.fit", false]], "fit() (hoi.metrics.redundancyphiid method)": [[21, "hoi.metrics.RedundancyphiID.fit", false]], "fit() (hoi.metrics.rsi method)": [[19, "hoi.metrics.RSI.fit", false]], "fit() (hoi.metrics.sinfo method)": [[22, "hoi.metrics.Sinfo.fit", false]], "fit() (hoi.metrics.synergymmi method)": [[23, "hoi.metrics.SynergyMMI.fit", false]], "fit() (hoi.metrics.synergyphiid method)": [[24, "hoi.metrics.SynergyphiID.fit", false]], "fit() (hoi.metrics.tc method)": [[25, "hoi.metrics.TC.fit", false]], "get_combinations() (hoi.metrics.dtc method)": [[14, "hoi.metrics.DTC.get_combinations", false]], "get_combinations() (hoi.metrics.gradientoinfo method)": [[15, "hoi.metrics.GradientOinfo.get_combinations", false]], "get_combinations() (hoi.metrics.infotopo method)": [[16, "hoi.metrics.InfoTopo.get_combinations", false]], "get_combinations() (hoi.metrics.infotot method)": [[17, "hoi.metrics.InfoTot.get_combinations", false]], "get_combinations() (hoi.metrics.oinfo method)": [[18, "hoi.metrics.Oinfo.get_combinations", false]], "get_combinations() (hoi.metrics.redundancymmi method)": [[20, "hoi.metrics.RedundancyMMI.get_combinations", false]], "get_combinations() (hoi.metrics.redundancyphiid method)": [[21, "hoi.metrics.RedundancyphiID.get_combinations", false]], "get_combinations() (hoi.metrics.rsi method)": [[19, "hoi.metrics.RSI.get_combinations", false]], "get_combinations() (hoi.metrics.sinfo method)": [[22, "hoi.metrics.Sinfo.get_combinations", false]], "get_combinations() (hoi.metrics.synergymmi method)": [[23, "hoi.metrics.SynergyMMI.get_combinations", false]], "get_combinations() (hoi.metrics.synergyphiid method)": [[24, "hoi.metrics.SynergyphiID.get_combinations", false]], "get_combinations() (hoi.metrics.tc method)": [[25, "hoi.metrics.TC.get_combinations", false]], "get_entropy() (in module hoi.core)": [[11, "hoi.core.get_entropy", false]], "get_mi() (in module hoi.core)": [[12, "hoi.core.get_mi", false]], "get_nbest_mult() (in module hoi.utils)": [[29, "hoi.utils.get_nbest_mult", false]], "gradientoinfo (class in hoi.metrics)": [[15, "hoi.metrics.GradientOinfo", false]], "higher order interactions": [[62, "term-Higher-Order-Interactions", true]], "hoi.metrics": [[1, "module-hoi.metrics", false]], "information theory": [[62, "term-Information-Theory", true]], "infotopo (class in hoi.metrics)": [[16, "hoi.metrics.InfoTopo", false]], "infotot (class in hoi.metrics)": [[17, "hoi.metrics.InfoTot", false]], "landscape() (in module hoi.utils)": [[30, "hoi.utils.landscape", false]], "module": [[1, "module-hoi.metrics", false]], "multiplets (hoi.metrics.dtc property)": [[14, "hoi.metrics.DTC.multiplets", false]], "multiplets (hoi.metrics.gradientoinfo property)": [[15, "hoi.metrics.GradientOinfo.multiplets", false]], "multiplets (hoi.metrics.infotopo property)": [[16, "hoi.metrics.InfoTopo.multiplets", false]], "multiplets (hoi.metrics.infotot property)": [[17, "hoi.metrics.InfoTot.multiplets", false]], "multiplets (hoi.metrics.oinfo property)": [[18, "hoi.metrics.Oinfo.multiplets", false]], "multiplets (hoi.metrics.redundancymmi property)": [[20, "hoi.metrics.RedundancyMMI.multiplets", false]], "multiplets (hoi.metrics.redundancyphiid property)": [[21, "hoi.metrics.RedundancyphiID.multiplets", false]], "multiplets (hoi.metrics.rsi property)": [[19, "hoi.metrics.RSI.multiplets", false]], "multiplets (hoi.metrics.sinfo property)": [[22, "hoi.metrics.Sinfo.multiplets", false]], "multiplets (hoi.metrics.synergymmi property)": [[23, "hoi.metrics.SynergyMMI.multiplets", false]], "multiplets (hoi.metrics.synergyphiid property)": [[24, "hoi.metrics.SynergyphiID.multiplets", false]], "multiplets (hoi.metrics.tc property)": [[25, "hoi.metrics.TC.multiplets", false]], "mutual information": [[62, "term-Mutual-Information", true]], "network behavior": [[62, "term-Network-behavior", true]], "network encoding": [[62, "term-Network-encoding", true]], "normalize() (in module hoi.utils)": [[31, "hoi.utils.normalize", false]], "oinfo (class in hoi.metrics)": [[18, "hoi.metrics.Oinfo", false]], "order (hoi.metrics.dtc property)": [[14, "hoi.metrics.DTC.order", false]], "order (hoi.metrics.gradientoinfo property)": [[15, "hoi.metrics.GradientOinfo.order", false]], "order (hoi.metrics.infotopo property)": [[16, "hoi.metrics.InfoTopo.order", false]], "order (hoi.metrics.infotot property)": [[17, "hoi.metrics.InfoTot.order", false]], "order (hoi.metrics.oinfo property)": [[18, "hoi.metrics.Oinfo.order", false]], "order (hoi.metrics.redundancymmi property)": [[20, "hoi.metrics.RedundancyMMI.order", false]], "order (hoi.metrics.redundancyphiid property)": [[21, "hoi.metrics.RedundancyphiID.order", false]], "order (hoi.metrics.rsi property)": [[19, "hoi.metrics.RSI.order", false]], "order (hoi.metrics.sinfo property)": [[22, "hoi.metrics.Sinfo.order", false]], "order (hoi.metrics.synergymmi property)": [[23, "hoi.metrics.SynergyMMI.order", false]], "order (hoi.metrics.synergyphiid property)": [[24, "hoi.metrics.SynergyphiID.order", false]], "order (hoi.metrics.tc property)": [[25, "hoi.metrics.TC.order", false]], "partial information decomposition": [[62, "term-Partial-Information-Decomposition", true]], "plot_landscape() (in module hoi.plot)": [[26, "hoi.plot.plot_landscape", false]], "prepare_for_it() (in module hoi.core)": [[13, "hoi.core.prepare_for_it", false]], "redundancy": [[62, "term-Redundancy", true]], "redundancymmi (class in hoi.metrics)": [[20, "hoi.metrics.RedundancyMMI", false]], "redundancyphiid (class in hoi.metrics)": [[21, "hoi.metrics.RedundancyphiID", false]], "rsi (class in hoi.metrics)": [[19, "hoi.metrics.RSI", false]], "simulate_hoi_gauss() (in module hoi.simulation)": [[27, "hoi.simulation.simulate_hoi_gauss", false]], "sinfo (class in hoi.metrics)": [[22, "hoi.metrics.Sinfo", false]], "synergy": [[62, "term-Synergy", true]], "synergymmi (class in hoi.metrics)": [[23, "hoi.metrics.SynergyMMI", false]], "synergyphiid (class in hoi.metrics)": [[24, "hoi.metrics.SynergyphiID", false]], "tc (class in hoi.metrics)": [[25, "hoi.metrics.TC", false]], "undersampling (hoi.metrics.dtc property)": [[14, "hoi.metrics.DTC.undersampling", false]], "undersampling (hoi.metrics.gradientoinfo property)": [[15, "hoi.metrics.GradientOinfo.undersampling", false]], "undersampling (hoi.metrics.infotopo property)": [[16, "hoi.metrics.InfoTopo.undersampling", false]], "undersampling (hoi.metrics.infotot property)": [[17, "hoi.metrics.InfoTot.undersampling", false]], "undersampling (hoi.metrics.oinfo property)": [[18, "hoi.metrics.Oinfo.undersampling", false]], "undersampling (hoi.metrics.redundancymmi property)": [[20, "hoi.metrics.RedundancyMMI.undersampling", false]], "undersampling (hoi.metrics.redundancyphiid property)": [[21, "hoi.metrics.RedundancyphiID.undersampling", false]], "undersampling (hoi.metrics.rsi property)": [[19, "hoi.metrics.RSI.undersampling", false]], "undersampling (hoi.metrics.sinfo property)": [[22, "hoi.metrics.Sinfo.undersampling", false]], "undersampling (hoi.metrics.synergymmi property)": [[23, "hoi.metrics.SynergyMMI.undersampling", false]], "undersampling (hoi.metrics.synergyphiid property)": [[24, "hoi.metrics.SynergyphiID.undersampling", false]], "undersampling (hoi.metrics.tc property)": [[25, "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_kernel"], [10, 0, 1, "", "entropy_knn"], [11, 0, 1, "", "get_entropy"], [12, 0, 1, "", "get_mi"], [13, 0, 1, "", "prepare_for_it"]], "hoi.metrics": [[14, 2, 1, "", "DTC"], [15, 2, 1, "", "GradientOinfo"], [16, 2, 1, "", "InfoTopo"], [17, 2, 1, "", "InfoTot"], [18, 2, 1, "", "Oinfo"], [19, 2, 1, "", "RSI"], [20, 2, 1, "", "RedundancyMMI"], [21, 2, 1, "", "RedundancyphiID"], [22, 2, 1, "", "Sinfo"], [23, 2, 1, "", "SynergyMMI"], [24, 2, 1, "", "SynergyphiID"], [25, 2, 1, "", "TC"]], "hoi.metrics.DTC": [[14, 3, 1, "", "__iter__"], [14, 3, 1, "", "compute_entropies"], [14, 4, 1, "", "entropies"], [14, 3, 1, "", "fit"], [14, 3, 1, "", "get_combinations"], [14, 4, 1, "", "multiplets"], [14, 4, 1, "", "order"], [14, 4, 1, "", "undersampling"]], "hoi.metrics.GradientOinfo": [[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.InfoTopo": [[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.InfoTot": [[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.Oinfo": [[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.RSI": [[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.RedundancyMMI": [[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.RedundancyphiID": [[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.Sinfo": [[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.SynergyMMI": [[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.SynergyphiID": [[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.TC": [[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.plot": [[26, 0, 1, "", "plot_landscape"]], "hoi.simulation": [[27, 0, 1, "", "simulate_hoi_gauss"]], "hoi.utils": [[28, 0, 1, "", "digitize"], [29, 0, 1, "", "get_nbest_mult"], [30, 0, 1, "", "landscape"], [31, 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": {"": [17, 19, 22, 35, 36, 37, 38, 39, 40, 43, 45, 46, 47, 50, 51, 55, 58, 59, 61, 64, 65], "0": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 31, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 65, 67, 68], "00": [40, 41, 43, 44, 45, 46, 47, 48, 50, 52, 53, 56, 59, 60, 67], "000": 53, "000010": 44, "000020": 44, "000216": 55, "000244": 55, "000275": 44, "000279": 44, "000437": 47, "000492": 44, "000500": 44, "000514": 47, "000553": [44, 47], "000677": 44, "000750": 44, "000798": 43, "000956": 55, "000992": 44, "001097": 43, "001109": 44, "001119": 44, "001132": 50, "001365": 44, "001399": 50, "001470": 43, "001529": 44, "001593": 50, "001671": 50, "001686": 44, "001733": 44, "001762": 50, "001798": 43, "001949": 43, "001978": 44, "001982": 44, "002075": 44, "002183": 45, "002257": 47, "002429": 44, "002511": 50, "002733": 45, "002877": 45, "003223": 45, "003272": 45, "003286": 44, "003959": 44, "004202": 50, "004351": 50, "005": [58, 60, 67], "006850": 45, "008015": 45, "008041": 45, "008269": 45, "008682": 47, "01": [43, 48, 52, 67], "010041": 46, "010094": 45, "012916": 47, "013025": 68, "014083": 45, "016348": 46, "017187": 45, "017516": 46, "02": 52, "022": [47, 48, 67], "03": [48, 67], "032305": 68, "032673": 46, "03it": 45, "04": [60, 67], "05": 46, "051622": 43, "052802": 68, "055452": 43, "05it": 50, "066138": 68, "07140": 68, "079220": 43, "07it": 59, "087119": 44, "088506": 44, "09": [60, 67], "098192": 43, "1": [5, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 31, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 56, 58, 59, 61, 64, 65, 68], "10": [19, 35, 36, 37, 38, 39, 44, 45, 47, 50, 51, 55, 65, 68], "100": [30, 37, 43, 44, 45, 46, 47, 50, 58, 59, 65, 68], "1000": [27, 35, 36, 38, 39, 40, 43, 44, 51, 55, 59, 65, 66], "10000": [37, 39], "100000": 51, "1004": 68, "106": 68, "107": 35, "1093": 68, "1098": 68, "1099": 68, "10e2": 65, "11": [44, 47, 50, 55, 65, 68], "1103": 68, "1134": 68, "119": 68, "12": [19, 40, 44, 45, 51, 55, 58, 68], "12482": 68, "13": [44, 45, 50, 55, 60, 65, 68], "1315": 68, "13186": 68, "1321": 68, "133": 68, "13637": 68, "13it": [44, 45], "14": [22, 36, 43, 45, 47, 50, 55, 68], "140": 68, "146778": 43, "15": [35, 44, 45, 48, 55, 56, 65, 67, 68], "152": 68, "1541": 68, "156": 68, "1573": 68, "159": 68, "16": [38, 41, 44, 45, 55, 67, 68], "17": [24, 35, 41, 44, 45, 50, 55, 67, 68], "17019176483154297": 59, "172979": 47, "174389": 44, "177": 68, "178324": 43, "179585": 43, "179876": 43, "179893": 43, "18": [44, 45, 47, 51, 55, 62, 68], "180534": 43, "180660": 43, "18it": 50, "19": [21, 44, 47, 50, 55, 68], "190": [46, 68], "192595": 44, "1940": 62, "1948": 68, "195104": 44, "195410": 45, "195496": 45, "195716": 44, "195971": 44, "1960": [25, 68], "196016": 44, "196290": 50, "1963": 68, "1975": 68, "1978": [14, 68], "1986": 68, "1995": 68, "1998": 68, "1999": 68, "19it": 43, "2": [6, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 52, 55, 58, 59, 60, 63, 65, 68], "20": [35, 36, 38, 40, 43, 44, 45, 46, 47, 51, 55, 59, 68], "200": [45, 46, 47, 50, 55], "2001": [19, 68], "2003": 68, "2004": [10, 68], "2005": 68, "2009": 68, "2010": 68, "2011": [22, 68], "2014": [19, 68], "2015": 68, "2017": 68, "2018": [16, 68], "2019": [16, 18, 43, 44, 68], "2020": 68, "2021": [21, 68], "20210246": 68, "2022": [24, 68], "2023": [15, 39, 68], "2024": 68, "20it": 59, "20th": 68, "21": [45, 67, 68], "2109": 68, "216": 51, "217146": 55, "217600": 55, "22": [37, 41, 45, 62, 64, 67, 68], "22015380859375": 59, "22138118743896484": 59, "222631": 50, "2227": 68, "223212242126465": 59, "224163": 44, "229": [40, 41, 67], "22it": 45, "23": [45, 68], "2304": 68, "231269": 45, "2318": 68, "232957": 45, "238000": 45, "238701": 68, "24": [18, 36, 41, 44, 50, 67, 68], "2404": 68, "244": [35, 41, 67], "246747": 45, "247822": 45, "24it": [44, 59], "25": [15, 45, 51, 68], "250811": 44, "2515": 68, "251705": 44, "25it": [45, 59], "26": [19, 47, 68], "261": 68, "26it": [50, 59], "27": [45, 47, 50, 51, 62, 68], "27657762299986643": 51, "279959": 45, "27it": [43, 59], "28": [45, 68], "280932": 45, "28618431091308594": 59, "289336": 45, "28it": 59, "29": [43, 68], "297": 68, "2d": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 51], "2f": 40, "2\u03c0e": 36, "2\u03c0e\u03c3": 35, "3": [10, 27, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 62, 64, 65, 66, 68], "30": [16, 44, 47, 50, 51, 59, 68], "300": 58, "302": [51, 52, 67], "31": [14, 35, 43, 45, 68], "31it": 46, "32": [19, 43, 68], "326": [39, 41, 67], "33": [41, 43, 45, 47, 50, 51, 62, 68], "335781": 47, "337": [37, 41, 67, 68], "3390": 68, "33it": 46, "34": [45, 62, 68], "34401702880859375": 59, "3490": 68, "3495": 68, "349639": 44, "35": 68, "36": [25, 51, 68], "360": 67, "362484": 43, "362663": 43, "362667": 43, "363335": 43, "363861": 43, "37": [39, 41, 43, 62, 67, 68], "3766": 68, "377251": 47, "3779": 68, "379": 68, "37it": 47, "38": [43, 68], "380": 68, "385": [55, 56, 67], "38it": [45, 59], "391648": 45, "39it": 44, "3d": 51, "4": [16, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 65, 66, 68], "40": [43, 58], "401570": 47, "401695": 47, "405968": 44, "40it": [43, 45], "41": 43, "416784": 47, "418695": 46, "41it": 59, "42": [39, 41, 50, 59, 67], "423": 68, "424": 41, "42it": [43, 59], "43": 43, "4300": 68, "447428": 44, "45": [55, 68], "453753": 45, "45it": 44, "461383": 45, "461864": 45, "462532": 47, "476156": 47, "476842": 44, "476857": 44, "476879": 44, "476956": 44, "477410": 44, "478775": 44, "47it": 43, "486": [43, 48, 67], "488034": 45, "488635": 47, "48it": [45, 47], "49it": 50, "5": [19, 29, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 50, 55, 58, 59, 65, 68], "50": [44, 50, 58, 59], "502848": 45, "50it": 59, "51": 68, "513817": 45, "51it": 43, "52": 68, "54": 51, "550452": 47, "57": [37, 41, 43, 67], "5714287757873535": 51, "574": [46, 48, 67], "5878607690001445": 51, "58it": [50, 59], "590573": 45, "59it": 45, "6": [36, 37, 39, 40, 41, 43, 44, 45, 46, 47, 50, 51, 55, 59, 65, 68], "60": [43, 58], "615": [38, 41, 67], "61it": [43, 47], "62it": 47, "632980": 44, "63it": 47, "644727": 44, "64it": 45, "65it": 59, "66": [41, 68], "67": [45, 47, 50, 67], "671": [36, 41, 67], "672": [50, 52, 67], "67it": 43, "68": 68, "69": [43, 68], "69it": 43, "7": [14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 43, 44, 45, 46, 47, 50, 55, 58, 65, 68], "70it": 47, "71": 43, "711": [44, 48, 67], "714": 48, "718938": 44, "729": 51, "72it": 59, "735169": 44, "74": 43, "75": 43, "76it": [44, 47], "771": 68, "782": 68, "79it": 45, "8": [14, 15, 17, 18, 19, 20, 22, 23, 25, 27, 36, 43, 44, 45, 47, 50, 51, 55, 58, 61, 64, 68], "80": [43, 44, 59], "81": 51, "81it": 46, "82": 68, "82it": 45, "83": 50, "83it": [43, 47], "84": 43, "844169": 46, "849980": 46, "84it": 45, "8529834747314453": 59, "859": [59, 60, 67], "85it": 43, "86": 43, "864": 60, "869": 68, "86it": 44, "874": 68, "88it": [44, 47], "89": 43, "89it": [44, 50], "9": [14, 15, 17, 18, 19, 20, 22, 23, 25, 43, 44, 46, 50, 51, 55, 58, 64, 68], "90": 58, "909558": 44, "90it": [44, 47], "91": 68, "914042": 44, "91it": [46, 47, 50], "92": 68, "920": [45, 48, 67], "926982": 46, "92it": 45, "9361505508422852": 59, "93it": 59, "94": 43, "95": [35, 36, 37, 38, 39, 43, 55], "953700": 44, "953835": 44, "956186": 44, "95it": 47, "96it": 43, "97": 43, "974": 52, "98it": 45, "99": 43, "99078": 50, "A": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 45, 46, 47, 53, 59, 66, 68], "As": [43, 44, 50, 51, 55, 58, 59, 66, 68], "Be": 59, "But": 44, "By": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28], "For": [24, 28, 35, 36, 40, 43, 44, 45, 46, 47, 50, 55, 58, 61, 66, 68], "IT": [62, 68], "If": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 61, 64, 66, 68], "In": [27, 35, 36, 37, 38, 39, 40, 43, 45, 47, 50, 51, 55, 59, 62, 65, 66, 68], "It": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 36, 46, 47, 62, 68], "Its": 68, "On": 65, "One": [43, 45, 47, 51, 65, 68], "That": [44, 45, 47, 59], "The": [6, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 36, 40, 43, 44, 45, 46, 50, 51, 55, 58, 61, 62, 63, 65, 68], "Their": 46, "Then": [36, 43, 44, 51, 59, 61, 68], "There": 43, "These": [40, 62, 68], "To": [43, 44, 50, 55, 58, 59, 61, 64, 65, 66, 68], "_": [15, 44, 58], "__iter__": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "_autosummari": 51, "_hoi": 55, "_trial": 58, "aa": 68, "ab": 59, "abil": 43, "abl": 47, "about": [19, 24, 27, 43, 44, 45, 46, 47, 55, 58, 59, 62, 68], "abov": [44, 45, 47, 55, 68], "academi": 68, "accuiti": 66, "accur": [66, 68], "accuraci": 58, "acheiv": 46, "achiev": [45, 47, 55], "across": [50, 55, 66], "activ": [59, 68], "ad": 68, "adam": 68, "adapt": 68, "add": [26, 44, 45, 47, 50, 61], "add_edges_from": 50, "add_nodes_from": 50, "add_subplot": [37, 39], "addit": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 55, 61], "address": [62, 68], "adopt": 63, "adrian": 68, "advanc": [62, 68], "advantag": 68, "advis": 68, "again": [43, 44, 45, 46, 47], "aggreg": 30, "aim": [62, 68], "al": [10, 15, 16, 18, 19, 21, 22, 24, 39, 43, 44, 68], "alain": 68, "alexand": 68, "alford": 68, "algebra": [51, 66], "alic": 68, "all": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 37, 39, 43, 44, 47, 55, 58, 59, 61, 65, 67, 68], "allanson": 68, "allow": [44, 51, 62, 63, 66, 68], "along": [28, 51], "alpha": [35, 36, 37, 38, 39, 50, 55], "alreadi": [6, 64, 68], "also": [10, 19, 22, 36, 43, 44, 45, 46, 47, 55, 62, 64, 66, 68], "altern": 50, "although": 66, "alwai": 68, "am": [21, 68], "american": 68, "amico": 68, "amir": 68, "ammount": [46, 47, 68], "among": [62, 68], "amount": [44, 62, 68], "an": [5, 14, 25, 30, 36, 40, 43, 44, 46, 47, 50, 51, 55, 59, 61, 62, 65, 66, 68], "analys": 50, "analysi": 68, "analyt": [40, 62], "anatomi": 68, "anderson": 68, "andrea": 68, "andrew": 68, "ani": [14, 50, 55, 65, 68], "anil": 68, "annal": 68, "anoth": [14, 40, 62, 68], "answer": 58, "antonacci": 68, "anywher": 63, "ap": 68, "apart": 68, "api": [63, 66], "append": [55, 65], "appli": [8, 51], "applic": 68, "approach": [15, 24, 33, 38, 47, 57, 60, 66, 67, 68], "approxim": [46, 47, 68], "approximatio": 68, "ar": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 47, 50, 51, 55, 58, 59, 61, 62, 65, 66, 68], "arang": [50, 55, 58, 65], "arbitrari": [14, 25, 68], "architectur": 68, "area": [30, 55, 66], "areg": 59, "argument": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 51], "around": [30, 58], "arrai": [5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 40, 51, 58], "array_lik": [6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 58], "array_split": 58, "arround": 55, "arruda": 68, "arxiv": 68, "asarrai": [51, 65], "ask": 44, "aspect": [46, 68], "assert": 58, "associ": [26, 29, 30, 46, 62, 68], "assum": 61, "assumpt": 66, "astyp": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 65], "atric": 68, "attent": 68, "attractor": 68, "attribut": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "auditori": 68, "auto": 46, "auto_exampl": [41, 48, 52, 53, 56, 60], "auto_examples_jupyt": 33, "auto_examples_python": 33, "autocorrel": 46, "automat": 51, "avail": [40, 68], "averag": 55, "avoid": [43, 68], "ax": [26, 36, 37, 39, 47, 50, 51, 55, 58], "axhlin": [35, 36, 37, 38, 39], "axi": [21, 24, 26, 28, 30, 35, 36, 37, 38, 39, 51, 55], "b": [35, 59, 61, 68], "backend": [63, 66], "background": 66, "balaji": 68, "balanc": 68, "bandwidth": 9, "bar": 30, "barrat": 68, "barrett": 68, "base": [6, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 40, 43, 47, 61, 68], "base_model": 15, "basic": [51, 61], "battiston": 68, "baudot": [16, 43, 68], "bayesian": 68, "becaus": [44, 59], "becom": 68, "been": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 68], "beer": 68, "beerenwinkel": 68, "befor": [13, 59], "begg": 68, "behavior": [14, 15, 18, 22, 25, 29, 33, 42, 48, 62, 66, 67], "behind": [44, 68], "being": 43, "bell": 68, "below": [36, 43, 50], "benchmark": 66, "benedetta": 68, "benjamin": 68, "bennequin": 68, "berri": 68, "besid": 68, "best": [29, 45, 46, 47], "better": 55, "between": [14, 15, 16, 17, 18, 22, 25, 31, 35, 36, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 62, 63, 66, 68], "betzeen": 46, "beyond": [62, 63, 66, 68], "bia": 8, "bialek": 68, "bianconi": 68, "biascorrect": [8, 37, 38, 39], "bibtex": 61, "big": 68, "bin": [6, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 30, 38, 68], "binari": 38, "bind": 68, "binom": 65, "biolog": 62, "biologi": [62, 68], "biorxiv": 68, "bit": [6, 7, 8, 9, 10, 35, 36, 37, 38, 39, 40, 44, 45, 47, 55, 58, 59, 68], "bivari": [44, 45, 47], "black": [36, 61], "blakeaw": 10, "block": 68, "blog": 51, "bodi": 68, "bold": [35, 36, 37, 38, 39, 44, 55, 58, 59, 65], "book": 61, "bool": [5, 8, 26, 27, 28, 30], "boostrap": [55, 66], "bootstrap": [18, 26, 29, 56, 66, 67, 68], "bor": 68, "both": [14, 43, 44, 59, 65, 66, 68], "bound": [35, 36, 37, 38, 39, 68], "boundari": 35, "brain": [66, 68], "brainet": [61, 64], "branch": 61, "branch_nam": 61, "brien": 68, "bring": 55, "broad": 68, "browser": 61, "bruno": 68, "bug": 61, "build": [30, 40, 61, 68], "built": [63, 66], "bump": 58, "button": 61, "bw_method": 9, "c": [35, 36, 37, 38, 39, 40, 58, 59], "c0": 58, "c_": [45, 47], "call": [22, 40, 43, 51, 66, 68], "callabl": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 40], "can": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 36, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 62, 64, 65, 66, 68], "cannot": [62, 68], "capabl": [43, 44, 45], "capac": 62, "captur": 66, "card": [16, 43, 68], "care": [59, 68], "carhart": 68, "carri": [19, 44, 45, 46, 47, 55, 58, 59, 62, 68], "case": [27, 30, 40, 47, 58, 62, 68], "categori": [62, 68], "causal": 68, "cbar": 26, "cd": 61, "cell": 65, "cencetti": 68, "center": 30, "central": 30, "centuri": 68, "certain": 68, "challeng": 68, "chang": [51, 61], "channel": 62, "chao": 68, "charact": [27, 44], "character": [44, 68], "characteris": 68, "characterist": 68, "chechik": [19, 68], "check": [30, 47, 61], "checkout": [43, 44, 45, 47, 55, 58, 61, 66], "chichek": 68, "choic": 68, "choos": 27, "christin": 68, "christof": 68, "christoph": 68, "circular": 50, "circular_layout": 50, "claim": 66, "class": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 63, 66], "claud": [62, 68], "clear": 43, "clf": 58, "clike": 61, "clone": 61, "close": 40, "closest": 10, "cmap": [43, 45, 47, 55], "code": [10, 33, 35, 36, 37, 38, 39, 40, 43, 45, 46, 47, 50, 51, 55, 58, 59, 63, 65, 68], "codecov": 61, "cognit": 68, "colab": 65, "collect": [44, 50, 68], "color": [35, 36, 37, 38, 39, 58], "colorbar": [26, 46], "column": [44, 45, 47], "com": [51, 61, 64, 68], "comb": 5, "combin": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 62, 66], "combinatori": 32, "come": 68, "command": [61, 66], "commit": 61, "common": 68, "commun": [62, 68], "compar": [35, 36, 37, 38, 39, 58, 65, 68], "comparison": [11, 12, 28, 33, 34, 40, 41, 55, 66, 67, 68], "compil": 65, "complet": 68, "complex": [62, 65, 68], "complic": 68, "compon": 62, "compos": 66, "compress": 62, "comput": [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 35, 36, 37, 38, 39, 40, 43, 44, 46, 47, 59, 61, 63, 68], "computation": 55, "compute_entropi": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36], "compute_hoi_beh": 59, "compute_hoi_enc": 59, "compute_tim": 65, "compute_true_entropi": 37, "compute_true_mi": 39, "concept": [62, 68], "concern": 44, "conclud": 55, "concret": 68, "condit": [16, 18, 26, 29, 33, 42, 44, 48, 55, 67, 68], "confid": [18, 26, 29, 33, 54, 56, 66, 67, 68], "connect": 68, "conscious": 68, "consequ": 44, "consid": [21, 24, 46, 47, 62, 65, 68], "consist": [59, 68], "constant": [35, 36], "constraint": [44, 68], "contain": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 36, 44, 68], "content": 68, "context": [59, 68], "continu": [28, 68], "contrast": 43, "contribut": [59, 62, 66, 68], "control": 68, "convei": [27, 68], "convent": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "converg": [35, 37, 38, 39], "cooper": 62, "coordin": 68, "copi": [44, 45, 46, 47, 58, 62, 68], "copnorm": 8, "copula": [8, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 40, 65, 66, 68], "core": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, 33, 34, 35, 36, 37, 38, 39, 41, 61, 65, 67], "correct": [8, 62], "correctli": 43, "correl": [14, 18, 22, 25], "correspond": 43, "cost": [65, 68], "could": 44, "count": 30, "coupl": [24, 46, 68], "cov": [36, 37, 39, 40, 61], "cov_matrix": [37, 38, 39], "covari": [36, 37, 38, 39, 40, 59], "cpu": [51, 63, 64], "craig": 68, "creat": [36, 37, 38, 39, 46, 50, 55, 58, 59, 61, 65], "create_cov_matrix": [37, 39], "cross_val_scor": 58, "crucial": 68, "crutchfield": 68, "cryptographi": 62, "current": 26, "custom": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "cut": 63, "cv": 58, "czy": 68, "czyz": 39, "d": [36, 40, 68], "da": 58, "da_": 58, "daniel": 68, "darbellai": 68, "data": [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 30, 33, 34, 36, 40, 41, 55, 59, 62, 65, 67, 68], "data_s": 65, "dataarrai": 30, "datafram": [29, 30, 50], "date": 63, "david": 68, "de": 68, "deal": [65, 68], "deciph": 68, "decode_i": 58, "decompos": [62, 68], "decomposit": [21, 24, 29, 33, 42, 48, 62, 67], "def": [35, 36, 37, 38, 39, 51, 58, 59, 65], "default": [5, 6, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29], "default_devic": 65, "defin": [14, 15, 16, 18, 19, 21, 22, 24, 25, 35, 36, 37, 38, 39, 40, 44, 45, 46, 47, 50, 51, 55, 59, 65, 66, 68], "definit": [43, 44, 66, 68], "delai": [21, 24, 68], "delv": 68, "dens": [37, 39], "densiti": [9, 30, 68], "depend": [16, 30, 58, 63, 66, 68], "depict": 55, "deriv": [14, 15, 18, 22, 25, 29, 33, 42, 48, 67, 68], "describ": [36, 62, 66, 68], "descriptor": 68, "design": [19, 68], "despit": 43, "det": [36, 37, 39, 40], "det_cov": 37, "det_i": 39, "det_x": 39, "det_xi": 39, "detail": [66, 68], "detect": 62, "determin": 36, "develop": [62, 65, 66, 68], "deviat": 35, "devic": 65, "df": [45, 46, 47], "df_best": 29, "diag": 36, "diag_indic": [37, 39], "diagon": [36, 37, 39], "dict": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 43, 45, 47, 55], "did": 43, "differ": [14, 15, 18, 40, 43, 44, 51, 55, 58, 59, 62, 65, 68], "differnt": [37, 39], "digit": 38, "dim": 37, "dimens": [37, 39, 51, 55], "dimension": [11, 12, 30, 33, 34, 36, 40, 41, 67, 68], "direct": [62, 68], "direction_axi": [21, 24], "directli": [47, 64, 68], "discret": [6, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 68], "discriminant_analysi": 58, "discuss": 68, "discusss": 61, "disentangl": [44, 45], "disord": 68, "distanc": 51, "distinguish": 68, "distribut": [11, 25, 30, 33, 34, 36, 40, 41, 66, 67, 68], "diverg": 25, "divid": [30, 51, 68], "do": [36, 45, 46, 47, 51, 61], "document": [51, 64, 66], "doe": 68, "doesn": [55, 65], "doi": 68, "domin": [44, 59, 68], "dominik": 68, "done": [39, 51, 59, 68], "dopaminerg": 68, "dot": [36, 51], "doubl": 47, "download": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59], "draft": 61, "draw": 50, "dry": [51, 65], "dtc": [18, 22, 68], "dual": [14, 18, 22], "due": 68, "dufour": 68, "dynam": [65, 68], "e": [35, 36, 37, 40, 44, 45, 47, 59, 61, 62, 65, 66, 68], "e1008289": 68, "e21090869": 68, "each": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 36, 37, 39, 43, 44, 45, 51, 55, 58, 59, 61, 62, 65, 68], "eas": 63, "easiest": 64, "ecolog": 62, "ecologi": 62, "edg": [30, 50, 63], "edge_fc": 50, "edge_fc_cmap": 50, "editor": 61, "effect": [36, 59, 62, 68], "effici": 51, "eilon": 68, "either": [5, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 35, 45, 58], "elad": 68, "electrophysiolog": 68, "elegantli": 68, "element": [5, 14, 19, 25, 36, 37, 39, 44, 51, 59, 62, 68], "elif": [37, 39, 58], "ellison": 68, "els": [37, 39], "elwood": 68, "emerg": [46, 59, 68], "emmanuel": 68, "empti": 55, "en": [51, 64], "encod": [14, 15, 18, 22, 25, 29, 33, 42, 48, 58, 62, 66, 67], "end": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61], "endr": 68, "eneuro": 68, "engag": 59, "engin": [62, 63], "enrico": 68, "ensur": 61, "ent": 37, "ent_theor": 37, "entropi": [6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, 38, 39, 41, 43, 44, 50, 61, 62, 66, 67], "entropy_analyt": 40, "entropy_bin": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "entropy_gauss": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "entropy_gc": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "entropy_kernel": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "entropy_knn": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "enumer": [35, 36, 37, 38, 39, 44, 46, 58], "environ": 65, "equal": [28, 30, 36], "equiv": [19, 45, 47], "equival": [25, 51], "eran": 68, "error": [35, 38, 62], "especi": 66, "essenc": 62, "estim": [8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 30, 32, 33, 34, 40, 41, 43, 59, 66, 67, 68], "estimat": 55, "et": [10, 15, 16, 18, 19, 21, 22, 24, 39, 43, 44, 68], "etc": [65, 66], "euler": [35, 36], "evalu": 68, "even": [44, 68], "eventu": 47, "evolut": [21, 24, 68], "exact": 55, "exampl": [17, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 63, 65, 66, 67], "exceed": 19, "except": [44, 51, 55], "excess": 68, "exclud": 68, "execut": [41, 48, 51, 52, 53, 56, 60, 63, 67], "exogen": [22, 68], "expect": [40, 45, 46, 62], "experimentalist": 68, "explain": 62, "explor": 68, "expon": 51, "exstens": 68, "exstrins": 62, "extend": 68, "extens": [14, 25, 68], "extern": [59, 62], "extract": [37, 38, 39, 40, 50], "ey": [37, 39], "f": [35, 36, 37, 38, 39, 51, 55, 58, 59, 68], "fact": [65, 68], "fae": 68, "failur": 62, "fall": 62, "fals": [5, 27, 28, 30, 37, 38, 39, 43, 45, 47, 55, 58, 59, 65, 68], "familiar": 63, "fascin": 68, "fast": [55, 65], "faster": [65, 66], "fault": 62, "favorit": 61, "fcn": [11, 12, 35, 36, 37, 38, 39, 51], "featur": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 43, 45, 46, 47, 58], "federico": 68, "fernando": 68, "ferraz": 68, "fetch": 61, "fi": 68, "field": [65, 68], "fig": [36, 37, 39, 58], "figsiz": [36, 37, 39, 58], "figur": [36, 37, 39], "file": [41, 48, 52, 53, 56, 60, 61, 67], "file1": 61, "file2": 61, "fill": 5, "fill_between": [35, 36, 37, 38, 39, 55], "fill_valu": 5, "final": [36, 44, 51, 59, 61, 65, 68], "find": [44, 47, 66], "finoia": 68, "first": [15, 28, 44, 45, 46, 47, 50, 51, 55, 59, 65], "fit": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65, 66], "fix": 55, "flake8": 61, "flecker": 68, "float": [6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 31, 51, 58], "focu": 68, "focus": [44, 68], "foldiak": 68, "follow": [21, 35, 46, 47, 59, 61, 65, 66, 68], "fonction": 61, "font_size_nod": 50, "fontweight": [35, 36, 37, 38, 39, 44, 55, 58, 59, 65], "fork": 61, "formal": 68, "formisano": 68, "formula": [40, 68], "found": [44, 62, 66], "foundat": 68, "frac": [35, 36, 37, 38, 39, 40], "framework": [46, 47, 62, 68], "franceschiello": 68, "fraser": 68, "freder": 68, "frequenc": [30, 68], "friendli": 51, "from": [30, 36, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 62, 64, 65, 66, 67], "fryer": 68, "full": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61], "fulli": [58, 62], "funciton": 59, "function": [2, 4, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 33, 35, 36, 37, 38, 39, 40, 50, 58, 59, 63, 66, 68], "functool": [38, 51], "fundament": [40, 62, 68], "further": [43, 44, 45, 47, 51, 55, 58, 66], "futur": [24, 46, 62, 68], "fx": [37, 38, 39], "g": [46, 66, 68], "gabert": 68, "gabriel": 68, "gal": 68, "galleri": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 67], "gastpar": 68, "gauss": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36], "gaussian": [7, 8, 9, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 35, 36, 37, 38, 39, 40, 59, 65, 66, 68], "gaussian_kd": 9, "gbauer": 68, "gc": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 40, 43, 44, 50, 55, 59, 65, 66], "gca": 55, "gcmi": [37, 39], "gener": [27, 33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65, 68], "genet": 68, "geomspac": [35, 36, 37, 38, 39], "georg": 68, "get": [5, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 35, 36, 37, 38, 39, 44, 55, 65, 66], "get_combin": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 46], "get_covari": 36, "get_entropi": [35, 36, 37, 40, 65], "get_mi": [38, 39, 40], "get_nbest_mult": [43, 44, 45, 46, 47, 50, 55, 66], "ggplot": [35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65], "ginestra": 68, "giordano": 68, "giovanni": 68, "git": [61, 64], "github": [61, 64], "giulia": 68, "give": 44, "given": [38, 39, 43, 44, 62, 68], "globerson": 68, "glossari": 66, "go": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 63, 65, 66, 68], "goaillard": 68, "gonig": 59, "goodman": 68, "gpu": [51, 63, 64], "grabowski": 68, "gradient": [15, 44, 47, 58], "gradientoinfo": [44, 58, 59, 66, 68], "graphic": 68, "grassberg": 68, "great": 68, "greater": [59, 62, 68], "griffith": 68, "gross": 68, "group": [47, 62, 68], "grow": [65, 68], "gui": 68, "guid": [40, 68], "guilherm": 68, "guillaum": 68, "h": [14, 18, 22, 25, 35, 36, 37, 40, 43, 44, 50, 68], "h_": [16, 43, 68], "h_idx": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "h_max": 59, "h_theoric": [35, 36], "h_x": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36], "ha": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 51, 68], "half": 68, "hallmark": 59, "han": [44, 58, 59, 68], "handl": 68, "hann": 58, "harald": 68, "harri": 68, "have": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 37, 39, 40, 44, 51, 64, 65, 66, 68], "height": 30, "henc": 68, "henrik": 68, "here": [44, 45, 46, 47, 50, 55, 58, 59, 64, 66], "high": [11, 12, 27, 33, 34, 41, 46, 67, 68], "higher": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 32, 33, 36, 40, 43, 45, 47, 49, 51, 52, 58, 62, 67], "highest": [43, 45, 46, 47, 50, 55], "highli": 66, "highlight": 68, "hist": 26, "hist_kwarg": 26, "histogram": [26, 30], "hoi": [32, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 51, 55, 57, 59, 60, 62, 64, 65, 66, 67, 68], "hoi_m": 55, "hoi_order_3": 50, "hoi_r": 47, "hoi_syn": 47, "hold": 43, "holland": 68, "horizont": 36, "how": [15, 18, 27, 30, 33, 43, 44, 45, 46, 47, 50, 51, 55, 57, 58, 60, 62, 66, 67, 68], "howev": [36, 43, 45, 47, 55, 58, 65, 68], "html": [51, 64], "http": [51, 61, 64, 68], "huge": 65, "hull": 50, "human": 68, "hx": [6, 7, 8, 9, 10], "hypergraph": 50, "hypothesi": 68, "i": [5, 6, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 51, 55, 58, 59, 61, 62, 63, 64, 65, 66, 68], "i_": [16, 43, 68], "i_2": 68, "i_3": 68, "i_k": 68, "iacopini": 68, "iacopo": 68, "ibm": 68, "idea": 44, "ident": 68, "identifi": [43, 68], "ieee": 68, "ignor": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "igor": 68, "ik": [15, 44], "il": 68, "illustr": [33, 36, 43, 44, 45, 46, 47, 50, 55], "imagin": 51, "implement": [50, 51, 61, 68], "import": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65, 66, 68], "improv": [61, 62], "imshow": 46, "in_ax": [51, 65], "inc": 68, "incept": 68, "includ": [27, 43, 55, 61, 63], "increas": [36, 65], "independ": [40, 46, 68], "index": [19, 20, 23, 26, 29, 33, 42, 43, 44, 46, 47, 48, 50, 55, 62, 67], "indic": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 68], "individu": [19, 44, 59, 62, 68], "inf": 68, "infer": [43, 68], "inflat": 46, "influenc": 44, "info": [15, 18, 22, 44, 55], "inform": [10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 37, 39, 41, 42, 45, 47, 48, 50, 57, 59, 60, 62, 63, 65, 66, 67], "infotopo": [43, 50, 68], "initi": 55, "inject": [44, 46, 50, 59], "input": [6, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 36, 40, 51], "insid": [45, 47, 61], "insight": 68, "inspect": [16, 26, 29, 33, 45, 46, 47, 49, 52, 67, 68], "inspir": 39, "instal": [29, 63, 65], "instead": [46, 47, 68], "int": [5, 6, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 35, 36, 37, 38, 39, 58, 65], "integr": [21, 24, 29, 33, 42, 48, 67, 68], "intens": 55, "interact": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 32, 33, 36, 44, 45, 47, 49, 52, 55, 58, 59, 62, 67], "interdepend": [46, 68], "interdisciplinari": 68, "interest": 68, "intern": 68, "interpol": 46, "interpret": [45, 46, 47, 68], "interv": [18, 26, 29, 33, 35, 36, 37, 38, 39, 40, 54, 56, 66, 67, 68], "intric": 68, "intrins": [14, 44, 62], "introduc": [43, 44, 45, 47, 51, 58, 68], "introduct": [11, 12, 33, 34, 41, 49, 52, 66, 67, 68], "intuit": [44, 59], "invalu": 68, "investig": [58, 65, 68], "involv": [36, 68], "io": [51, 64], "ipynb": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59], "isol": 44, "israel": 68, "issu": [61, 65], "item": [35, 36, 37, 38, 39], "iter": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "its": [14, 15, 18, 22, 25, 29, 33, 35, 36, 42, 43, 47, 48, 55, 66, 67, 68], "j": [14, 18, 22, 25, 44, 68], "jame": [22, 68], "jax": [5, 9, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 49, 52, 63, 64, 66, 67, 68], "jax_eucl": 51, "jean": 68, "jensen": 68, "jirina": 68, "jnp": [5, 51, 65], "joachim": 68, "john": 68, "joint": [25, 37, 38, 39, 68], "journal": 68, "judith": 68, "julia": 68, "jupyt": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59], "just": 44, "k": [5, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 43, 44, 58, 65, 68], "kayser": 68, "kazuto": 68, "kbinsdiscret": 28, "keep": 55, "kei": [35, 36, 37, 38, 39], "kernel": [9, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 46, 68], "kind": [26, 43, 45, 47, 50, 51, 55, 68], "knn": [10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 68], "know": [45, 47, 59, 68], "knowledg": [61, 62], "known": [51, 58, 68], "kobayashi": 68, "koch": 68, "kraskov": [10, 68], "kullback": 25, "kwarg": [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 38], "l": 68, "label": [35, 36, 37, 38, 39, 44, 58, 65], "lall": 68, "lambda": 35, "lambda_": 35, "landcap": 30, "landscap": [26, 43, 55, 66], "lapish": 68, "larg": 25, "larger": 65, "largest": [44, 50], "lasserr": 68, "last": 68, "latest": [51, 64], "latora": 68, "launch": [45, 46, 47], "lax": 51, "layout": 50, "ldot": 68, "lead": [35, 51, 65], "learn": [15, 33, 55, 57, 60, 63, 64, 67, 68], "least": [51, 55, 68], "left": [40, 68], "legend": [35, 36, 37, 38, 39, 44, 58, 65], "len": [35, 36, 37, 38, 39], "length": [21, 24], "less": 68, "let": [35, 36, 37, 38, 40, 43, 44, 45, 46, 47, 51, 55, 58, 59, 65], "letter": 68, "leverag": 47, "li": 55, "librari": [51, 65, 68], "liebler": 25, "light": 68, "like": [51, 66], "limit": [47, 55, 66, 68], "linalg": [36, 37, 39, 40], "line": [36, 55, 66, 68], "linear": [51, 66, 68], "lineardiscriminantanalysi": 58, "linearli": 65, "linestyl": [35, 36, 37, 38, 39], "link": [38, 39, 44, 68], "linspac": 65, "lint": 61, "list": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 35, 36, 37, 38, 39, 55, 63, 64, 66], "literatur": 68, "locat": 61, "log": [35, 36, 40], "log2": [35, 37, 38, 39], "log_": [35, 37, 38, 39, 68], "logarithm": 6, "look": [45, 46, 47, 66], "lost": 68, "low": 68, "lower": [35, 36, 37, 38, 39, 43, 55, 68], "lowest": [45, 46, 47, 50], "luca": 68, "luppi": [24, 68], "lw": [35, 36, 37, 38, 39, 55, 58], "m": [35, 44, 46, 55, 61, 68], "machin": [15, 33, 57, 60, 67, 68], "main": [33, 61, 65, 68], "mainli": [55, 68], "maintain": 61, "make": [36, 61, 68], "mani": 68, "manon": 68, "map": 68, "marc": 68, "margin": 25, "marinazzo": 68, "marker": 36, "marqu": 68, "martial": 68, "marx": 68, "mass": 68, "math": [25, 44], "mathcal": [35, 37, 38, 39], "mathemat": [43, 44, 62, 68], "matplotlib": [35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 50, 55, 58, 59, 61, 65], "matrix": [36, 37, 38, 39, 40, 46, 59], "matrix_to_plot": 46, "max": [24, 46, 51, 59, 68], "max_": [47, 68], "maxim": [19, 68], "maximum": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 66], "maxsiz": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 44, 45, 46, 47, 50, 58, 59, 65, 66], "mb": [41, 48, 52, 53, 56, 60, 67], "mdpi": 68, "mean": [35, 36, 37, 38, 39, 40, 45, 47, 51, 55, 58, 59, 65], "measur": [25, 32, 44, 45, 46, 47, 59, 62, 66], "mediano": [21, 68], "mem": [41, 48, 52, 53, 56, 60, 67], "menon": 68, "mention": 68, "messag": [61, 62], "method": [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 40, 43, 44, 50, 55, 59, 65, 66, 68], "metric": [11, 12, 26, 29, 32, 34, 35, 36, 37, 38, 39, 41, 43, 44, 45, 46, 47, 48, 50, 55, 58, 59, 62, 63, 65, 66, 67, 68], "metric_nam": [35, 36, 37, 38, 39], "mi": [8, 12, 17, 19, 20, 21, 23, 24, 33, 34, 37, 40, 41, 62, 67], "mi_bin": 38, "mi_binning_fcn": 38, "mi_theor": [38, 39], "michael": 68, "mid": 55, "midbrain": 68, "milan": 68, "min": [21, 46, 51, 59, 68], "min_": [47, 68], "minimum": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 46, 47, 66, 68], "minmax": 51, "minmax_2d": 51, "minmax_3d": 51, "minmax_3d_jit": 51, "minmaxscal": 50, "minsiz": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65, 66], "minu": [15, 18, 22, 44], "minut": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59], "miscellan": [52, 67], "miss": 5, "mitig": 66, "mmi": [20, 21, 23, 24, 26, 29, 33, 42, 46, 48, 67], "mode": [37, 39, 61], "model": [26, 29, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65, 66, 68], "model_r": 47, "model_select": 58, "model_syn": 47, "modifi": [61, 65], "modul": [59, 62, 65], "monica": 68, "monoton": 68, "moon": 68, "more": [43, 45, 47, 55, 59, 62, 63, 68], "moreno": 68, "most": [40, 45, 46, 47, 63, 68], "move": [45, 47], "mu": [35, 37, 39], "mu_": [38, 39], "mu_i": 38, "mu_x": 38, "much": [46, 55, 68], "mult_order_3": 50, "mult_siz": 30, "multi_s": 30, "multiinform": 68, "multipl": [59, 62, 63, 65], "multiplet": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 44, 45, 46, 47, 55, 66, 68], "multivari": [11, 16, 33, 34, 37, 39, 40, 41, 58, 59, 66, 67, 68], "multivariate_norm": [36, 37, 38, 39], "musician": 66, "must": 65, "mutual": [10, 12, 14, 16, 17, 20, 21, 23, 24, 25, 28, 32, 37, 39, 41, 43, 46, 47, 50, 62, 66, 67], "n": [5, 14, 15, 17, 18, 19, 22, 25, 29, 35, 36, 37, 38, 39, 44, 45, 47, 51, 53, 58, 65, 66, 68], "n_": [35, 36, 37, 38, 39, 65, 68], "n_b": 55, "n_best": [29, 44, 45, 46, 47, 50], "n_bin": [28, 30, 38], "n_boot": 55, "n_combin": 5, "n_dim": [37, 39], "n_f": 65, "n_featur": [6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 40, 46, 65], "n_hoi": 30, "n_m": [35, 36, 37, 38, 39, 44], "n_mult": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "n_multiplet": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "n_node": [55, 59], "n_r": [35, 36, 37, 38, 39, 58], "n_repeat": [35, 36, 37, 38, 39], "n_sampl": [6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 35, 36, 37, 38, 39, 40, 55, 58, 59, 65, 66], "n_time": 58, "n_v": 65, "n_variabl": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 65], "n_x": 58, "n_y": 58, "naftali": 68, "name": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 51, 61], "nathaniel": 68, "nation": 68, "natur": [58, 59, 68], "ncode": 66, "ndarrai": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27], "ndata": [35, 38], "nearest": [10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 68], "necessari": 68, "need": 59, "neg": [19, 27, 43, 44, 45, 50, 58, 59, 62, 68], "negin": 68, "neglect": 68, "neighbor": [10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 68], "nelken": 68, "nelsontang": 51, "neq": [15, 44], "network": [14, 15, 18, 22, 25, 29, 33, 42, 43, 48, 55, 59, 62, 65, 66, 67], "neural": 68, "neurip": 39, "neuroimag": 68, "neuron": 68, "neurosci": [66, 68], "neurotransmitt": 68, "new": [65, 68], "next": 65, "nh": [22, 44, 68], "nica": 68, "nice": 51, "nichola": 68, "niko": 68, "node": [43, 44, 50, 55, 59, 65, 66], "node_label": 50, "node_s": 50, "nois": 46, "non": [55, 62], "none": [5, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 36, 37, 39, 46], "nonlinear": 68, "nonneg": 68, "normal": [8, 11, 30, 33, 34, 37, 39, 40, 41, 44, 66, 67, 68], "note": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 68], "notebook": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65, 66], "notic": [47, 51], "now": [36, 40, 43, 44, 45, 46, 47, 51, 55, 58, 59], "np": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65], "nthe": [37, 39], "nuanc": 62, "number": [5, 14, 25, 27, 28, 29, 30, 35, 36, 37, 38, 39, 51, 55, 58, 65, 68], "numpi": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 55, 58, 59, 64, 65], "numpy_eucl": 51, "numpydoc": 61, "nuzzi": 68, "o": [14, 15, 18, 22, 25, 27, 29, 33, 36, 42, 47, 48, 62, 65, 66, 67], "object": 50, "observ": [30, 45, 46, 47, 68], "obtain": [59, 62, 68], "occur": 62, "occurr": 68, "off": [37, 39], "offer": 68, "offici": 51, "often": 62, "oinfo": [15, 43, 44, 55, 58, 59, 65, 66, 68], "oldest": [25, 68], "omega": [15, 18, 22, 44, 68], "omega_": 58, "onc": [61, 66], "one": [36, 44, 55, 59, 62, 65, 68], "onli": [27, 37, 39, 43, 45, 46, 47, 50, 55, 58, 61, 62, 64], "open": 61, "oper": [46, 51, 65, 68], "option": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 51, 64], "orchestra": 66, "order": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 33, 36, 40, 42, 44, 45, 46, 47, 48, 49, 52, 58, 62, 67], "org": 68, "organ": 68, "origin": [10, 61], "other": [14, 40, 44, 45, 47, 59, 62, 68], "otherwis": 66, "our": [43, 50, 51, 61, 66, 68], "output": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 50], "over": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 51, 55], "owen": 68, "own": [46, 68], "p": [25, 68], "p_high": 55, "p_low": 55, "packag": [50, 61, 63, 66], "page": [61, 66, 68], "pair": [37, 39, 58, 68], "pairwis": [17, 46, 62, 63, 66], "panda": [29, 30, 50, 61, 64], "paola": 68, "paramet": [5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 35, 58, 59], "parametr": [55, 68], "part": [14, 47, 50, 58, 59, 62, 65, 68], "partial": [38, 51, 58, 62, 68], "partial_": [15, 44, 68], "particular": [35, 38, 39, 51, 68], "partit": 68, "pass": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 61], "past": [46, 65], "patania": 68, "path_to_test_fil": 61, "pathwai": 68, "pattern": [59, 68], "paul": 68, "paw": 68, "pcolormesh": 26, "pedro": [21, 68], "pep8": 61, "per": [30, 37, 39], "percent": 30, "percentil": [35, 36, 37, 38, 39, 55], "perform": [28, 36, 51, 66, 68], "permut": 58, "perspect": 68, "peter": 68, "petri": 68, "phenomena": 68, "phenomenon": 62, "phenotyp": 68, "phiid": [21, 24], "philipp": 68, "philosoph": 68, "phy": 10, "physic": 68, "physrev": 68, "pi": [35, 36, 37, 40], "pickard": 68, "pid": [62, 68], "pierr": 68, "pip": [61, 64, 65, 66], "plai": 68, "pleas": [61, 64], "plethora": 68, "plo": 68, "plot": [16, 29, 32, 33, 35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 49, 52, 58, 59, 65, 66, 67, 68], "plot_bootstrap": [55, 56, 67], "plot_decod": 58, "plot_entropi": [35, 41, 67], "plot_entropies_mvar": [36, 41, 67], "plot_entropy_high_dimension": [37, 41, 67], "plot_infotopo": [43, 48, 67], "plot_inspect_result": [50, 52, 67], "plot_jax": [51, 52, 67], "plot_landscap": [43, 45, 47, 50, 55, 66], "plot_mi": [38, 41, 67], "plot_mi_high_dimension": [39, 41, 67], "plot_ml_vs_it": [58, 60, 67], "plot_oinfo": [44, 48, 67], "plot_rsi": [45, 48, 67], "plot_sim_red_syn": [59, 60, 67], "plot_syn_phiid": [46, 48, 67], "plot_syn_red_mmi": [47, 48, 67], "plot_tutorial_cor": [40, 41, 67], "plot_xi": 58, "plt": [26, 35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65], "plt_kwarg": [26, 43, 45, 47, 55], "plu": [44, 46, 68], "po": 50, "point": [10, 43, 44, 51, 58, 65, 68], "popul": 28, "pose": 65, "posit": [19, 27, 36, 43, 44, 45, 46, 47, 50, 51, 58, 59, 68], "possibl": [5, 45, 47, 59, 65, 68], "post": 32, "potenti": 66, "pouei": 68, "pre": 32, "predict": 46, "predictor": 62, "prepar": 13, "preprint": 68, "preprocess": [28, 50], "presenc": [46, 47, 62, 68], "present": [43, 59, 68], "pretti": 66, "prevail": 68, "previou": [44, 59], "principl": 68, "print": [40, 43, 44, 45, 46, 47, 50, 51, 55, 59, 66], "probabl": [30, 68], "problem": [65, 68], "procedur": 68, "proceed": 68, "process": [32, 62, 68], "produc": [59, 62, 68], "product": [25, 36, 51], "program": 65, "promin": 68, "properti": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 46, 68], "proport": 30, "propos": [61, 68], "proven": 68, "provid": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 58, 62, 63, 66, 68], "proxi": 68, "publish": [43, 68], "pure": 51, "purport": 19, "pursuit": 68, "push": 61, "py": [35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 56, 58, 59, 60, 61, 67], "pyplot": [35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65], "pytest": 61, "python": [10, 33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 63, 64, 65, 66, 68], "quadruplet": [43, 55], "quantif": 62, "quantifi": [16, 44, 62, 63, 66, 68], "quantil": 28, "quantiti": 44, "quatifi": 68, "question": [44, 58, 61, 68], "quick": [33, 49, 52, 67], "quickli": 68, "r": [55, 58, 68], "rajagopalan": 68, "rand": [40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65], "randal": 68, "random": [16, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 62, 65, 68], "random_st": 55, "randomli": 55, "rang": [35, 36, 37, 38, 39, 46, 55, 58, 68], "rate": 35, "ravel": 58, "rder": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "re": [43, 59], "read": 44, "readthedoc": [51, 64], "real": [65, 68], "realli": 55, "rebas": 61, "receiv": [45, 46, 47, 58, 59], "recent": [65, 68], "recommand": 55, "recommend": [44, 65], "reconcil": 68, "reconduct": 68, "recoveri": 62, "red": [21, 46, 47, 58, 68], "red_result": 46, "redmmi": 47, "redphiidmmi": 46, "reduand": 43, "reduc": 68, "reduct": [62, 68], "redud": 44, "redund": [14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 27, 29, 33, 42, 48, 50, 57, 58, 60, 62, 66, 67], "redundancymmi": [47, 68], "redundancyphiid": [46, 68], "refer": [10, 14, 15, 16, 18, 19, 21, 22, 24, 25, 27, 50, 62, 64, 68], "reflect": [45, 68], "regard": 55, "rel": [51, 66], "rel_strength": 58, "rel_typ": 58, "relat": [14, 15, 18, 22, 25, 44, 46, 58, 68], "relationship": [58, 62, 66, 68], "reli": [43, 65, 66], "reliabl": 62, "rememb": 47, "remind": [43, 55], "remot": 61, "remov": 44, "repeat": [51, 55], "repetit": [35, 36, 37, 38, 39], "repo": 61, "report": 68, "repositori": 61, "repres": [5, 30, 44, 55, 59, 62, 68], "represent": 26, "requir": [29, 38, 62, 64, 65], "resampl": 55, "research": [63, 65, 68], "reshap": [35, 51, 58, 59], "respect": [27, 44, 46, 47, 58, 66, 68], "ressourc": 51, "result": [35, 37, 38, 39, 45, 46, 47, 55, 59, 65, 68], "retriev": [44, 45, 47, 50, 58, 66], "return": [5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 36, 37, 38, 39, 43, 50, 51, 58, 59, 65], "rev": 10, "reveal": 68, "review": 68, "rf": 58, "right": [40, 68], "rightarrow": [15, 16, 18, 19], "robin": 68, "robust": [46, 66, 68], "role": 68, "rosa": [18, 44, 68], "rotat": 55, "rousselet": 68, "row": 68, "rowvar": 40, "royal": 68, "rsi": [17, 45, 47, 62], "rule": 68, "run": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 63, 65, 66], "ryan": 68, "s_": 47, "sai": [51, 55, 59], "said": 44, "same": [28, 43, 45, 46, 47, 51, 55, 59, 62, 63, 66, 68], "sampl": [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 36, 40, 43, 44, 45, 46, 47, 55, 58, 59, 65], "satisfi": 61, "satosi": 68, "sca": [36, 58], "scagliarini": [15, 68], "scale": 65, "scan": 51, "scatter": [26, 43, 45, 47, 50, 55], "scenario": 68, "schneidman": 68, "schyn": 68, "scienc": 68, "scientif": 68, "scientist": 68, "scikit": [55, 63, 64], "scipi": [9, 51, 64], "script": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 66], "sebastiano": 68, "second": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65, 68], "section": [44, 66, 68], "see": [9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 66, 68], "seed": [50, 59], "seen": 68, "select": [45, 46, 47, 65], "self": 68, "semi": 36, "semin": 68, "sen": 59, "send": [44, 45, 47], "sens": 68, "sensit": [14, 25, 68], "sent": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "sentiv": 68, "separ": [46, 62, 68], "septemb": 68, "seri": 68, "serv": 68, "set": [5, 14, 17, 19, 27, 40, 51, 59, 61, 62, 65, 68], "set_text": [37, 39], "set_xlabel": [37, 39], "set_xticklabel": 55, "set_ylabel": [37, 39], "seth": 68, "sever": [35, 36, 38], "shade": 55, "shannon": [62, 68], "shape": [5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 30, 36, 37, 39, 40, 45, 47, 51, 55, 58], "share": [14, 25, 44, 46, 62, 68], "sharei": 58, "sharex": 58, "shed": 68, "short": [43, 51], "should": [6, 8, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 43, 61, 68], "show": [30, 35, 37, 38, 39, 43, 44, 45, 46, 50, 55, 58], "showcas": [44, 50], "shown": 68, "sigma": [35, 36, 37, 39, 40], "sigma_": [38, 39], "sigma_i": 38, "sigma_x": 38, "sign": 68, "signal": [59, 61], "sim": [35, 38, 39], "simeq": 65, "similar": 39, "simmetr": 46, "simon": 68, "simpl": [45, 46, 47, 55, 59, 68], "simpli": [62, 68], "simul": [15, 18, 32, 33, 35, 36, 37, 38, 39, 55, 57, 60, 67, 68], "simulate_data": 58, "simulate_hoi_gauss": [59, 66], "sinc": [40, 68], "sinfo": [44, 68], "singl": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 45, 47, 61, 68], "situat": 68, "six": 47, "size": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 35, 36, 40, 45, 46, 47, 65, 66, 68], "sklearn": [28, 50, 55, 58], "sl": 58, "slice": 58, "slow": 51, "small": [43, 68], "smallest": [44, 50], "smooth": 68, "so": [36, 40, 58, 61, 68], "social": [62, 66], "societi": 68, "softwar": [61, 64], "some": [35, 36, 44, 46, 51, 55, 59, 65, 68], "sonia": 68, "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, 33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 68], "space": 68, "spars": [37, 39], "spatial": 55, "special": 38, "specif": [35, 59, 61], "specifi": [5, 8, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 37, 39, 51, 58], "spectral_r": [43, 50, 55], "sphinx": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61], "sphinx_gallery_thumbnail_numb": [50, 55], "sphinxcontrib": 61, "spread": [45, 50, 66], "springer": 68, "sqrt": [36, 51], "squeez": [55, 58, 59], "st": 68, "stack": 55, "stamataki": 68, "stand": [43, 45, 47], "standard": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 38, 68], "stark": 68, "start": [40, 43, 45, 46, 47, 58, 65], "stat": [9, 30], "state": [46, 62, 68], "static": [59, 68], "static_argnum": 51, "statist": [16, 30, 55, 56, 58, 63, 67, 68], "step": [55, 61], "still": 68, "stochast": 68, "storag": 62, "store": 46, "str": [9, 44, 55], "stramaglia": 68, "strang": 68, "strategi": [28, 62], "strength": [44, 58, 68], "stroger": 46, "strongest": 66, "strongli": 66, "structur": [65, 68], "studen": 68, "studi": [46, 62, 65, 68], "style": [35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 50, 55, 58, 59, 63, 65], "subgroup": 47, "subplot": [36, 58], "subselect": 55, "subset": [16, 43, 44, 45, 47, 68], "subtl": [45, 47], "subtract": 44, "success": 68, "suffer": 66, "suggest": [51, 61, 68], "sum": [22, 30, 44, 46, 51, 62, 68], "sum_": [14, 15, 16, 18, 19, 22, 25, 43, 44, 45, 68], "summari": 66, "sun": [14, 68], "suptitl": [37, 39], "sure": 61, "surround": 55, "susann": 68, "swinnei": 68, "switch": 59, "symmetr": [36, 68], "syn": [24, 46, 47, 58, 68], "syn_result": 46, "sync": 61, "synergi": [14, 15, 16, 18, 19, 20, 23, 24, 26, 27, 29, 33, 42, 43, 44, 48, 50, 57, 58, 60, 62, 66, 67], "synergist": [19, 45, 46, 47, 50, 55, 58, 62, 66, 68], "synergy_phiid": 46, "synergymmi": [47, 68], "synergyphiid": [46, 68], "synmmi": 47, "synphiidmmi": 46, "synsum": 19, "system": [44, 59, 62, 65, 66, 68], "t": [21, 24, 36, 37, 38, 39, 43, 46, 55, 58, 65, 68], "t1": 51, "t2": 51, "t_end": 58, "t_start": 58, "tabl": [43, 44, 45, 46, 47, 50, 55, 66], "take": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 40, 44, 45, 46, 47, 51, 59, 65, 68], "taken": [51, 65], "tapia": [16, 68], "target": [5, 15, 27, 47, 58, 59, 62, 68], "task": [14, 15, 18, 22, 25], "tau": [21, 24, 46, 68], "taxonomi": 68, "tc": [18, 22, 68], "tdmi": 68, "te": [14, 68], "technic": 68, "techniqu": 62, "tempor": 68, "tend": [44, 66], "term": [44, 59, 66, 68], "termin": 66, "test": [51, 61, 68], "tests_entropi": 61, "text": [55, 59], "th": [10, 35, 36, 37, 38, 39, 68], "tha": 59, "than": [45, 59, 62, 65, 68], "thei": 68, "them": [40, 46, 58, 68], "theme": 61, "theoret": [0, 11, 12, 15, 32, 33, 34, 35, 36, 37, 38, 39, 41, 57, 60, 63, 65, 66, 67], "theori": [40, 43, 62, 66, 68], "therefor": [44, 51, 55, 59], "thi": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 62, 65, 66, 68], "thick": 55, "thing": [43, 51], "thoma": 68, "those": [43, 66], "though": 68, "three": [59, 62, 65, 66], "threshold": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "through": [40, 68], "tight_layout": [37, 39], "tim": 68, "time": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65, 68], "timeit": 51, "timings_cpu": 65, "timings_gpu": 65, "timm": [19, 68], "tishbi": 68, "titl": [35, 36, 37, 38, 39, 44, 55, 58, 59, 65], "to_max": 31, "to_min": 31, "togeth": [59, 62, 66], "toi": [65, 66], "toler": 62, "tolist": 50, "toma": 68, "tool": [65, 68], "toolbox": [65, 68], "top": [61, 63, 66], "topolog": [16, 18, 26, 29, 33, 42, 48, 55, 67], "total": [5, 14, 17, 18, 19, 22, 25, 30, 35, 36, 37, 38, 39, 40, 41, 43, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 58, 59, 60, 67], "toward": [35, 37, 38, 39, 68], "tpu": [63, 65], "tqdm": 64, "tr": 68, "tradit": 62, "tradition": 66, "transact": 68, "transmit": 62, "transpos": 36, "trend": 68, "trial": 55, "trial_block": 58, "triplet": [27, 43, 44, 45, 47, 50, 55, 59], "triplet_charact": [27, 59, 66], "true": [5, 8, 26, 27, 28, 37, 39, 40, 50, 58, 59], "try": 58, "tup": 46, "turbo": [45, 47], "tutori": [35, 38, 39, 40, 51, 59, 60, 67, 68], "twice": 51, "two": [38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 58, 59, 62, 68], "type": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 43, 44, 61, 66, 68], "u": [35, 36, 38, 58, 64, 66], "u_x": 58, "uncertainti": [62, 68], "under": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 46, 68], "underli": 68, "undersampl": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 43, 45, 47], "understand": [62, 68], "understood": [14, 62], "undirect": [62, 68], "uniform": [36, 40, 46, 68], "uniqu": [30, 51, 58, 62], "unit": [40, 63, 68], "univari": 58, "unveil": 68, "up": [50, 63, 65], "updat": [51, 66], "upmanu": 68, "upper": [35, 36, 37, 38, 39, 68], "upstream": 61, "url": 68, "us": [5, 6, 9, 10, 17, 30, 35, 36, 37, 38, 39, 40, 45, 46, 47, 50, 59, 62, 63, 64, 65, 66, 68], "use_sklearn": 28, "user": 66, "usual": 66, "util": [32, 38, 43, 44, 45, 46, 47, 50, 55, 66], "v": [15, 33, 57, 60, 61, 67, 68], "vaadia": 68, "vajda": 68, "valu": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 59, 68], "vari": [35, 37, 38, 39, 59], "variabl": [11, 12, 14, 15, 16, 17, 19, 21, 24, 25, 27, 28, 29, 36, 37, 38, 39, 40, 44, 45, 46, 47, 58, 59, 62, 65, 66, 68], "varianc": [37, 39, 40, 68], "variat": 68, "varibl": 46, "variou": [11, 33, 34, 36, 37, 38, 39, 41, 66, 67, 68], "varlei": 68, "vast": 68, "ve": 51, "vec": [37, 39], "vejnarov": 68, "verbos": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 55, 58, 65], "veri": [40, 45, 46, 47], "version": [62, 64], "via": 68, "virgil": 68, "visit": 68, "visual": 50, "vito": 68, "vmap": 65, "vogt": 68, "vulner": 68, "wa": [47, 62], "wai": [45, 46, 47, 59, 62, 64, 68], "want": [44, 51, 61, 66], "watab": 25, "watanab": 68, "we": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 65, 66, 68], "web": [61, 68], "well": [36, 62, 66, 68], "were": 68, "weslei": 68, "what": [30, 44, 59, 62], "when": [19, 27, 35, 36, 37, 38, 39, 44, 46, 47, 55, 58, 59, 62, 65, 68], "where": [40, 55, 61, 68], "whether": [8, 27, 30, 44, 45, 58, 59, 66, 68], "which": [21, 24, 28, 40, 44, 47, 58, 59, 62, 68], "while": [40, 43, 44, 45, 46, 50, 65], "whole": [44, 46, 68], "wholeminussum": 19, "why": 44, "width": 30, "william": 68, "win": [44, 59], "window": [44, 59], "within": 68, "without": [15, 27, 44], "word": 62, "work": [59, 62, 64, 68], "workspac": 68, "would": 62, "wrap": 51, "write": 51, "written": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 51, 68], "www": [51, 68], "x": [6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 30, 31, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 59, 65, 68], "x_": [14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 37, 43, 44, 45, 46, 47, 58, 68], "x_0": 68, "x_1": [37, 68], "x_2": 37, "x_axi": 55, "x_bin": 28, "x_high": [35, 36, 37, 38, 39], "x_i": [37, 68], "x_j": [14, 44, 68], "x_jax": 51, "x_low": [35, 36, 37, 38, 39], "x_m": 58, "x_n": [37, 68], "x_np": 51, "x_red": 58, "x_ref": 59, "x_syn": 58, "x_t": [21, 24, 46, 68], "xarrai": [30, 61, 64], "xgi": 50, "xi": [37, 39], "xla": 65, "xlabel": [35, 36, 38, 44, 47, 55, 59, 65], "xlim": 59, "xn": 31, "xtick": 55, "y": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 37, 38, 39, 40, 44, 45, 46, 47, 59, 68], "y_": [21, 24, 46, 58, 68], "y_jax": 51, "y_norm": 58, "y_np": 51, "y_red": 58, "y_syn": 58, "y_t": [21, 24, 46, 68], "yamir": 68, "year": 68, "yi": 39, "ylabel": [35, 36, 38, 44, 47, 55, 58, 59, 65], "ylim": 59, "you": [40, 45, 46, 47, 50, 51, 61, 64, 66], "young": 68, "your": [51, 61, 65, 66], "your_usernam": 61, "yuri": 68, "z": 68, "ze": 68, "zero": [30, 35, 36, 37, 38, 39, 40, 46, 58], "zini": 68, "zip": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65], "\u00e1": 68, "\u00e8": 68, "\u00e9": 68, "\u00f3": 68, "\u00f6": 68, "\u0142": 68, "\u017c": 68, "\u03c3": 35}, "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_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", "Introduction to core information theoretical metrics", "Computation times", "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", "Quick introduction to jax", "Computation times", "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", "Glossary", "HOI : High-Performance Estimation of Higher-Order Interactions", "Installation", "Jax: linear algebra backend", "Quickstart", "Computation times", "Theoretical background"], "titleterms": {"": [44, 68], "For": 51, "algebra": 65, "an": 35, "approach": [55, 58], "arrai": 65, "backend": 65, "background": 68, "behavior": [1, 44, 59, 68], "bibliographi": 68, "bootstrap": [33, 54, 55], "class": 32, "code": [44, 61], "combin": [5, 44, 45, 46, 47], "combinatori": 0, "comparison": [35, 36, 37, 38, 39, 65], "compil": 51, "comput": [41, 48, 52, 53, 55, 56, 60, 65, 66, 67], "condit": 43, "confid": 55, "contribut": 61, "copi": 59, "core": [0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 68], "correl": [44, 68], "cpu": 65, "data": [35, 37, 38, 39, 44, 50, 58, 66], "decod": 58, "decomposit": [46, 68], "definit": [35, 36, 37, 38, 39, 45, 46, 47], "depend": 64, "deriv": 44, "develop": 61, "digit": 28, "dimension": [37, 39, 65], "distribut": [35, 37, 38, 39], "document": 61, "dtc": [14, 44], "dual": [44, 68], "dynam": [44, 59], "encod": [1, 44, 59, 68], "entropi": [0, 33, 34, 35, 36, 37, 40, 65, 68], "entropy_bin": 6, "entropy_gauss": 7, "entropy_gc": 8, "entropy_kernel": 9, "entropy_knn": 10, "estim": [35, 36, 37, 38, 39, 50, 55, 63], "exampl": [11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 33], "exponenti": 35, "from": [35, 37, 38, 39, 68], "function": [32, 51], "get": 50, "get_entropi": 11, "get_mi": 12, "get_nbest_mult": 29, "glossari": 62, "gpu": 65, "gradient": 68, "gradientoinfo": 15, "high": [37, 39, 63], "higher": [50, 55, 63, 65, 66, 68], "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, 33, 42, 50, 58, 61, 63], "how": 59, "index": [45, 68], "individu": 50, "inform": [0, 33, 34, 38, 40, 43, 44, 46, 55, 58, 68], "infotopo": 16, "infotot": 17, "inspect": [50, 66], "instal": [61, 64, 66], "integr": 46, "integra": 68, "interact": [43, 50, 63, 65, 66, 68], "interv": 55, "introduct": [40, 51], "isol": 43, "its": 44, "jax": [51, 65], "jit": 51, "landscap": [30, 50], "larg": 65, "learn": 58, "linear": 65, "list": 32, "loop": 51, "machin": 58, "measur": [0, 68], "metric": [1, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 40, 42], "mi": [38, 39, 68], "miscellan": [33, 49], "mmi": [47, 68], "modul": 51, "multi": 65, "multinorm": [37, 39], "multiplet": [43, 50, 65], "multivari": [36, 44, 45, 47], "mutual": [0, 33, 34, 38, 40, 68], "network": [1, 44, 68], "normal": [31, 35, 36, 38], "numpi": 51, "o": [43, 44, 55, 68], "oinfo": 18, "oper": 59, "order": [43, 50, 55, 63, 65, 66, 68], "pairwis": 68, "perform": [63, 65], "permut": [33, 54], "plot": [2, 26, 50, 55], "plot_landscap": 26, "postprocess": 4, "practic": 66, "prepare_for_it": 13, "preprocess": 4, "problem": 43, "pull": 61, "quick": 51, "quickstart": 66, "recommend": 66, "redund": [43, 44, 45, 46, 47, 55, 59, 68], "redundancymmi": 20, "redundancyphiid": 21, "request": 61, "result": [50, 66], "rsi": [19, 68], "sampl": [35, 37, 38, 39], "simul": [3, 27, 43, 44, 45, 46, 47, 50, 58, 59, 66], "simulate_hoi_gauss": 27, "sinfo": 22, "spatial": 43, "split": 39, "spread": [43, 55], "statist": [33, 54], "sum": 59, "summari": 50, "synergi": [45, 46, 47, 55, 59, 68], "synergist": [43, 44, 59], "synergymmi": 23, "synergyphiid": 24, "target": 44, "tc": [25, 44], "theoret": [40, 58, 68], "time": [41, 48, 52, 53, 56, 60, 67], "topolog": [43, 68], "total": [44, 68], "tutori": [33, 57], "uniform": 35, "univari": [45, 47], "us": [11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 43, 44, 51, 55, 58, 61], "user": 64, "util": [4, 28, 29, 30, 31], "v": [58, 65], "variou": 35, "vector": 51, "vmap": 51, "x": 58, "y": 58}})
\ No newline at end of file
+Search.setIndex({"alltitles": {"Bibliography": [[68, "bibliography"]], "Bootstrapping and confidence interval": [[55, null]], "CPU vs. GPU : Performance comparison": [[65, "cpu-vs-gpu-performance-comparison"]], "Combinatory": [[0, "combinatory"]], "Combining redundancy and synergy": [[45, "combining-redundancy-and-synergy"], [46, "combining-redundancy-and-synergy"], [47, "combining-redundancy-and-synergy"]], "Combining redundant and synergistic codings using a multivariate target": [[44, "combining-redundant-and-synergistic-codings-using-a-multivariate-target"]], "Comparison of MI estimators with high-dimensional data": [[39, null]], "Comparison of entropy estimators for a multivariate normal": [[36, null]], "Comparison of entropy estimators for various distributions": [[35, null]], "Comparison of entropy estimators with high-dimensional data": [[37, null]], "Comparison of estimators": [[36, "comparison-of-estimators"]], "Comparison of mutual-information estimators": [[38, null]], "Compiling functions using jit": [[51, "compiling-functions-using-jit"]], "Computation times": [[41, null], [48, null], [52, null], [53, null], [56, null], [60, null], [67, null]], "Compute Higher-Order Interactions": [[66, "compute-higher-order-interactions"]], "Compute bootstrap": [[55, "compute-bootstrap"]], "Computing Higher-Order Interactions on large multiplets": [[65, "computing-higher-order-interactions-on-large-multiplets"]], "Computing entropy on large multi-dimensional arrays": [[65, "computing-entropy-on-large-multi-dimensional-arrays"]], "Contributing code using pull requests": [[61, "contributing-code-using-pull-requests"]], "Contributing to HOI": [[61, "contributing-to-hoi"]], "Core information theoretic measures": [[68, "core-information-theoretic-measures"]], "Data simulation": [[44, "data-simulation"], [58, "data-simulation"]], "Decoding Y using X": [[58, "decoding-y-using-x"]], "Definition": [[45, "definition"], [46, "definition"], [47, "definition"]], "Definition of MI estimators": [[38, "definition-of-mi-estimators"], [39, "definition-of-mi-estimators"]], "Definition of entropy estimators": [[37, "definition-of-entropy-estimators"]], "Definition of estimators of entropy": [[35, "definition-of-estimators-of-entropy"], [36, "definition-of-estimators-of-entropy"]], "Dependencies": [[64, "dependencies"]], "Developer Documentation": [[61, null]], "Dual Total Correlation (DTC)": [[44, "dual-total-correlation-dtc"]], "Dual Total correlation": [[68, "dual-total-correlation"]], "Dynamic redundant and synergistic codings": [[44, "dynamic-redundant-and-synergistic-codings"]], "Entropy": [[40, "entropy"]], "Entropy and mutual information": [[33, "entropy-and-mutual-information"], [34, null]], "Entropy of data sampled from a uniform distribution": [[35, "entropy-of-data-sampled-from-a-uniform-distribution"]], "Entropy of data sampled from an exponential distribution": [[35, "entropy-of-data-sampled-from-an-exponential-distribution"]], "Entropy of data sampled from multinormal distribution": [[37, "entropy-of-data-sampled-from-multinormal-distribution"]], "Entropy of data sampled from normal distribution": [[35, "entropy-of-data-sampled-from-normal-distribution"]], "Estimate HOI": [[50, "estimate-hoi"]], "Estimation of the confidence interval using a bootstrapping approach": [[55, "estimation-of-the-confidence-interval-using-a-bootstrapping-approach"]], "Examples": [[33, null]], "Examples using hoi.core.get_entropy": [[11, "examples-using-hoi-core-get-entropy"]], "Examples using hoi.core.get_mi": [[12, "examples-using-hoi-core-get-mi"]], "Examples using hoi.metrics.DTC": [[14, "examples-using-hoi-metrics-dtc"]], "Examples using hoi.metrics.GradientOinfo": [[15, "examples-using-hoi-metrics-gradientoinfo"]], "Examples using hoi.metrics.InfoTopo": [[16, "examples-using-hoi-metrics-infotopo"]], "Examples using hoi.metrics.Oinfo": [[18, "examples-using-hoi-metrics-oinfo"]], "Examples using hoi.metrics.RSI": [[19, "examples-using-hoi-metrics-rsi"]], "Examples using hoi.metrics.RedundancyMMI": [[20, "examples-using-hoi-metrics-redundancymmi"]], "Examples using hoi.metrics.RedundancyphiID": [[21, "examples-using-hoi-metrics-redundancyphiid"]], "Examples using hoi.metrics.Sinfo": [[22, "examples-using-hoi-metrics-sinfo"]], "Examples using hoi.metrics.SynergyMMI": [[23, "examples-using-hoi-metrics-synergymmi"]], "Examples using hoi.metrics.SynergyphiID": [[24, "examples-using-hoi-metrics-synergyphiid"]], "Examples using hoi.metrics.TC": [[25, "examples-using-hoi-metrics-tc"]], "Examples using hoi.plot.plot_landscape": [[26, "examples-using-hoi-plot-plot-landscape"]], "Examples using hoi.simulation.simulate_hoi_gauss": [[27, "examples-using-hoi-simulation-simulate-hoi-gauss"]], "Examples using hoi.utils.digitize": [[28, "examples-using-hoi-utils-digitize"]], "Examples using hoi.utils.get_nbest_mult": [[29, "examples-using-hoi-utils-get-nbest-mult"]], "For loops with jax": [[51, "for-loops-with-jax"]], "From pairwise to higher-order interactions": [[68, "from-pairwise-to-higher-order-interactions"]], "Get a summary of the results": [[50, "get-a-summary-of-the-results"]], "Glossary": [[62, null]], "Gradient of O-information": [[68, "gradient-of-o-information"]], "HOI : High-Performance Estimation of Higher-Order Interactions": [[63, null]], "How to simulate redundancy and synergy": [[59, null]], "Inspect and plot Higher-Order Interactions": [[50, null]], "Inspect the results": [[66, "inspect-the-results"]], "Installation": [[64, null], [66, "installation"]], "Installation for developers": [[61, "installation-for-developers"]], "Integrated Information Decomposition": [[46, null]], "Introduction to core information theoretical metrics": [[40, null]], "Jax.numpy module": [[51, "jax-numpy-module"]], "Jax: linear algebra backend": [[65, null]], "Landscape plot": [[50, "landscape-plot"]], "List of classes and functions": [[32, null]], "MI of data sampled from normal distribution": [[38, "mi-of-data-sampled-from-normal-distribution"]], "MI of data sampled from splitted multinormal distribution": [[39, "mi-of-data-sampled-from-splitted-multinormal-distribution"]], "Machine-learning vs. Information theoretic approaches for HOI": [[58, null]], "Measures of Entropy": [[0, "measures-of-entropy"]], "Measures of Mutual Information": [[0, "measures-of-mutual-information"]], "Measuring Entropy": [[68, "measuring-entropy"]], "Measuring Mutual Information (MI)": [[68, "measuring-mutual-information-mi"]], "Metrics of HOI": [[33, "metrics-of-hoi"], [42, null]], "Miscellaneous": [[33, "miscellaneous"], [49, null]], "Multiplet isolation using the Topological Information": [[43, "multiplet-isolation-using-the-topological-information"]], "Mutual information": [[40, "mutual-information"]], "Network behavior": [[1, "network-behavior"], [68, "network-behavior"]], "Network encoding": [[1, "network-encoding"], [68, "network-encoding"]], "O-information": [[44, "o-information"], [68, "o-information"]], "O-information : Redundancy and synergy spread to higher orders": [[55, "o-information-redundancy-and-synergy-spread-to-higher-orders"]], "O-information and its derivatives for network behavior and encoding": [[44, null]], "O-information for network behavior": [[44, "o-information-for-network-behavior"]], "O-information for network encoding": [[44, "o-information-for-network-encoding"]], "Plot the O-information with the confidence interval": [[55, "plot-the-o-information-with-the-confidence-interval"]], "Plotting individual multiplets": [[50, "plotting-individual-multiplets"]], "Postprocessing": [[4, "postprocessing"]], "Practical recommendations": [[66, "practical-recommendations"]], "Preprocessing": [[4, "preprocessing"]], "Quick introduction to jax": [[51, null]], "Quickstart": [[66, null]], "Redundancy and Synergy MMI": [[47, null]], "Redundancy-Synergy Index": [[45, null]], "Redundancy-Synergy index (RSI)": [[68, "redundancy-synergy-index-rsi"]], "Redundant and synergistic behavior": [[59, "redundant-and-synergistic-behavior"]], "Redundant and synergistic encoding": [[59, "redundant-and-synergistic-encoding"]], "S information": [[68, "s-information"]], "S-information": [[44, "s-information"]], "Simulate data": [[50, "simulate-data"], [66, "simulate-data"]], "Simulate multivariate redundancy": [[45, "simulate-multivariate-redundancy"], [47, "simulate-multivariate-redundancy"]], "Simulate redundancy": [[46, "simulate-redundancy"]], "Simulate redundant and synergistic interactions": [[43, "simulate-redundant-and-synergistic-interactions"]], "Simulate synergy": [[46, "simulate-synergy"]], "Simulate univariate and multivariate synergy": [[45, "simulate-univariate-and-multivariate-synergy"], [47, "simulate-univariate-and-multivariate-synergy"]], "Simulate univariate redundancy": [[45, "simulate-univariate-redundancy"], [47, "simulate-univariate-redundancy"]], "Simulating dynamic redundancy and synergy": [[59, "simulating-dynamic-redundancy-and-synergy"]], "Simulating dynamic redundant and synergistic encoding": [[59, "simulating-dynamic-redundant-and-synergistic-encoding"]], "Simulating redundant behavior": [[59, "simulating-redundant-behavior"]], "Simulating redundant behavior by copy operator": [[59, "simulating-redundant-behavior-by-copy-operator"]], "Simulating redundant encoding": [[44, "simulating-redundant-encoding"], [59, "simulating-redundant-encoding"]], "Simulating redundant encoding by copy operation": [[59, "simulating-redundant-encoding-by-copy-operation"]], "Simulating synergistic behavior": [[59, "simulating-synergistic-behavior"]], "Simulating synergistic behavior by sum operation": [[59, "simulating-synergistic-behavior-by-sum-operation"]], "Simulating synergistic encoding": [[44, "simulating-synergistic-encoding"], [59, "simulating-synergistic-encoding"]], "Simulating synergistic encoding by sum operation": [[59, "simulating-synergistic-encoding-by-sum-operation"]], "Spatial spreading : the problem with the O-information": [[43, "spatial-spreading-the-problem-with-the-o-information"]], "Statistics : bootstrapping and permutations": [[33, "statistics-bootstrapping-and-permutations"], [54, null]], "Synergy and redundancy (MMI)": [[68, "synergy-and-redundancy-mmi"]], "Synergy and redundancy integraed Information Decomposition (MMI)": [[68, "synergy-and-redundancy-integraed-information-decomposition-mmi"]], "Theoretical background": [[68, null]], "Topological Information : conditioning on orders": [[43, null]], "Topological information": [[68, "topological-information"]], "Total Correlation (TC)": [[44, "total-correlation-tc"]], "Total correlation": [[68, "total-correlation"]], "Tutorials": [[33, "tutorials"], [57, null]], "User installation": [[64, "user-installation"]], "Using information-theoretic approaches": [[58, "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_kernel": [[9, null]], "hoi.core.entropy_knn": [[10, null]], "hoi.core.get_entropy": [[11, null]], "hoi.core.get_mi": [[12, null]], "hoi.core.prepare_for_it": [[13, null]], "hoi.metrics": [[1, null]], "hoi.metrics.DTC": [[14, null]], "hoi.metrics.GradientOinfo": [[15, null]], "hoi.metrics.InfoTopo": [[16, null]], "hoi.metrics.InfoTot": [[17, null]], "hoi.metrics.Oinfo": [[18, null]], "hoi.metrics.RSI": [[19, null]], "hoi.metrics.RedundancyMMI": [[20, null]], "hoi.metrics.RedundancyphiID": [[21, null]], "hoi.metrics.Sinfo": [[22, null]], "hoi.metrics.SynergyMMI": [[23, null]], "hoi.metrics.SynergyphiID": [[24, null]], "hoi.metrics.TC": [[25, null]], "hoi.plot": [[2, null]], "hoi.plot.plot_landscape": [[26, null]], "hoi.simulation": [[3, null]], "hoi.simulation.simulate_hoi_gauss": [[27, null]], "hoi.utils": [[4, null]], "hoi.utils.digitize": [[28, null]], "hoi.utils.get_nbest_mult": [[29, null]], "hoi.utils.landscape": [[30, null]], "hoi.utils.normalize": [[31, null]], "vmap : vectorize a function": [[51, "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_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/plot_tutorial_core", "auto_examples/it/sg_execution_times", "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/plot_jax", "auto_examples/miscellaneous/sg_execution_times", "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", "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_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/plot_tutorial_core.rst", "auto_examples/it/sg_execution_times.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/plot_jax.rst", "auto_examples/miscellaneous/sg_execution_times.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", "glossary.rst", "index.rst", "install.rst", "jax.rst", "quickstart.rst", "sg_execution_times.rst", "theory.rst"], "indexentries": {"__iter__() (hoi.metrics.dtc method)": [[14, "hoi.metrics.DTC.__iter__", false]], "__iter__() (hoi.metrics.gradientoinfo method)": [[15, "hoi.metrics.GradientOinfo.__iter__", false]], "__iter__() (hoi.metrics.infotopo method)": [[16, "hoi.metrics.InfoTopo.__iter__", false]], "__iter__() (hoi.metrics.infotot method)": [[17, "hoi.metrics.InfoTot.__iter__", false]], "__iter__() (hoi.metrics.oinfo method)": [[18, "hoi.metrics.Oinfo.__iter__", false]], "__iter__() (hoi.metrics.redundancymmi method)": [[20, "hoi.metrics.RedundancyMMI.__iter__", false]], "__iter__() (hoi.metrics.redundancyphiid method)": [[21, "hoi.metrics.RedundancyphiID.__iter__", false]], "__iter__() (hoi.metrics.rsi method)": [[19, "hoi.metrics.RSI.__iter__", false]], "__iter__() (hoi.metrics.sinfo method)": [[22, "hoi.metrics.Sinfo.__iter__", false]], "__iter__() (hoi.metrics.synergymmi method)": [[23, "hoi.metrics.SynergyMMI.__iter__", false]], "__iter__() (hoi.metrics.synergyphiid method)": [[24, "hoi.metrics.SynergyphiID.__iter__", false]], "__iter__() (hoi.metrics.tc method)": [[25, "hoi.metrics.TC.__iter__", false]], "combinations() (in module hoi.core)": [[5, "hoi.core.combinations", false]], "compute_entropies() (hoi.metrics.dtc method)": [[14, "hoi.metrics.DTC.compute_entropies", false]], "compute_entropies() (hoi.metrics.gradientoinfo method)": [[15, "hoi.metrics.GradientOinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.infotopo method)": [[16, "hoi.metrics.InfoTopo.compute_entropies", false]], "compute_entropies() (hoi.metrics.infotot method)": [[17, "hoi.metrics.InfoTot.compute_entropies", false]], "compute_entropies() (hoi.metrics.oinfo method)": [[18, "hoi.metrics.Oinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.redundancymmi method)": [[20, "hoi.metrics.RedundancyMMI.compute_entropies", false]], "compute_entropies() (hoi.metrics.redundancyphiid method)": [[21, "hoi.metrics.RedundancyphiID.compute_entropies", false]], "compute_entropies() (hoi.metrics.rsi method)": [[19, "hoi.metrics.RSI.compute_entropies", false]], "compute_entropies() (hoi.metrics.sinfo method)": [[22, "hoi.metrics.Sinfo.compute_entropies", false]], "compute_entropies() (hoi.metrics.synergymmi method)": [[23, "hoi.metrics.SynergyMMI.compute_entropies", false]], "compute_entropies() (hoi.metrics.synergyphiid method)": [[24, "hoi.metrics.SynergyphiID.compute_entropies", false]], "compute_entropies() (hoi.metrics.tc method)": [[25, "hoi.metrics.TC.compute_entropies", false]], "digitize() (in module hoi.utils)": [[28, "hoi.utils.digitize", false]], "dtc (class in hoi.metrics)": [[14, "hoi.metrics.DTC", false]], "entropies (hoi.metrics.dtc property)": [[14, "hoi.metrics.DTC.entropies", false]], "entropies (hoi.metrics.gradientoinfo property)": [[15, "hoi.metrics.GradientOinfo.entropies", false]], "entropies (hoi.metrics.infotopo property)": [[16, "hoi.metrics.InfoTopo.entropies", false]], "entropies (hoi.metrics.infotot property)": [[17, "hoi.metrics.InfoTot.entropies", false]], "entropies (hoi.metrics.oinfo property)": [[18, "hoi.metrics.Oinfo.entropies", false]], "entropies (hoi.metrics.redundancymmi property)": [[20, "hoi.metrics.RedundancyMMI.entropies", false]], "entropies (hoi.metrics.redundancyphiid property)": [[21, "hoi.metrics.RedundancyphiID.entropies", false]], "entropies (hoi.metrics.rsi property)": [[19, "hoi.metrics.RSI.entropies", false]], "entropies (hoi.metrics.sinfo property)": [[22, "hoi.metrics.Sinfo.entropies", false]], "entropies (hoi.metrics.synergymmi property)": [[23, "hoi.metrics.SynergyMMI.entropies", false]], "entropies (hoi.metrics.synergyphiid property)": [[24, "hoi.metrics.SynergyphiID.entropies", false]], "entropies (hoi.metrics.tc property)": [[25, "hoi.metrics.TC.entropies", false]], "entropy": [[62, "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_kernel() (in module hoi.core)": [[9, "hoi.core.entropy_kernel", false]], "entropy_knn() (in module hoi.core)": [[10, "hoi.core.entropy_knn", false]], "fit() (hoi.metrics.dtc method)": [[14, "hoi.metrics.DTC.fit", false]], "fit() (hoi.metrics.gradientoinfo method)": [[15, "hoi.metrics.GradientOinfo.fit", false]], "fit() (hoi.metrics.infotopo method)": [[16, "hoi.metrics.InfoTopo.fit", false]], "fit() (hoi.metrics.infotot method)": [[17, "hoi.metrics.InfoTot.fit", false]], "fit() (hoi.metrics.oinfo method)": [[18, "hoi.metrics.Oinfo.fit", false]], "fit() (hoi.metrics.redundancymmi method)": [[20, "hoi.metrics.RedundancyMMI.fit", false]], "fit() (hoi.metrics.redundancyphiid method)": [[21, "hoi.metrics.RedundancyphiID.fit", false]], "fit() (hoi.metrics.rsi method)": [[19, "hoi.metrics.RSI.fit", false]], "fit() (hoi.metrics.sinfo method)": [[22, "hoi.metrics.Sinfo.fit", false]], "fit() (hoi.metrics.synergymmi method)": [[23, "hoi.metrics.SynergyMMI.fit", false]], "fit() (hoi.metrics.synergyphiid method)": [[24, "hoi.metrics.SynergyphiID.fit", false]], "fit() (hoi.metrics.tc method)": [[25, "hoi.metrics.TC.fit", false]], "get_combinations() (hoi.metrics.dtc method)": [[14, "hoi.metrics.DTC.get_combinations", false]], "get_combinations() (hoi.metrics.gradientoinfo method)": [[15, "hoi.metrics.GradientOinfo.get_combinations", false]], "get_combinations() (hoi.metrics.infotopo method)": [[16, "hoi.metrics.InfoTopo.get_combinations", false]], "get_combinations() (hoi.metrics.infotot method)": [[17, "hoi.metrics.InfoTot.get_combinations", false]], "get_combinations() (hoi.metrics.oinfo method)": [[18, "hoi.metrics.Oinfo.get_combinations", false]], "get_combinations() (hoi.metrics.redundancymmi method)": [[20, "hoi.metrics.RedundancyMMI.get_combinations", false]], "get_combinations() (hoi.metrics.redundancyphiid method)": [[21, "hoi.metrics.RedundancyphiID.get_combinations", false]], "get_combinations() (hoi.metrics.rsi method)": [[19, "hoi.metrics.RSI.get_combinations", false]], "get_combinations() (hoi.metrics.sinfo method)": [[22, "hoi.metrics.Sinfo.get_combinations", false]], "get_combinations() (hoi.metrics.synergymmi method)": [[23, "hoi.metrics.SynergyMMI.get_combinations", false]], "get_combinations() (hoi.metrics.synergyphiid method)": [[24, "hoi.metrics.SynergyphiID.get_combinations", false]], "get_combinations() (hoi.metrics.tc method)": [[25, "hoi.metrics.TC.get_combinations", false]], "get_entropy() (in module hoi.core)": [[11, "hoi.core.get_entropy", false]], "get_mi() (in module hoi.core)": [[12, "hoi.core.get_mi", false]], "get_nbest_mult() (in module hoi.utils)": [[29, "hoi.utils.get_nbest_mult", false]], "gradientoinfo (class in hoi.metrics)": [[15, "hoi.metrics.GradientOinfo", false]], "higher order interactions": [[62, "term-Higher-Order-Interactions", true]], "hoi.metrics": [[1, "module-hoi.metrics", false]], "information theory": [[62, "term-Information-Theory", true]], "infotopo (class in hoi.metrics)": [[16, "hoi.metrics.InfoTopo", false]], "infotot (class in hoi.metrics)": [[17, "hoi.metrics.InfoTot", false]], "landscape() (in module hoi.utils)": [[30, "hoi.utils.landscape", false]], "module": [[1, "module-hoi.metrics", false]], "multiplets (hoi.metrics.dtc property)": [[14, "hoi.metrics.DTC.multiplets", false]], "multiplets (hoi.metrics.gradientoinfo property)": [[15, "hoi.metrics.GradientOinfo.multiplets", false]], "multiplets (hoi.metrics.infotopo property)": [[16, "hoi.metrics.InfoTopo.multiplets", false]], "multiplets (hoi.metrics.infotot property)": [[17, "hoi.metrics.InfoTot.multiplets", false]], "multiplets (hoi.metrics.oinfo property)": [[18, "hoi.metrics.Oinfo.multiplets", false]], "multiplets (hoi.metrics.redundancymmi property)": [[20, "hoi.metrics.RedundancyMMI.multiplets", false]], "multiplets (hoi.metrics.redundancyphiid property)": [[21, "hoi.metrics.RedundancyphiID.multiplets", false]], "multiplets (hoi.metrics.rsi property)": [[19, "hoi.metrics.RSI.multiplets", false]], "multiplets (hoi.metrics.sinfo property)": [[22, "hoi.metrics.Sinfo.multiplets", false]], "multiplets (hoi.metrics.synergymmi property)": [[23, "hoi.metrics.SynergyMMI.multiplets", false]], "multiplets (hoi.metrics.synergyphiid property)": [[24, "hoi.metrics.SynergyphiID.multiplets", false]], "multiplets (hoi.metrics.tc property)": [[25, "hoi.metrics.TC.multiplets", false]], "mutual information": [[62, "term-Mutual-Information", true]], "network behavior": [[62, "term-Network-behavior", true]], "network encoding": [[62, "term-Network-encoding", true]], "normalize() (in module hoi.utils)": [[31, "hoi.utils.normalize", false]], "oinfo (class in hoi.metrics)": [[18, "hoi.metrics.Oinfo", false]], "order (hoi.metrics.dtc property)": [[14, "hoi.metrics.DTC.order", false]], "order (hoi.metrics.gradientoinfo property)": [[15, "hoi.metrics.GradientOinfo.order", false]], "order (hoi.metrics.infotopo property)": [[16, "hoi.metrics.InfoTopo.order", false]], "order (hoi.metrics.infotot property)": [[17, "hoi.metrics.InfoTot.order", false]], "order (hoi.metrics.oinfo property)": [[18, "hoi.metrics.Oinfo.order", false]], "order (hoi.metrics.redundancymmi property)": [[20, "hoi.metrics.RedundancyMMI.order", false]], "order (hoi.metrics.redundancyphiid property)": [[21, "hoi.metrics.RedundancyphiID.order", false]], "order (hoi.metrics.rsi property)": [[19, "hoi.metrics.RSI.order", false]], "order (hoi.metrics.sinfo property)": [[22, "hoi.metrics.Sinfo.order", false]], "order (hoi.metrics.synergymmi property)": [[23, "hoi.metrics.SynergyMMI.order", false]], "order (hoi.metrics.synergyphiid property)": [[24, "hoi.metrics.SynergyphiID.order", false]], "order (hoi.metrics.tc property)": [[25, "hoi.metrics.TC.order", false]], "partial information decomposition": [[62, "term-Partial-Information-Decomposition", true]], "plot_landscape() (in module hoi.plot)": [[26, "hoi.plot.plot_landscape", false]], "prepare_for_it() (in module hoi.core)": [[13, "hoi.core.prepare_for_it", false]], "redundancy": [[62, "term-Redundancy", true]], "redundancymmi (class in hoi.metrics)": [[20, "hoi.metrics.RedundancyMMI", false]], "redundancyphiid (class in hoi.metrics)": [[21, "hoi.metrics.RedundancyphiID", false]], "rsi (class in hoi.metrics)": [[19, "hoi.metrics.RSI", false]], "simulate_hoi_gauss() (in module hoi.simulation)": [[27, "hoi.simulation.simulate_hoi_gauss", false]], "sinfo (class in hoi.metrics)": [[22, "hoi.metrics.Sinfo", false]], "synergy": [[62, "term-Synergy", true]], "synergymmi (class in hoi.metrics)": [[23, "hoi.metrics.SynergyMMI", false]], "synergyphiid (class in hoi.metrics)": [[24, "hoi.metrics.SynergyphiID", false]], "tc (class in hoi.metrics)": [[25, "hoi.metrics.TC", false]], "undersampling (hoi.metrics.dtc property)": [[14, "hoi.metrics.DTC.undersampling", false]], "undersampling (hoi.metrics.gradientoinfo property)": [[15, "hoi.metrics.GradientOinfo.undersampling", false]], "undersampling (hoi.metrics.infotopo property)": [[16, "hoi.metrics.InfoTopo.undersampling", false]], "undersampling (hoi.metrics.infotot property)": [[17, "hoi.metrics.InfoTot.undersampling", false]], "undersampling (hoi.metrics.oinfo property)": [[18, "hoi.metrics.Oinfo.undersampling", false]], "undersampling (hoi.metrics.redundancymmi property)": [[20, "hoi.metrics.RedundancyMMI.undersampling", false]], "undersampling (hoi.metrics.redundancyphiid property)": [[21, "hoi.metrics.RedundancyphiID.undersampling", false]], "undersampling (hoi.metrics.rsi property)": [[19, "hoi.metrics.RSI.undersampling", false]], "undersampling (hoi.metrics.sinfo property)": [[22, "hoi.metrics.Sinfo.undersampling", false]], "undersampling (hoi.metrics.synergymmi property)": [[23, "hoi.metrics.SynergyMMI.undersampling", false]], "undersampling (hoi.metrics.synergyphiid property)": [[24, "hoi.metrics.SynergyphiID.undersampling", false]], "undersampling (hoi.metrics.tc property)": [[25, "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_kernel"], [10, 0, 1, "", "entropy_knn"], [11, 0, 1, "", "get_entropy"], [12, 0, 1, "", "get_mi"], [13, 0, 1, "", "prepare_for_it"]], "hoi.metrics": [[14, 2, 1, "", "DTC"], [15, 2, 1, "", "GradientOinfo"], [16, 2, 1, "", "InfoTopo"], [17, 2, 1, "", "InfoTot"], [18, 2, 1, "", "Oinfo"], [19, 2, 1, "", "RSI"], [20, 2, 1, "", "RedundancyMMI"], [21, 2, 1, "", "RedundancyphiID"], [22, 2, 1, "", "Sinfo"], [23, 2, 1, "", "SynergyMMI"], [24, 2, 1, "", "SynergyphiID"], [25, 2, 1, "", "TC"]], "hoi.metrics.DTC": [[14, 3, 1, "", "__iter__"], [14, 3, 1, "", "compute_entropies"], [14, 4, 1, "", "entropies"], [14, 3, 1, "", "fit"], [14, 3, 1, "", "get_combinations"], [14, 4, 1, "", "multiplets"], [14, 4, 1, "", "order"], [14, 4, 1, "", "undersampling"]], "hoi.metrics.GradientOinfo": [[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.InfoTopo": [[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.InfoTot": [[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.Oinfo": [[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.RSI": [[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.RedundancyMMI": [[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.RedundancyphiID": [[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.Sinfo": [[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.SynergyMMI": [[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.SynergyphiID": [[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.TC": [[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.plot": [[26, 0, 1, "", "plot_landscape"]], "hoi.simulation": [[27, 0, 1, "", "simulate_hoi_gauss"]], "hoi.utils": [[28, 0, 1, "", "digitize"], [29, 0, 1, "", "get_nbest_mult"], [30, 0, 1, "", "landscape"], [31, 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": {"": [17, 19, 22, 35, 36, 37, 38, 39, 40, 43, 45, 46, 47, 50, 51, 55, 58, 59, 61, 64, 65], "0": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 31, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 65, 67, 68], "00": [40, 41, 43, 44, 45, 46, 47, 48, 50, 52, 53, 56, 59, 60, 67], "000": 53, "000010": 44, "000020": 44, "000216": 55, "000244": 55, "000275": 44, "000279": 44, "000437": 47, "000492": 44, "000500": 44, "000514": 47, "000553": [44, 47], "000677": 44, "000750": 44, "000798": 43, "000956": 55, "000992": 44, "001097": 43, "001109": 44, "001119": 44, "001132": 50, "001365": 44, "001399": 50, "001470": 43, "001529": 44, "001593": 50, "001671": 50, "001686": 44, "001733": 44, "001762": 50, "001798": 43, "001949": 43, "001978": 44, "001982": 44, "002075": 44, "002183": 45, "002257": 47, "002429": 44, "002511": 50, "002733": 45, "002877": 45, "003223": 45, "003272": 45, "003286": 44, "003959": 44, "004202": 50, "004351": 50, "006850": 45, "008015": 45, "008041": 45, "008269": 45, "008682": 47, "01": [43, 48, 50, 52, 67], "010": 67, "010041": 46, "010094": 45, "012916": 47, "013025": 68, "014083": 45, "016348": 46, "017187": 45, "017516": 46, "01it": 47, "02": [48, 52, 67], "03": [48, 67], "032305": 68, "032673": 46, "03it": 47, "04": [60, 67], "04it": 45, "05": 46, "051622": 43, "052802": 68, "055452": 43, "066138": 68, "07140": 68, "079220": 43, "08": [60, 67], "087119": 44, "088506": 44, "08it": 44, "098192": 43, "09it": 45, "1": [5, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 31, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 56, 58, 59, 61, 64, 65, 68], "10": [19, 35, 36, 37, 38, 39, 44, 45, 47, 50, 51, 55, 65, 68], "100": [30, 37, 43, 44, 45, 46, 47, 50, 58, 59, 65, 68], "1000": [27, 35, 36, 38, 39, 40, 43, 44, 51, 55, 59, 65, 66], "10000": [37, 39], "100000": 51, "1004": 68, "106": 68, "107": 35, "1093": 68, "109416": 50, "1098": 68, "1099": 68, "10e2": 65, "10it": 44, "11": [44, 47, 50, 55, 65, 68], "1103": 68, "1134": 68, "119": 68, "11it": 43, "12": [19, 40, 44, 45, 51, 55, 58, 68], "12482": 68, "13": [44, 45, 50, 55, 60, 65, 68], "1315": 68, "13186": 68, "1321": 68, "133": 68, "13637": 68, "14": [22, 36, 43, 45, 47, 50, 55, 68], "140": 68, "14it": 59, "15": [35, 44, 45, 48, 55, 56, 65, 67, 68], "152": 68, "152436": 43, "1541": 68, "156": 68, "157": [35, 41, 67], "1573": 68, "159": 68, "15it": 59, "16": [38, 41, 44, 45, 55, 67, 68], "16it": 43, "17": [24, 35, 41, 44, 45, 50, 55, 67, 68], "17019176483154297": 59, "172979": 47, "174389": 44, "177": 68, "178324": 43, "179585": 43, "179876": 43, "179893": 43, "18": [44, 45, 47, 51, 55, 62, 68], "180534": 43, "180660": 43, "18it": 59, "19": [21, 44, 47, 50, 55, 67, 68], "190": [46, 68], "192595": 44, "1940": 62, "1948": 68, "195104": 44, "195410": 45, "195496": 45, "195716": 44, "195971": 44, "1960": [25, 68], "196016": 44, "196290": 50, "1963": 68, "1975": 68, "1978": [14, 68], "1986": 68, "1995": 68, "1998": 68, "1999": 68, "2": [6, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 52, 55, 58, 59, 60, 63, 65, 68], "20": [35, 36, 38, 40, 43, 44, 45, 46, 47, 51, 55, 59, 68], "200": [45, 46, 47, 50, 55], "2001": [19, 68], "2003": 68, "2004": [10, 68], "2005": 68, "2009": 68, "2010": 68, "2011": [22, 68], "2014": [19, 68], "2015": 68, "2017": 68, "2018": [16, 68], "2019": [16, 18, 43, 44, 68], "2020": 68, "2021": [21, 68], "20210246": 68, "2022": [24, 68], "2023": [15, 39, 68], "2024": 68, "20th": 68, "21": [45, 68], "2109": 68, "216": 51, "217146": 55, "217600": 55, "21it": 59, "22": [37, 41, 45, 62, 64, 67, 68], "22015380859375": 59, "22138118743896484": 59, "222631": 50, "2227": 68, "223212242126465": 59, "224163": 44, "229": [40, 41, 67], "23": [45, 68], "2304": 68, "231269": 45, "2318": 68, "232957": 45, "238000": 45, "238701": 68, "23it": 45, "24": [18, 36, 41, 44, 50, 67, 68], "2404": 68, "246747": 45, "247822": 45, "25": [15, 45, 51, 68], "250811": 44, "2515": 68, "251705": 44, "26": [19, 47, 68], "260": [51, 52, 67], "261": 68, "2678242389993102": 51, "26it": [43, 50], "27": [45, 47, 50, 51, 62, 68], "279959": 45, "27it": [44, 59], "28": [45, 68], "280932": 45, "28618431091308594": 59, "289336": 45, "29": [43, 68], "292": [55, 56, 67], "297": 68, "29it": 45, "2d": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 51], "2f": 40, "2\u03c0e": 36, "2\u03c0e\u03c3": 35, "3": [10, 27, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 62, 64, 65, 66, 68], "30": [16, 44, 47, 50, 51, 59, 68], "300": 58, "31": [14, 35, 41, 43, 45, 68], "31it": 59, "32": [19, 43, 68], "33": [43, 45, 47, 50, 51, 62, 68], "335781": 47, "337": 68, "3390": 68, "33it": 50, "34": [45, 62, 68], "34401702880859375": 59, "3490": 68, "3495": 68, "349639": 44, "35": 68, "35it": 43, "36": [25, 51, 68], "362484": 43, "362663": 43, "362667": 43, "363335": 43, "363861": 43, "37": [43, 62, 68], "3766": 68, "377251": 47, "3779": 68, "379": 68, "38": [43, 68], "380": 68, "388": [39, 41, 67], "38it": 45, "39": [39, 41, 67], "391648": 45, "3d": 51, "4": [16, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 65, 66, 68], "40": [43, 58], "401570": 47, "401695": 47, "405968": 44, "40it": 59, "41": 43, "416784": 47, "418695": 46, "42": [39, 41, 50, 59, 67], "423": 68, "42it": [43, 46], "43": 43, "4300": 68, "434": [43, 48, 67], "447428": 44, "44it": 59, "45": [55, 68], "453753": 45, "45it": [45, 59], "461383": 45, "461864": 45, "462532": 47, "46it": 47, "476156": 47, "476842": 44, "476857": 44, "476879": 44, "476956": 44, "477410": 44, "478775": 44, "488034": 45, "488635": 47, "492": [46, 48, 67], "49it": [44, 45], "5": [19, 29, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 50, 55, 58, 59, 65, 68], "50": [44, 50, 58, 59], "502848": 45, "50it": [43, 44], "51": 68, "513817": 45, "52": 68, "528": 48, "52it": [46, 59], "53": [37, 41, 67], "53it": 47, "54": 51, "547": [36, 41, 67], "54it": 43, "550452": 47, "55it": 43, "57": 43, "5714287757873535": 51, "582": 60, "5857861679996859": 51, "590573": 45, "6": [36, 37, 39, 40, 41, 43, 44, 45, 46, 47, 50, 51, 55, 59, 65, 68], "60": [43, 58], "602": [38, 41, 67], "624": 41, "62it": 59, "632980": 44, "63it": 50, "644727": 44, "64it": 43, "65it": 47, "66": [41, 68], "66it": [50, 59], "67": [45, 47, 50, 67], "67it": [45, 47], "68": 68, "684": [59, 60, 67], "68it": [45, 47], "69": [43, 68], "69it": 43, "7": [14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 43, 44, 45, 46, 47, 50, 55, 58, 65, 68], "701": [37, 41, 67], "707": [44, 48, 67], "70it": 50, "71": 43, "718938": 44, "71it": 47, "725": [50, 52, 67], "729": 51, "735169": 44, "73it": [44, 47], "74": 43, "75": 43, "771": 68, "77it": 59, "782": 68, "8": [14, 15, 17, 18, 19, 20, 22, 23, 25, 27, 36, 43, 44, 45, 47, 50, 51, 55, 58, 61, 64, 68], "80": [43, 44, 59], "81": 51, "81it": 47, "82": 68, "83": 50, "83it": 43, "84": 43, "844169": 46, "849980": 46, "84it": 44, "8529834747314453": 59, "85it": [43, 47], "86": 43, "869": 68, "86it": [45, 46], "874": 68, "87it": 45, "89": 43, "897": [58, 60, 67], "89it": 43, "9": [14, 15, 17, 18, 19, 20, 22, 23, 25, 43, 44, 46, 50, 51, 55, 64, 68], "90": 58, "908": [45, 48, 67], "909558": 44, "91": 68, "914042": 44, "92": 68, "926982": 46, "92it": [44, 45], "9361505508422852": 59, "93it": [44, 50], "94": 43, "94it": 44, "95": [35, 36, 37, 38, 39, 43, 55], "953700": 44, "953835": 44, "956186": 44, "95it": [44, 47], "97": 43, "985": 52, "986": [47, 48, 67], "98it": [46, 47], "99": 43, "A": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 45, 46, 47, 53, 59, 66, 68], "As": [43, 44, 50, 51, 55, 58, 59, 66, 68], "Be": 59, "But": 44, "By": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28], "For": [24, 28, 35, 36, 40, 43, 44, 45, 46, 47, 50, 55, 58, 61, 66, 68], "IT": [62, 68], "If": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 61, 64, 66, 68], "In": [27, 35, 36, 37, 38, 39, 40, 43, 45, 47, 50, 51, 55, 59, 62, 65, 66, 68], "It": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 36, 46, 47, 62, 68], "Its": 68, "On": 65, "One": [43, 45, 47, 51, 65, 68], "That": [44, 45, 47, 59], "The": [6, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 36, 40, 43, 44, 45, 46, 50, 51, 55, 58, 61, 62, 63, 65, 68], "Their": 46, "Then": [36, 43, 44, 51, 59, 61, 68], "There": 43, "These": [40, 62, 68], "To": [43, 44, 50, 55, 58, 59, 61, 64, 65, 66, 68], "_": [15, 44, 58], "__iter__": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "_autosummari": 51, "_hoi": 55, "_trial": 58, "aa": 68, "ab": 59, "abil": 43, "abl": 47, "about": [19, 24, 27, 43, 44, 45, 46, 47, 55, 58, 59, 62, 68], "abov": [44, 45, 47, 55, 68], "academi": 68, "accuiti": 66, "accur": [66, 68], "accuraci": 58, "acheiv": 46, "achiev": [45, 47, 55], "across": [50, 55, 66], "activ": [59, 68], "ad": 68, "adam": 68, "adapt": 68, "add": [26, 44, 45, 47, 50, 61], "add_edges_from": 50, "add_nodes_from": 50, "add_subplot": [37, 39], "addit": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 55, 61], "address": [62, 68], "adopt": 63, "adrian": 68, "advanc": [62, 68], "advantag": 68, "advis": 68, "again": [43, 44, 45, 46, 47], "aggreg": 30, "aim": [62, 68], "al": [10, 15, 16, 18, 19, 21, 22, 24, 39, 43, 44, 68], "alain": 68, "alexand": 68, "alford": 68, "algebra": [51, 66], "alic": 68, "all": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 37, 39, 43, 44, 47, 55, 58, 59, 61, 65, 67, 68], "allanson": 68, "allow": [44, 51, 62, 63, 66, 68], "along": [28, 51], "alpha": [35, 36, 37, 38, 39, 50, 55], "alreadi": [6, 64, 68], "also": [10, 19, 22, 36, 43, 44, 45, 46, 47, 55, 62, 64, 66, 68], "altern": 50, "although": 66, "alwai": 68, "am": [21, 68], "american": 68, "amico": 68, "amir": 68, "ammount": [46, 47, 68], "among": [62, 68], "amount": [44, 62, 68], "an": [5, 14, 25, 30, 36, 40, 43, 44, 46, 47, 50, 51, 55, 59, 61, 62, 65, 66, 68], "analys": 50, "analysi": 68, "analyt": [40, 62], "anatomi": 68, "anderson": 68, "andrea": 68, "andrew": 68, "ani": [14, 50, 55, 65, 68], "anil": 68, "annal": 68, "anoth": [14, 40, 62, 68], "answer": 58, "antonacci": 68, "anywher": 63, "ap": 68, "apart": 68, "api": [63, 66], "append": [55, 65], "appli": [8, 51], "applic": 68, "approach": [15, 24, 33, 38, 47, 57, 60, 66, 67, 68], "approxim": [46, 47, 68], "approximatio": 68, "ar": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 47, 50, 51, 55, 58, 59, 61, 62, 65, 66, 68], "arang": [50, 55, 58, 65], "arbitrari": [14, 25, 68], "architectur": 68, "area": [30, 55, 66], "areg": 59, "argument": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 51], "around": [30, 58], "arrai": [5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 40, 51, 58], "array_lik": [6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 58], "array_split": 58, "arround": 55, "arruda": 68, "arxiv": 68, "asarrai": [51, 65], "ask": 44, "aspect": [46, 68], "assert": 58, "associ": [26, 29, 30, 46, 62, 68], "assum": 61, "assumpt": 66, "astyp": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 65], "atric": 68, "attent": 68, "attractor": 68, "attribut": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "auditori": 68, "auto": 46, "auto_exampl": [41, 48, 52, 53, 56, 60], "auto_examples_jupyt": 33, "auto_examples_python": 33, "autocorrel": 46, "automat": 51, "avail": [40, 68], "averag": 55, "avoid": [43, 68], "ax": [26, 36, 37, 39, 47, 50, 51, 55, 58], "axhlin": [35, 36, 37, 38, 39], "axi": [21, 24, 26, 28, 30, 35, 36, 37, 38, 39, 51, 55], "b": [35, 59, 61, 68], "backend": [63, 66], "background": 66, "balaji": 68, "balanc": 68, "bandwidth": 9, "bar": 30, "barrat": 68, "barrett": 68, "base": [6, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 40, 43, 47, 61, 68], "base_model": 15, "basic": [51, 61], "battiston": 68, "baudot": [16, 43, 68], "bayesian": 68, "becaus": [44, 59], "becom": 68, "been": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 68], "beer": 68, "beerenwinkel": 68, "befor": [13, 59], "begg": 68, "behavior": [14, 15, 18, 22, 25, 29, 33, 42, 48, 62, 66, 67], "behind": [44, 68], "being": 43, "bell": 68, "below": [36, 43, 50], "benchmark": 66, "benedetta": 68, "benjamin": 68, "bennequin": 68, "berri": 68, "besid": 68, "best": [29, 45, 46, 47], "better": 55, "between": [14, 15, 16, 17, 18, 22, 25, 31, 35, 36, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 62, 63, 66, 68], "betzeen": 46, "beyond": [62, 63, 66, 68], "bia": 8, "bialek": 68, "bianconi": 68, "biascorrect": [8, 37, 38, 39], "bibtex": 61, "big": 68, "bin": [6, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 30, 38, 68], "binari": 38, "bind": 68, "binom": 65, "biolog": 62, "biologi": [62, 68], "biorxiv": 68, "bit": [6, 7, 8, 9, 10, 35, 36, 37, 38, 39, 40, 44, 45, 47, 55, 58, 59, 68], "bivari": [44, 45, 47], "black": [36, 61], "blakeaw": 10, "block": 68, "blog": 51, "bodi": 68, "bold": [35, 36, 37, 38, 39, 44, 55, 58, 59, 65], "book": 61, "bool": [5, 8, 26, 27, 28, 30], "boostrap": [55, 66], "bootstrap": [18, 26, 29, 56, 66, 67, 68], "bor": 68, "both": [14, 43, 44, 59, 65, 66, 68], "bound": [35, 36, 37, 38, 39, 68], "boundari": 35, "brain": [66, 68], "brainet": [61, 64], "branch": 61, "branch_nam": 61, "brien": 68, "bring": 55, "broad": 68, "browser": 61, "bruno": 68, "bug": 61, "build": [30, 40, 61, 68], "built": [63, 66], "bump": 58, "button": 61, "bw_method": 9, "c": [35, 36, 37, 38, 39, 40, 58, 59], "c0": 58, "c_": [45, 47], "call": [22, 40, 43, 51, 66, 68], "callabl": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 40], "can": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 36, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 62, 64, 65, 66, 68], "cannot": [62, 68], "capabl": [43, 44, 45], "capac": 62, "captur": 66, "card": [16, 43, 68], "care": [59, 68], "carhart": 68, "carri": [19, 44, 45, 46, 47, 55, 58, 59, 62, 68], "case": [27, 30, 40, 47, 58, 62, 68], "categori": [62, 68], "causal": 68, "cbar": 26, "cd": 61, "cell": 65, "cencetti": 68, "center": 30, "central": 30, "centuri": 68, "certain": 68, "challeng": 68, "chang": [51, 61], "channel": 62, "chao": 68, "charact": [27, 44], "character": [44, 68], "characteris": 68, "characterist": 68, "chechik": [19, 68], "check": [30, 47, 61], "checkout": [43, 44, 45, 47, 55, 58, 61, 66], "chichek": 68, "choic": 68, "choos": 27, "christin": 68, "christof": 68, "christoph": 68, "circular": 50, "circular_layout": 50, "claim": 66, "class": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 63, 66], "claud": [62, 68], "clear": 43, "clf": 58, "clike": 61, "clone": 61, "close": 40, "closest": 10, "cmap": [43, 45, 47, 55], "code": [10, 33, 35, 36, 37, 38, 39, 40, 43, 45, 46, 47, 50, 51, 55, 58, 59, 63, 65, 68], "codecov": 61, "cognit": 68, "colab": 65, "collect": [44, 50, 68], "color": [35, 36, 37, 38, 39, 58], "colorbar": [26, 46], "column": [44, 45, 47], "com": [51, 61, 64, 68], "comb": 5, "combin": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 62, 66], "combinatori": 32, "come": 68, "command": [61, 66], "commit": 61, "common": 68, "commun": [62, 68], "compar": [35, 36, 37, 38, 39, 58, 65, 68], "comparison": [11, 12, 28, 33, 34, 40, 41, 55, 66, 67, 68], "compil": 65, "complet": 68, "complex": [62, 65, 68], "complic": 68, "compon": 62, "compos": 66, "compress": 62, "comput": [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 35, 36, 37, 38, 39, 40, 43, 44, 46, 47, 59, 61, 63, 68], "computation": 55, "compute_entropi": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36], "compute_hoi_beh": 59, "compute_hoi_enc": 59, "compute_tim": 65, "compute_true_entropi": 37, "compute_true_mi": 39, "concept": [62, 68], "concern": 44, "conclud": 55, "concret": 68, "condit": [16, 18, 26, 29, 33, 42, 44, 48, 55, 67, 68], "confid": [18, 26, 29, 33, 54, 56, 66, 67, 68], "connect": 68, "conscious": 68, "consequ": 44, "consid": [21, 24, 46, 47, 62, 65, 68], "consist": [59, 68], "constant": [35, 36], "constraint": [44, 68], "contain": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 36, 44, 68], "content": 68, "context": [59, 68], "continu": [28, 68], "contrast": 43, "contribut": [59, 62, 66, 68], "control": 68, "convei": [27, 68], "convent": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "converg": [35, 37, 38, 39], "cooper": 62, "coordin": 68, "copi": [44, 45, 46, 47, 58, 62, 68], "copnorm": 8, "copula": [8, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 40, 65, 66, 68], "core": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, 33, 34, 35, 36, 37, 38, 39, 41, 61, 65, 67], "correct": [8, 62], "correctli": 43, "correl": [14, 18, 22, 25], "correspond": 43, "cost": [65, 68], "could": 44, "count": 30, "coupl": [24, 46, 68], "cov": [36, 37, 39, 40, 61], "cov_matrix": [37, 38, 39], "covari": [36, 37, 38, 39, 40, 59], "cpu": [51, 63, 64], "craig": 68, "creat": [36, 37, 38, 39, 46, 50, 55, 58, 59, 61, 65], "create_cov_matrix": [37, 39], "cross_val_scor": 58, "crucial": 68, "crutchfield": 68, "cryptographi": 62, "current": 26, "custom": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "cut": 63, "cv": 58, "czy": 68, "czyz": 39, "d": [36, 40, 68], "da": 58, "da_": 58, "daniel": 68, "darbellai": 68, "data": [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 30, 33, 34, 36, 40, 41, 55, 59, 62, 65, 67, 68], "data_s": 65, "dataarrai": 30, "datafram": [29, 30, 50], "date": 63, "david": 68, "de": 68, "deal": [65, 68], "deciph": 68, "decode_i": 58, "decompos": [62, 68], "decomposit": [21, 24, 29, 33, 42, 48, 62, 67], "def": [35, 36, 37, 38, 39, 51, 58, 59, 65], "default": [5, 6, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29], "default_devic": 65, "defin": [14, 15, 16, 18, 19, 21, 22, 24, 25, 35, 36, 37, 38, 39, 40, 44, 45, 46, 47, 50, 51, 55, 59, 65, 66, 68], "definit": [43, 44, 66, 68], "delai": [21, 24, 68], "delv": 68, "dens": [37, 39], "densiti": [9, 30, 68], "depend": [16, 30, 58, 63, 66, 68], "depict": 55, "deriv": [14, 15, 18, 22, 25, 29, 33, 42, 48, 67, 68], "describ": [36, 62, 66, 68], "descriptor": 68, "design": [19, 68], "despit": 43, "det": [36, 37, 39, 40], "det_cov": 37, "det_i": 39, "det_x": 39, "det_xi": 39, "detail": [66, 68], "detect": 62, "determin": 36, "develop": [62, 65, 66, 68], "deviat": 35, "devic": 65, "df": [45, 46, 47], "df_best": 29, "diag": 36, "diag_indic": [37, 39], "diagon": [36, 37, 39], "dict": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 43, 45, 47, 55], "did": 43, "differ": [14, 15, 18, 40, 43, 44, 51, 55, 58, 59, 62, 65, 68], "differnt": [37, 39], "digit": 38, "dim": 37, "dimens": [37, 39, 51, 55], "dimension": [11, 12, 30, 33, 34, 36, 40, 41, 67, 68], "direct": [62, 68], "direction_axi": [21, 24], "directli": [47, 64, 68], "discret": [6, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 68], "discriminant_analysi": 58, "discuss": 68, "discusss": 61, "disentangl": [44, 45], "disord": 68, "distanc": 51, "distinguish": 68, "distribut": [11, 25, 30, 33, 34, 36, 40, 41, 66, 67, 68], "diverg": 25, "divid": [30, 51, 68], "do": [36, 45, 46, 47, 51, 61], "document": [51, 64, 66], "doe": 68, "doesn": [55, 65], "doi": 68, "domin": [44, 59, 68], "dominik": 68, "done": [39, 51, 59, 68], "dopaminerg": 68, "dot": [36, 51], "doubl": 47, "download": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59], "draft": 61, "draw": 50, "dry": [51, 65], "dtc": [18, 22, 68], "dual": [14, 18, 22], "due": 68, "dufour": 68, "dynam": [65, 68], "e": [35, 36, 37, 40, 44, 45, 47, 59, 61, 62, 65, 66, 68], "e1008289": 68, "e21090869": 68, "each": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 36, 37, 39, 43, 44, 45, 51, 55, 58, 59, 61, 62, 65, 68], "eas": 63, "easiest": 64, "ecolog": 62, "ecologi": 62, "edg": [30, 50, 63], "edge_fc": 50, "edge_fc_cmap": 50, "editor": 61, "effect": [36, 59, 62, 68], "effici": 51, "eilon": 68, "either": [5, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 35, 45, 58], "elad": 68, "electrophysiolog": 68, "elegantli": 68, "element": [5, 14, 19, 25, 36, 37, 39, 44, 51, 59, 62, 68], "elif": [37, 39, 58], "ellison": 68, "els": [37, 39], "elwood": 68, "emerg": [46, 59, 68], "emmanuel": 68, "empti": 55, "en": [51, 64], "encod": [14, 15, 18, 22, 25, 29, 33, 42, 48, 58, 62, 66, 67], "end": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61], "endr": 68, "eneuro": 68, "engag": 59, "engin": [62, 63], "enrico": 68, "ensur": 61, "ent": 37, "ent_theor": 37, "entropi": [6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, 38, 39, 41, 43, 44, 50, 61, 62, 66, 67], "entropy_analyt": 40, "entropy_bin": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "entropy_gauss": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "entropy_gc": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "entropy_kernel": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "entropy_knn": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "enumer": [35, 36, 37, 38, 39, 44, 46, 58], "environ": 65, "equal": [28, 30, 36], "equiv": [19, 45, 47], "equival": [25, 51], "eran": 68, "error": [35, 38, 62], "especi": 66, "essenc": 62, "estim": [8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 30, 32, 33, 34, 40, 41, 43, 59, 66, 67, 68], "estimat": 55, "et": [10, 15, 16, 18, 19, 21, 22, 24, 39, 43, 44, 68], "etc": [65, 66], "euler": [35, 36], "evalu": 68, "even": [44, 68], "eventu": 47, "evolut": [21, 24, 68], "exact": 55, "exampl": [17, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 63, 65, 66, 67], "exceed": 19, "except": [44, 51, 55], "excess": 68, "exclud": 68, "execut": [41, 48, 51, 52, 53, 56, 60, 63, 67], "exogen": [22, 68], "expect": [40, 45, 46, 62], "experimentalist": 68, "explain": 62, "explor": 68, "expon": 51, "exstens": 68, "exstrins": 62, "extend": 68, "extens": [14, 25, 68], "extern": [59, 62], "extract": [37, 38, 39, 40, 50], "ey": [37, 39], "f": [35, 36, 37, 38, 39, 51, 55, 58, 59, 68], "fact": [65, 68], "fae": 68, "failur": 62, "fall": 62, "fals": [5, 27, 28, 30, 37, 38, 39, 43, 45, 47, 55, 58, 59, 65, 68], "familiar": 63, "fascin": 68, "fast": [55, 65], "faster": [65, 66], "fault": 62, "favorit": 61, "fcn": [11, 12, 35, 36, 37, 38, 39, 51], "featur": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 43, 45, 46, 47, 58], "federico": 68, "fernando": 68, "ferraz": 68, "fetch": 61, "fi": 68, "field": [65, 68], "fig": [36, 37, 39, 58], "figsiz": [36, 37, 39, 58], "figur": [36, 37, 39], "file": [41, 48, 52, 53, 56, 60, 61, 67], "file1": 61, "file2": 61, "fill": 5, "fill_between": [35, 36, 37, 38, 39, 55], "fill_valu": 5, "final": [36, 44, 51, 59, 61, 65, 68], "find": [44, 47, 66], "finoia": 68, "first": [15, 28, 44, 45, 46, 47, 50, 51, 55, 59, 65], "fit": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65, 66], "fix": 55, "flake8": 61, "flecker": 68, "float": [6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 31, 51, 58], "focu": 68, "focus": [44, 68], "foldiak": 68, "follow": [21, 35, 46, 47, 59, 61, 65, 66, 68], "fonction": 61, "font_size_nod": 50, "fontweight": [35, 36, 37, 38, 39, 44, 55, 58, 59, 65], "fork": 61, "formal": 68, "formisano": 68, "formula": [40, 68], "found": [44, 62, 66], "foundat": 68, "frac": [35, 36, 37, 38, 39, 40], "framework": [46, 47, 62, 68], "franceschiello": 68, "fraser": 68, "freder": 68, "frequenc": [30, 68], "friendli": 51, "from": [30, 36, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 62, 64, 65, 66, 67], "fryer": 68, "full": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61], "fulli": [58, 62], "funciton": 59, "function": [2, 4, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 33, 35, 36, 37, 38, 39, 40, 50, 58, 59, 63, 66, 68], "functool": [38, 51], "fundament": [40, 62, 68], "further": [43, 44, 45, 47, 51, 55, 58, 66], "futur": [24, 46, 62, 68], "fx": [37, 38, 39], "g": [46, 66, 68], "gabert": 68, "gabriel": 68, "gal": 68, "galleri": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 67], "gastpar": 68, "gauss": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36], "gaussian": [7, 8, 9, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 35, 36, 37, 38, 39, 40, 59, 65, 66, 68], "gaussian_kd": 9, "gbauer": 68, "gc": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 40, 43, 44, 50, 55, 59, 65, 66], "gca": 55, "gcmi": [37, 39], "gener": [27, 33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65, 68], "genet": 68, "geomspac": [35, 36, 37, 38, 39], "georg": 68, "get": [5, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 35, 36, 37, 38, 39, 44, 55, 65, 66], "get_combin": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 46], "get_covari": 36, "get_entropi": [35, 36, 37, 40, 65], "get_mi": [38, 39, 40], "get_nbest_mult": [43, 44, 45, 46, 47, 50, 55, 66], "ggplot": [35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65], "ginestra": 68, "giordano": 68, "giovanni": 68, "git": [61, 64], "github": [61, 64], "giulia": 68, "give": 44, "given": [38, 39, 43, 44, 62, 68], "globerson": 68, "glossari": 66, "go": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 63, 65, 66, 68], "goaillard": 68, "gonig": 59, "goodman": 68, "gpu": [51, 63, 64], "grabowski": 68, "gradient": [15, 44, 47, 58], "gradientoinfo": [44, 58, 59, 66, 68], "graphic": 68, "grassberg": 68, "great": 68, "greater": [59, 62, 68], "griffith": 68, "gross": 68, "group": [47, 62, 68], "grow": [65, 68], "gui": 68, "guid": [40, 68], "guilherm": 68, "guillaum": 68, "h": [14, 18, 22, 25, 35, 36, 37, 40, 43, 44, 50, 68], "h_": [16, 43, 68], "h_idx": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "h_max": 59, "h_theoric": [35, 36], "h_x": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36], "ha": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 51, 68], "half": 68, "hallmark": 59, "han": [44, 58, 59, 68], "handl": 68, "hann": 58, "harald": 68, "harri": 68, "have": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 37, 39, 40, 44, 51, 64, 65, 66, 68], "height": 30, "henc": 68, "henrik": 68, "here": [44, 45, 46, 47, 50, 55, 58, 59, 64, 66], "high": [11, 12, 27, 33, 34, 41, 46, 67, 68], "higher": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 32, 33, 36, 40, 43, 45, 47, 49, 51, 52, 58, 62, 67], "highest": [43, 45, 46, 47, 50, 55], "highli": 66, "highlight": 68, "hist": 26, "hist_kwarg": 26, "histogram": [26, 30], "hoi": [32, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 51, 55, 57, 59, 60, 62, 64, 65, 66, 67, 68], "hoi_m": 55, "hoi_order_3": 50, "hoi_r": 47, "hoi_syn": 47, "hold": 43, "holland": 68, "horizont": 36, "how": [15, 18, 27, 30, 33, 43, 44, 45, 46, 47, 50, 51, 55, 57, 58, 60, 62, 66, 67, 68], "howev": [36, 43, 45, 47, 55, 58, 65, 68], "html": [51, 64], "http": [51, 61, 64, 68], "huge": 65, "hull": 50, "human": 68, "hx": [6, 7, 8, 9, 10], "hypergraph": 50, "hypothesi": 68, "i": [5, 6, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 51, 55, 58, 59, 61, 62, 63, 64, 65, 66, 68], "i_": [16, 43, 68], "i_2": 68, "i_3": 68, "i_k": 68, "iacopini": 68, "iacopo": 68, "ibm": 68, "idea": 44, "ident": 68, "identifi": [43, 68], "ieee": 68, "ignor": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "igor": 68, "ik": [15, 44], "il": 68, "illustr": [33, 36, 43, 44, 45, 46, 47, 50, 55], "imagin": 51, "implement": [50, 51, 61, 68], "import": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65, 66, 68], "improv": [61, 62], "imshow": 46, "in_ax": [51, 65], "inc": 68, "incept": 68, "includ": [27, 43, 55, 61, 63], "increas": [36, 65], "independ": [40, 46, 68], "index": [19, 20, 23, 26, 29, 33, 42, 43, 44, 46, 47, 48, 50, 55, 62, 67], "indic": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 68], "individu": [19, 44, 59, 62, 68], "inf": 68, "infer": [43, 68], "inflat": 46, "influenc": 44, "info": [15, 18, 22, 44, 55], "inform": [10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 37, 39, 41, 42, 45, 47, 48, 50, 57, 59, 60, 62, 63, 65, 66, 67], "infotopo": [43, 50, 68], "initi": 55, "inject": [44, 46, 50, 59], "input": [6, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 36, 40, 51], "insid": [45, 47, 61], "insight": 68, "inspect": [16, 26, 29, 33, 45, 46, 47, 49, 52, 67, 68], "inspir": 39, "instal": [29, 63, 65], "instead": [46, 47, 68], "int": [5, 6, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 35, 36, 37, 38, 39, 58, 65], "integr": [21, 24, 29, 33, 42, 48, 67, 68], "intens": 55, "interact": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 32, 33, 36, 44, 45, 47, 49, 52, 55, 58, 59, 62, 67], "interdepend": [46, 68], "interdisciplinari": 68, "interest": 68, "intern": 68, "interpol": 46, "interpret": [45, 46, 47, 68], "interv": [18, 26, 29, 33, 35, 36, 37, 38, 39, 40, 54, 56, 66, 67, 68], "intric": 68, "intrins": [14, 44, 62], "introduc": [43, 44, 45, 47, 51, 58, 68], "introduct": [11, 12, 33, 34, 41, 49, 52, 66, 67, 68], "intuit": [44, 59], "invalu": 68, "investig": [58, 65, 68], "involv": [36, 68], "io": [51, 64], "ipynb": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59], "isol": 44, "israel": 68, "issu": [61, 65], "item": [35, 36, 37, 38, 39], "iter": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "its": [14, 15, 18, 22, 25, 29, 33, 35, 36, 42, 43, 47, 48, 55, 66, 67, 68], "j": [14, 18, 22, 25, 44, 68], "jame": [22, 68], "jax": [5, 9, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 49, 52, 63, 64, 66, 67, 68], "jax_eucl": 51, "jean": 68, "jensen": 68, "jirina": 68, "jnp": [5, 51, 65], "joachim": 68, "john": 68, "joint": [25, 37, 38, 39, 68], "journal": 68, "judith": 68, "julia": 68, "jupyt": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59], "just": 44, "k": [5, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 43, 44, 58, 65, 68], "kayser": 68, "kazuto": 68, "kbinsdiscret": 28, "keep": 55, "kei": [35, 36, 37, 38, 39], "kernel": [9, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 46, 68], "kind": [26, 43, 45, 47, 50, 51, 55, 68], "knn": [10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 68], "know": [45, 47, 59, 68], "knowledg": [61, 62], "known": [51, 58, 68], "kobayashi": 68, "koch": 68, "kraskov": [10, 68], "kullback": 25, "kwarg": [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 38], "l": 68, "label": [35, 36, 37, 38, 39, 44, 58, 65], "lall": 68, "lambda": 35, "lambda_": 35, "landcap": 30, "landscap": [26, 43, 55, 66], "lapish": 68, "larg": 25, "larger": 65, "largest": [44, 50], "lasserr": 68, "last": 68, "latest": [51, 64], "latora": 68, "launch": [45, 46, 47], "lax": 51, "layout": 50, "ldot": 68, "lead": [35, 51, 65], "learn": [15, 33, 55, 57, 60, 63, 64, 67, 68], "least": [51, 55, 68], "left": [40, 68], "legend": [35, 36, 37, 38, 39, 44, 58, 65], "len": [35, 36, 37, 38, 39], "length": [21, 24], "less": 68, "let": [35, 36, 37, 38, 40, 43, 44, 45, 46, 47, 51, 55, 58, 59, 65], "letter": 68, "leverag": 47, "li": 55, "librari": [51, 65, 68], "liebler": 25, "light": 68, "like": [51, 66], "limit": [47, 55, 66, 68], "linalg": [36, 37, 39, 40], "line": [36, 55, 66, 68], "linear": [51, 66, 68], "lineardiscriminantanalysi": 58, "linearli": 65, "linestyl": [35, 36, 37, 38, 39], "link": [38, 39, 44, 68], "linspac": 65, "lint": 61, "list": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 35, 36, 37, 38, 39, 55, 63, 64, 66], "literatur": 68, "locat": 61, "log": [35, 36, 40], "log2": [35, 37, 38, 39], "log_": [35, 37, 38, 39, 68], "logarithm": 6, "look": [45, 46, 47, 66], "lost": 68, "low": 68, "lower": [35, 36, 37, 38, 39, 43, 55, 68], "lowest": [45, 46, 47, 50], "luca": 68, "luppi": [24, 68], "lw": [35, 36, 37, 38, 39, 55, 58], "m": [35, 44, 46, 55, 61, 68], "machin": [15, 33, 57, 60, 67, 68], "main": [33, 61, 65, 68], "mainli": [55, 68], "maintain": 61, "make": [36, 61, 68], "mani": 68, "manon": 68, "map": 68, "marc": 68, "margin": 25, "marinazzo": 68, "marker": 36, "marqu": 68, "martial": 68, "marx": 68, "mass": 68, "math": [25, 44], "mathcal": [35, 37, 38, 39], "mathemat": [43, 44, 62, 68], "matplotlib": [35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 50, 55, 58, 59, 61, 65], "matrix": [36, 37, 38, 39, 40, 46, 59], "matrix_to_plot": 46, "max": [24, 46, 51, 59, 68], "max_": [47, 68], "maxim": [19, 68], "maximum": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 66], "maxsiz": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 44, 45, 46, 47, 50, 58, 59, 65, 66], "mb": [41, 48, 52, 53, 56, 60, 67], "mdpi": 68, "mean": [35, 36, 37, 38, 39, 40, 45, 47, 51, 55, 58, 59, 65], "measur": [25, 32, 44, 45, 46, 47, 59, 62, 66], "mediano": [21, 68], "mem": [41, 48, 52, 53, 56, 60, 67], "menon": 68, "mention": 68, "messag": [61, 62], "method": [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 40, 43, 44, 50, 55, 59, 65, 66, 68], "metric": [11, 12, 26, 29, 32, 34, 35, 36, 37, 38, 39, 41, 43, 44, 45, 46, 47, 48, 50, 55, 58, 59, 62, 63, 65, 66, 67, 68], "metric_nam": [35, 36, 37, 38, 39], "mi": [8, 12, 17, 19, 20, 21, 23, 24, 33, 34, 37, 40, 41, 62, 67], "mi_bin": 38, "mi_binning_fcn": 38, "mi_theor": [38, 39], "michael": 68, "mid": 55, "midbrain": 68, "milan": 68, "min": [21, 46, 51, 59, 68], "min_": [47, 68], "minimum": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 46, 47, 66, 68], "minmax": 51, "minmax_2d": 51, "minmax_3d": 51, "minmax_3d_jit": 51, "minmaxscal": 50, "minsiz": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65, 66], "minu": [15, 18, 22, 44], "minut": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59], "miscellan": [52, 67], "miss": 5, "mitig": 66, "mmi": [20, 21, 23, 24, 26, 29, 33, 42, 46, 48, 67], "mode": [37, 39, 61], "model": [26, 29, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65, 66, 68], "model_r": 47, "model_select": 58, "model_syn": 47, "modifi": [61, 65], "modul": [59, 62, 65], "monica": 68, "monoton": 68, "moon": 68, "more": [43, 45, 47, 55, 59, 62, 63, 68], "moreno": 68, "most": [40, 45, 46, 47, 63, 68], "move": [45, 47], "mu": [35, 37, 39], "mu_": [38, 39], "mu_i": 38, "mu_x": 38, "much": [46, 55, 68], "mult_order_3": 50, "mult_siz": 30, "multi_s": 30, "multiinform": 68, "multipl": [59, 62, 63, 65], "multiplet": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 44, 45, 46, 47, 55, 66, 68], "multivari": [11, 16, 33, 34, 37, 39, 40, 41, 58, 59, 66, 67, 68], "multivariate_norm": [36, 37, 38, 39], "musician": 66, "must": 65, "mutual": [10, 12, 14, 16, 17, 20, 21, 23, 24, 25, 28, 32, 37, 39, 41, 43, 46, 47, 50, 62, 66, 67], "n": [5, 14, 15, 17, 18, 19, 22, 25, 29, 35, 36, 37, 38, 39, 44, 45, 47, 51, 53, 58, 65, 66, 68], "n_": [35, 36, 37, 38, 39, 65, 68], "n_b": 55, "n_best": [29, 44, 45, 46, 47, 50], "n_bin": [28, 30, 38], "n_boot": 55, "n_combin": 5, "n_dim": [37, 39], "n_f": 65, "n_featur": [6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 40, 46, 65], "n_hoi": 30, "n_m": [35, 36, 37, 38, 39, 44], "n_mult": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "n_multiplet": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "n_node": [55, 59], "n_r": [35, 36, 37, 38, 39, 58], "n_repeat": [35, 36, 37, 38, 39], "n_sampl": [6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 35, 36, 37, 38, 39, 40, 55, 58, 59, 65, 66], "n_time": 58, "n_v": 65, "n_variabl": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 65], "n_x": 58, "n_y": 58, "naftali": 68, "name": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 51, 61], "nathaniel": 68, "nation": 68, "natur": [58, 59, 68], "ncode": 66, "ndarrai": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27], "ndata": [35, 38], "nearest": [10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 68], "necessari": 68, "need": 59, "neg": [19, 27, 43, 44, 45, 50, 58, 59, 62, 68], "negin": 68, "neglect": 68, "neighbor": [10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 68], "nelken": 68, "nelsontang": 51, "neq": [15, 44], "network": [14, 15, 18, 22, 25, 29, 33, 42, 43, 48, 55, 59, 62, 65, 66, 67], "neural": 68, "neurip": 39, "neuroimag": 68, "neuron": 68, "neurosci": [66, 68], "neurotransmitt": 68, "new": [65, 68], "next": 65, "nh": [22, 44, 68], "nica": 68, "nice": 51, "nichola": 68, "niko": 68, "node": [43, 44, 50, 55, 59, 65, 66], "node_label": 50, "node_s": 50, "nois": 46, "non": [55, 62], "none": [5, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 36, 37, 39, 46], "nonlinear": 68, "nonneg": 68, "normal": [8, 11, 30, 33, 34, 37, 39, 40, 41, 44, 66, 67, 68], "note": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 68], "notebook": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65, 66], "notic": [47, 51], "now": [36, 40, 43, 44, 45, 46, 47, 51, 55, 58, 59], "np": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65], "nthe": [37, 39], "nuanc": 62, "number": [5, 14, 25, 27, 28, 29, 30, 35, 36, 37, 38, 39, 51, 55, 58, 65, 68], "numpi": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 55, 58, 59, 64, 65], "numpy_eucl": 51, "numpydoc": 61, "nuzzi": 68, "o": [14, 15, 18, 22, 25, 27, 29, 33, 36, 42, 47, 48, 62, 65, 66, 67], "object": 50, "observ": [30, 45, 46, 47, 68], "obtain": [59, 62, 68], "occur": 62, "occurr": 68, "off": [37, 39], "offer": 68, "offici": 51, "often": 62, "oinfo": [15, 43, 44, 55, 58, 59, 65, 66, 68], "oldest": [25, 68], "omega": [15, 18, 22, 44, 68], "omega_": 58, "onc": [61, 66], "one": [36, 44, 55, 59, 62, 65, 68], "onli": [27, 37, 39, 43, 45, 46, 47, 50, 55, 58, 61, 62, 64], "open": 61, "oper": [46, 51, 65, 68], "option": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 51, 64], "orchestra": 66, "order": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 33, 36, 40, 42, 44, 45, 46, 47, 48, 49, 52, 58, 62, 67], "org": 68, "organ": 68, "origin": [10, 61], "other": [14, 40, 44, 45, 47, 59, 62, 68], "otherwis": 66, "our": [43, 50, 51, 61, 66, 68], "output": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 50], "over": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 51, 55], "owen": 68, "own": [46, 68], "p": [25, 68], "p_high": 55, "p_low": 55, "packag": [50, 61, 63, 66], "page": [61, 66, 68], "pair": [37, 39, 58, 68], "pairwis": [17, 46, 62, 63, 66], "panda": [29, 30, 50, 61, 64], "paola": 68, "paramet": [5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 35, 58, 59], "parametr": [55, 68], "part": [14, 47, 50, 58, 59, 62, 65, 68], "partial": [38, 51, 58, 62, 68], "partial_": [15, 44, 68], "particular": [35, 38, 39, 51, 68], "partit": 68, "pass": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 61], "past": [46, 65], "patania": 68, "path_to_test_fil": 61, "pathwai": 68, "pattern": [59, 68], "paul": 68, "paw": 68, "pcolormesh": 26, "pedro": [21, 68], "pep8": 61, "per": [30, 37, 39], "percent": 30, "percentil": [35, 36, 37, 38, 39, 55], "perform": [28, 36, 51, 66, 68], "permut": 58, "perspect": 68, "peter": 68, "petri": 68, "phenomena": 68, "phenomenon": 62, "phenotyp": 68, "phiid": [21, 24], "philipp": 68, "philosoph": 68, "phy": 10, "physic": 68, "physrev": 68, "pi": [35, 36, 37, 40], "pickard": 68, "pid": [62, 68], "pierr": 68, "pip": [61, 64, 65, 66], "plai": 68, "pleas": [61, 64], "plethora": 68, "plo": 68, "plot": [16, 29, 32, 33, 35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 49, 52, 58, 59, 65, 66, 67, 68], "plot_bootstrap": [55, 56, 67], "plot_decod": 58, "plot_entropi": [35, 41, 67], "plot_entropies_mvar": [36, 41, 67], "plot_entropy_high_dimension": [37, 41, 67], "plot_infotopo": [43, 48, 67], "plot_inspect_result": [50, 52, 67], "plot_jax": [51, 52, 67], "plot_landscap": [43, 45, 47, 50, 55, 66], "plot_mi": [38, 41, 67], "plot_mi_high_dimension": [39, 41, 67], "plot_ml_vs_it": [58, 60, 67], "plot_oinfo": [44, 48, 67], "plot_rsi": [45, 48, 67], "plot_sim_red_syn": [59, 60, 67], "plot_syn_phiid": [46, 48, 67], "plot_syn_red_mmi": [47, 48, 67], "plot_tutorial_cor": [40, 41, 67], "plot_xi": 58, "plt": [26, 35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65], "plt_kwarg": [26, 43, 45, 47, 55], "plu": [44, 46, 68], "po": 50, "point": [10, 43, 44, 51, 58, 65, 68], "popul": 28, "pose": 65, "posit": [19, 27, 36, 43, 44, 45, 46, 47, 50, 51, 58, 59, 68], "possibl": [5, 45, 47, 59, 65, 68], "post": 32, "potenti": 66, "pouei": 68, "pre": 32, "predict": 46, "predictor": 62, "prepar": 13, "preprint": 68, "preprocess": [28, 50], "presenc": [46, 47, 62, 68], "present": [43, 59, 68], "pretti": 66, "prevail": 68, "previou": [44, 59], "principl": 68, "print": [40, 43, 44, 45, 46, 47, 50, 51, 55, 59, 66], "probabl": [30, 68], "problem": [65, 68], "procedur": 68, "proceed": 68, "process": [32, 62, 68], "produc": [59, 62, 68], "product": [25, 36, 51], "program": 65, "promin": 68, "properti": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 46, 68], "proport": 30, "propos": [61, 68], "proven": 68, "provid": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 58, 62, 63, 66, 68], "proxi": 68, "publish": [43, 68], "pure": 51, "purport": 19, "pursuit": 68, "push": 61, "py": [35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 56, 58, 59, 60, 61, 67], "pyplot": [35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 50, 55, 58, 59, 65], "pytest": 61, "python": [10, 33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 63, 64, 65, 66, 68], "quadruplet": [43, 55], "quantif": 62, "quantifi": [16, 44, 62, 63, 66, 68], "quantil": 28, "quantiti": 44, "quatifi": 68, "question": [44, 58, 61, 68], "quick": [33, 49, 52, 67], "quickli": 68, "r": [55, 58, 68], "rajagopalan": 68, "rand": [40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65], "randal": 68, "random": [16, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 62, 65, 68], "random_st": 55, "randomli": 55, "rang": [35, 36, 37, 38, 39, 46, 55, 58, 68], "rate": 35, "ravel": 58, "rder": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "re": [43, 59], "read": 44, "readthedoc": [51, 64], "real": [65, 68], "realli": 55, "rebas": 61, "receiv": [45, 46, 47, 58, 59], "recent": [65, 68], "recommand": 55, "recommend": [44, 65], "reconcil": 68, "reconduct": 68, "recoveri": 62, "red": [21, 46, 47, 58, 68], "red_result": 46, "redmmi": 47, "redphiidmmi": 46, "reduand": 43, "reduc": 68, "reduct": [62, 68], "redud": 44, "redund": [14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 27, 29, 33, 42, 48, 50, 57, 58, 60, 62, 66, 67], "redundancymmi": [47, 68], "redundancyphiid": [46, 68], "refer": [10, 14, 15, 16, 18, 19, 21, 22, 24, 25, 27, 50, 62, 64, 68], "reflect": [45, 68], "regard": 55, "rel": [51, 66], "rel_strength": 58, "rel_typ": 58, "relat": [14, 15, 18, 22, 25, 44, 46, 58, 68], "relationship": [58, 62, 66, 68], "reli": [43, 65, 66], "reliabl": 62, "rememb": 47, "remind": [43, 55], "remot": 61, "remov": 44, "repeat": [51, 55], "repetit": [35, 36, 37, 38, 39], "repo": 61, "report": 68, "repositori": 61, "repres": [5, 30, 44, 55, 59, 62, 68], "represent": 26, "requir": [29, 38, 62, 64, 65], "resampl": 55, "research": [63, 65, 68], "reshap": [35, 51, 58, 59], "respect": [27, 44, 46, 47, 58, 66, 68], "ressourc": 51, "result": [35, 37, 38, 39, 45, 46, 47, 55, 59, 65, 68], "retriev": [44, 45, 47, 50, 58, 66], "return": [5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 36, 37, 38, 39, 43, 50, 51, 58, 59, 65], "rev": 10, "reveal": 68, "review": 68, "rf": 58, "right": [40, 68], "rightarrow": [15, 16, 18, 19], "robin": 68, "robust": [46, 66, 68], "role": 68, "rosa": [18, 44, 68], "rotat": 55, "rousselet": 68, "row": 68, "rowvar": 40, "royal": 68, "rsi": [17, 45, 47, 62], "rule": 68, "run": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 63, 65, 66], "ryan": 68, "s_": 47, "sai": [51, 55, 59], "said": 44, "same": [28, 43, 45, 46, 47, 51, 55, 59, 62, 63, 66, 68], "sampl": [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 36, 40, 43, 44, 45, 46, 47, 55, 58, 59, 65], "satisfi": 61, "satosi": 68, "sca": [36, 58], "scagliarini": [15, 68], "scale": 65, "scan": 51, "scatter": [26, 43, 45, 47, 50, 55], "scenario": 68, "schneidman": 68, "schyn": 68, "scienc": 68, "scientif": 68, "scientist": 68, "scikit": [55, 63, 64], "scipi": [9, 51, 64], "script": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 66], "sebastiano": 68, "second": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65, 68], "section": [44, 66, 68], "see": [9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 66, 68], "seed": [50, 59], "seen": 68, "select": [45, 46, 47, 65], "self": 68, "semi": 36, "semin": 68, "sen": 59, "send": [44, 45, 47], "sens": 68, "sensit": [14, 25, 68], "sent": [11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], "sentiv": 68, "separ": [46, 62, 68], "septemb": 68, "seri": 68, "serv": 68, "set": [5, 14, 17, 19, 27, 40, 51, 59, 61, 62, 65, 68], "set_text": [37, 39], "set_xlabel": [37, 39], "set_xticklabel": 55, "set_ylabel": [37, 39], "seth": 68, "sever": [35, 36, 38], "shade": 55, "shannon": [62, 68], "shape": [5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 30, 36, 37, 39, 40, 45, 47, 51, 55, 58], "share": [14, 25, 44, 46, 62, 68], "sharei": 58, "sharex": 58, "shed": 68, "short": [43, 51], "should": [6, 8, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 43, 61, 68], "show": [30, 35, 37, 38, 39, 43, 44, 45, 46, 50, 55, 58], "showcas": [44, 50], "shown": 68, "sigma": [35, 36, 37, 39, 40], "sigma_": [38, 39], "sigma_i": 38, "sigma_x": 38, "sign": 68, "signal": [59, 61], "sim": [35, 38, 39], "simeq": 65, "similar": 39, "simmetr": 46, "simon": 68, "simpl": [45, 46, 47, 55, 59, 68], "simpli": [62, 68], "simul": [15, 18, 32, 33, 35, 36, 37, 38, 39, 55, 57, 60, 67, 68], "simulate_data": 58, "simulate_hoi_gauss": [59, 66], "sinc": [40, 68], "sinfo": [44, 68], "singl": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 45, 47, 61, 68], "situat": 68, "six": 47, "size": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 35, 36, 40, 45, 46, 47, 65, 66, 68], "sklearn": [28, 50, 55, 58], "sl": 58, "slice": 58, "slow": 51, "small": [43, 68], "smallest": [44, 50], "smooth": 68, "so": [36, 40, 58, 61, 68], "social": [62, 66], "societi": 68, "softwar": [61, 64], "some": [35, 36, 44, 46, 51, 55, 59, 65, 68], "sonia": 68, "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, 33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 68], "space": 68, "spars": [37, 39], "spatial": 55, "special": 38, "specif": [35, 59, 61], "specifi": [5, 8, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 37, 39, 51, 58], "spectral_r": [43, 50, 55], "sphinx": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61], "sphinx_gallery_thumbnail_numb": [50, 55], "sphinxcontrib": 61, "spread": [45, 50, 66], "springer": 68, "sqrt": [36, 51], "squeez": [55, 58, 59], "st": 68, "stack": 55, "stamataki": 68, "stand": [43, 45, 47], "standard": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 38, 68], "stark": 68, "start": [40, 43, 45, 46, 47, 58, 65], "stat": [9, 30], "state": [46, 62, 68], "static": [59, 68], "static_argnum": 51, "statist": [16, 30, 55, 56, 58, 63, 67, 68], "step": [55, 61], "still": 68, "stochast": 68, "storag": 62, "store": 46, "str": [9, 44, 55], "stramaglia": 68, "strang": 68, "strategi": [28, 62], "strength": [44, 58, 68], "stroger": 46, "strongest": 66, "strongli": 66, "structur": [65, 68], "studen": 68, "studi": [46, 62, 65, 68], "style": [35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 50, 55, 58, 59, 63, 65], "subgroup": 47, "subplot": [36, 58], "subselect": 55, "subset": [16, 43, 44, 45, 47, 68], "subtl": [45, 47], "subtract": 44, "success": 68, "suffer": 66, "suggest": [51, 61, 68], "sum": [22, 30, 44, 46, 51, 62, 68], "sum_": [14, 15, 16, 18, 19, 22, 25, 43, 44, 45, 68], "summari": 66, "sun": [14, 68], "suptitl": [37, 39], "sure": 61, "surround": 55, "susann": 68, "swinnei": 68, "switch": 59, "symmetr": [36, 68], "syn": [24, 46, 47, 58, 68], "syn_result": 46, "sync": 61, "synergi": [14, 15, 16, 18, 19, 20, 23, 24, 26, 27, 29, 33, 42, 43, 44, 48, 50, 57, 58, 60, 62, 66, 67], "synergist": [19, 45, 46, 47, 50, 55, 58, 62, 66, 68], "synergy_phiid": 46, "synergymmi": [47, 68], "synergyphiid": [46, 68], "synmmi": 47, "synphiidmmi": 46, "synsum": 19, "system": [44, 59, 62, 65, 66, 68], "t": [21, 24, 36, 37, 38, 39, 43, 46, 55, 58, 65, 68], "t1": 51, "t2": 51, "t_end": 58, "t_start": 58, "tabl": [43, 44, 45, 46, 47, 50, 55, 66], "take": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 40, 44, 45, 46, 47, 51, 59, 65, 68], "taken": [51, 65], "tapia": [16, 68], "target": [5, 15, 27, 47, 58, 59, 62, 68], "task": [14, 15, 18, 22, 25], "tau": [21, 24, 46, 68], "taxonomi": 68, "tc": [18, 22, 68], "tdmi": 68, "te": [14, 68], "technic": 68, "techniqu": 62, "tempor": 68, "tend": [44, 66], "term": [44, 59, 66, 68], "termin": 66, "test": [51, 61, 68], "tests_entropi": 61, "text": [55, 59], "th": [10, 35, 36, 37, 38, 39, 68], "tha": 59, "than": [45, 59, 62, 65, 68], "thei": 68, "them": [40, 46, 58, 68], "theme": 61, "theoret": [0, 11, 12, 15, 32, 33, 34, 35, 36, 37, 38, 39, 41, 57, 60, 63, 65, 66, 67], "theori": [40, 43, 62, 66, 68], "therefor": [44, 51, 55, 59], "thi": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 62, 65, 66, 68], "thick": 55, "thing": [43, 51], "thoma": 68, "those": [43, 66], "though": 68, "three": [59, 62, 65, 66], "threshold": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], "through": [40, 68], "tight_layout": [37, 39], "tim": 68, "time": [35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65, 68], "timeit": 51, "timings_cpu": 65, "timings_gpu": 65, "timm": [19, 68], "tishbi": 68, "titl": [35, 36, 37, 38, 39, 44, 55, 58, 59, 65], "to_max": 31, "to_min": 31, "togeth": [59, 62, 66], "toi": [65, 66], "toler": 62, "tolist": 50, "toma": 68, "tool": [65, 68], "toolbox": [65, 68], "top": [61, 63, 66], "topolog": [16, 18, 26, 29, 33, 42, 48, 55, 67], "total": [5, 14, 17, 18, 19, 22, 25, 30, 35, 36, 37, 38, 39, 40, 41, 43, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 58, 59, 60, 67], "toward": [35, 37, 38, 39, 68], "tpu": [63, 65], "tqdm": 64, "tr": 68, "tradit": 62, "tradition": 66, "transact": 68, "transmit": 62, "transpos": 36, "trend": 68, "trial": 55, "trial_block": 58, "triplet": [27, 43, 44, 45, 47, 50, 55, 59], "triplet_charact": [27, 59, 66], "true": [5, 8, 26, 27, 28, 37, 39, 40, 50, 58, 59], "try": 58, "tup": 46, "turbo": [45, 47], "tutori": [35, 38, 39, 40, 51, 59, 60, 67, 68], "twice": 51, "two": [38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 58, 59, 62, 68], "type": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 43, 44, 61, 66, 68], "u": [35, 36, 38, 58, 64, 66], "u_x": 58, "uncertainti": [62, 68], "under": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 46, 68], "underli": 68, "undersampl": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 43, 45, 47], "understand": [62, 68], "understood": [14, 62], "undirect": [62, 68], "uniform": [36, 40, 46, 68], "uniqu": [30, 51, 58, 62], "unit": [40, 63, 68], "univari": 58, "unveil": 68, "up": [50, 63, 65], "updat": [51, 66], "upmanu": 68, "upper": [35, 36, 37, 38, 39, 68], "upstream": 61, "url": 68, "us": [5, 6, 9, 10, 17, 30, 35, 36, 37, 38, 39, 40, 45, 46, 47, 50, 59, 62, 63, 64, 65, 66, 68], "use_sklearn": 28, "user": 66, "usual": 66, "util": [32, 38, 43, 44, 45, 46, 47, 50, 55, 66], "v": [15, 33, 57, 60, 61, 67, 68], "vaadia": 68, "vajda": 68, "valu": [5, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 59, 68], "vari": [35, 37, 38, 39, 59], "variabl": [11, 12, 14, 15, 16, 17, 19, 21, 24, 25, 27, 28, 29, 36, 37, 38, 39, 40, 44, 45, 46, 47, 58, 59, 62, 65, 66, 68], "varianc": [37, 39, 40, 68], "variat": 68, "varibl": 46, "variou": [11, 33, 34, 36, 37, 38, 39, 41, 66, 67, 68], "varlei": 68, "vast": 68, "ve": 51, "vec": [37, 39], "vejnarov": 68, "verbos": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 55, 58, 65], "veri": [40, 45, 46, 47], "version": [62, 64], "via": 68, "virgil": 68, "visit": 68, "visual": 50, "vito": 68, "vmap": 65, "vogt": 68, "vulner": 68, "wa": [47, 62], "wai": [45, 46, 47, 59, 62, 64, 68], "want": [44, 51, 61, 66], "watab": 25, "watanab": 68, "we": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 61, 65, 66, 68], "web": [61, 68], "well": [36, 62, 66, 68], "were": 68, "weslei": 68, "what": [30, 44, 59, 62], "when": [19, 27, 35, 36, 37, 38, 39, 44, 46, 47, 55, 58, 59, 62, 65, 68], "where": [40, 55, 61, 68], "whether": [8, 27, 30, 44, 45, 58, 59, 66, 68], "which": [21, 24, 28, 40, 44, 47, 58, 59, 62, 68], "while": [40, 43, 44, 45, 46, 50, 65], "whole": [44, 46, 68], "wholeminussum": 19, "why": 44, "width": 30, "william": 68, "win": [44, 59], "window": [44, 59], "within": 68, "without": [15, 27, 44], "word": 62, "work": [59, 62, 64, 68], "workspac": 68, "would": 62, "wrap": 51, "write": 51, "written": [11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 51, 68], "www": [51, 68], "x": [6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 30, 31, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 59, 65, 68], "x_": [14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 37, 43, 44, 45, 46, 47, 58, 68], "x_0": 68, "x_1": [37, 68], "x_2": 37, "x_axi": 55, "x_bin": 28, "x_high": [35, 36, 37, 38, 39], "x_i": [37, 68], "x_j": [14, 44, 68], "x_jax": 51, "x_low": [35, 36, 37, 38, 39], "x_m": 58, "x_n": [37, 68], "x_np": 51, "x_red": 58, "x_ref": 59, "x_syn": 58, "x_t": [21, 24, 46, 68], "xarrai": [30, 61, 64], "xgi": 50, "xi": [37, 39], "xla": 65, "xlabel": [35, 36, 38, 44, 47, 55, 59, 65], "xlim": 59, "xn": 31, "xtick": 55, "y": [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 37, 38, 39, 40, 44, 45, 46, 47, 59, 68], "y_": [21, 24, 46, 58, 68], "y_jax": 51, "y_norm": 58, "y_np": 51, "y_red": 58, "y_syn": 58, "y_t": [21, 24, 46, 68], "yamir": 68, "year": 68, "yi": 39, "ylabel": [35, 36, 38, 44, 47, 55, 58, 59, 65], "ylim": 59, "you": [40, 45, 46, 47, 50, 51, 61, 64, 66], "young": 68, "your": [51, 61, 65, 66], "your_usernam": 61, "yuri": 68, "z": 68, "ze": 68, "zero": [30, 35, 36, 37, 38, 39, 40, 46, 58], "zini": 68, "zip": [33, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 55, 58, 59, 65], "\u00e1": 68, "\u00e8": 68, "\u00e9": 68, "\u00f3": 68, "\u00f6": 68, "\u0142": 68, "\u017c": 68, "\u03c3": 35}, "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_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", "Introduction to core information theoretical metrics", "Computation times", "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", "Quick introduction to jax", "Computation times", "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", "Glossary", "HOI : High-Performance Estimation of Higher-Order Interactions", "Installation", "Jax: linear algebra backend", "Quickstart", "Computation times", "Theoretical background"], "titleterms": {"": [44, 68], "For": 51, "algebra": 65, "an": 35, "approach": [55, 58], "arrai": 65, "backend": 65, "background": 68, "behavior": [1, 44, 59, 68], "bibliographi": 68, "bootstrap": [33, 54, 55], "class": 32, "code": [44, 61], "combin": [5, 44, 45, 46, 47], "combinatori": 0, "comparison": [35, 36, 37, 38, 39, 65], "compil": 51, "comput": [41, 48, 52, 53, 55, 56, 60, 65, 66, 67], "condit": 43, "confid": 55, "contribut": 61, "copi": 59, "core": [0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 68], "correl": [44, 68], "cpu": 65, "data": [35, 37, 38, 39, 44, 50, 58, 66], "decod": 58, "decomposit": [46, 68], "definit": [35, 36, 37, 38, 39, 45, 46, 47], "depend": 64, "deriv": 44, "develop": 61, "digit": 28, "dimension": [37, 39, 65], "distribut": [35, 37, 38, 39], "document": 61, "dtc": [14, 44], "dual": [44, 68], "dynam": [44, 59], "encod": [1, 44, 59, 68], "entropi": [0, 33, 34, 35, 36, 37, 40, 65, 68], "entropy_bin": 6, "entropy_gauss": 7, "entropy_gc": 8, "entropy_kernel": 9, "entropy_knn": 10, "estim": [35, 36, 37, 38, 39, 50, 55, 63], "exampl": [11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 33], "exponenti": 35, "from": [35, 37, 38, 39, 68], "function": [32, 51], "get": 50, "get_entropi": 11, "get_mi": 12, "get_nbest_mult": 29, "glossari": 62, "gpu": 65, "gradient": 68, "gradientoinfo": 15, "high": [37, 39, 63], "higher": [50, 55, 63, 65, 66, 68], "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, 33, 42, 50, 58, 61, 63], "how": 59, "index": [45, 68], "individu": 50, "inform": [0, 33, 34, 38, 40, 43, 44, 46, 55, 58, 68], "infotopo": 16, "infotot": 17, "inspect": [50, 66], "instal": [61, 64, 66], "integr": 46, "integra": 68, "interact": [43, 50, 63, 65, 66, 68], "interv": 55, "introduct": [40, 51], "isol": 43, "its": 44, "jax": [51, 65], "jit": 51, "landscap": [30, 50], "larg": 65, "learn": 58, "linear": 65, "list": 32, "loop": 51, "machin": 58, "measur": [0, 68], "metric": [1, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 40, 42], "mi": [38, 39, 68], "miscellan": [33, 49], "mmi": [47, 68], "modul": 51, "multi": 65, "multinorm": [37, 39], "multiplet": [43, 50, 65], "multivari": [36, 44, 45, 47], "mutual": [0, 33, 34, 38, 40, 68], "network": [1, 44, 68], "normal": [31, 35, 36, 38], "numpi": 51, "o": [43, 44, 55, 68], "oinfo": 18, "oper": 59, "order": [43, 50, 55, 63, 65, 66, 68], "pairwis": 68, "perform": [63, 65], "permut": [33, 54], "plot": [2, 26, 50, 55], "plot_landscap": 26, "postprocess": 4, "practic": 66, "prepare_for_it": 13, "preprocess": 4, "problem": 43, "pull": 61, "quick": 51, "quickstart": 66, "recommend": 66, "redund": [43, 44, 45, 46, 47, 55, 59, 68], "redundancymmi": 20, "redundancyphiid": 21, "request": 61, "result": [50, 66], "rsi": [19, 68], "sampl": [35, 37, 38, 39], "simul": [3, 27, 43, 44, 45, 46, 47, 50, 58, 59, 66], "simulate_hoi_gauss": 27, "sinfo": 22, "spatial": 43, "split": 39, "spread": [43, 55], "statist": [33, 54], "sum": 59, "summari": 50, "synergi": [45, 46, 47, 55, 59, 68], "synergist": [43, 44, 59], "synergymmi": 23, "synergyphiid": 24, "target": 44, "tc": [25, 44], "theoret": [40, 58, 68], "time": [41, 48, 52, 53, 56, 60, 67], "topolog": [43, 68], "total": [44, 68], "tutori": [33, 57], "uniform": 35, "univari": [45, 47], "us": [11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 43, 44, 51, 55, 58, 61], "user": 64, "util": [4, 28, 29, 30, 31], "v": [58, 65], "variou": 35, "vector": 51, "vmap": 51, "x": 58, "y": 58}})
\ No newline at end of file
diff --git a/sg_execution_times.html b/sg_execution_times.html
index 6c89e4a2..8761155e 100644
--- a/sg_execution_times.html
+++ b/sg_execution_times.html
@@ -420,7 +420,7 @@ <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>67:21.360</strong> total execution time for 16 files <strong>from all galleries</strong>:</p>
+<p><strong>67:19.010</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" />
@@ -442,63 +442,63 @@ <h1>Computation times</h1>
 </thead>
 <tbody>
 <tr class="row-even"><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>42:37.326</p></td>
+<td><p>42:39.388</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><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>22:57.337</p></td>
+<td><p>22:53.701</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_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>00:24.671</p></td>
+<td><p>00:24.547</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><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>00:17.244</p></td>
+<td><p>00:17.157</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><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>00:16.615</p></td>
+<td><p>00:16.602</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>00:15.385</p></td>
+<td><p>00:15.292</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>00:09.005</p></td>
+<td><p>00:08.897</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>00:04.859</p></td>
+<td><p>00:04.684</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>00:03.920</p></td>
+<td><p>00:03.908</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>00:03.711</p></td>
+<td><p>00:03.707</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>00:03.486</p></td>
+<td><p>00:03.434</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>00:03.022</p></td>
+<td><p>00:02.986</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>00:01.672</p></td>
+<td><p>00:01.725</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>00:01.574</p></td>
+<td><p>00:01.492</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="auto_examples/miscellaneous/plot_jax.html#sphx-glr-auto-examples-miscellaneous-plot-jax-py"><span class="std std-ref">Quick introduction to jax</span></a> (<code class="docutils literal notranslate"><span class="pre">../examples/miscellaneous/plot_jax.py</span></code>)</p></td>
-<td><p>00:01.302</p></td>
+<td><p>00:01.260</p></td>
 <td><p>0.0</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="auto_examples/it/plot_tutorial_core.html#sphx-glr-auto-examples-it-plot-tutorial-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/plot_tutorial_core.py</span></code>)</p></td>