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brainets · Jul 4, 2024 · 801a142 · 801a142
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diff --git a/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip b/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip
diff --git a/_downloads/4481fca80fcd36eb6fde9d9cb4e3134c/plot_entropies.py b/_downloads/4481fca80fcd36eb6fde9d9cb4e3134c/plot_entropies.py
@@ -33,9 +33,9 @@
 
 # list of estimators to compare
 metrics = {
-    "GC": get_entropy("gc", biascorrect=False),
+    "GC": get_entropy("gc"),
+    "Gaussian": get_entropy("gauss"),
     "KNN-3": get_entropy("knn", k=3),
-    "KNN-10": get_entropy("knn", k=10),
     "Kernel": get_entropy("kernel"),
 }
 

diff --git a/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip b/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip
diff --git a/_downloads/a1ef8dbbc19c785bec2a5cc12335798e/plot_entropies.ipynb b/_downloads/a1ef8dbbc19c785bec2a5cc12335798e/plot_entropies.ipynb
@@ -33,7 +33,7 @@
       },
       "outputs": [],
       "source": [
-        "# list of estimators to compare\nmetrics = {\n    \"GC\": get_entropy(\"gc\", biascorrect=False),\n    \"KNN-3\": get_entropy(\"knn\", k=3),\n    \"KNN-10\": get_entropy(\"knn\", k=10),\n    \"Kernel\": get_entropy(\"kernel\"),\n}\n\n# number of samples to simulate data\nn_samples = np.geomspace(20, 1000, 15).astype(int)\n\n# number of repetitions to estimate the percentile interval\nn_repeat = 10\n\n\n# plotting function\ndef plot(h_x, h_theoric):\n    \"\"\"Plotting function.\"\"\"\n    for n_m, metric_name in enumerate(h_x.keys()):\n        # get the entropies\n        x = h_x[metric_name]\n\n        # get the color\n        color = f\"C{n_m}\"\n\n        # estimate lower and upper bounds of the [5, 95]th percentile interval\n        x_low, x_high = np.percentile(x, [5, 95], axis=0)\n\n        # plot the entropy as a function of the number of samples and interval\n        plt.plot(n_samples, x.mean(0), color=color, lw=2, label=metric_name)\n        plt.fill_between(n_samples, x_low, x_high, color=color, alpha=0.2)\n\n    # plot the theoretical value\n    plt.axhline(\n        h_theoric, linestyle=\"--\", color=\"k\", label=\"Theoretical entropy\"\n    )\n    plt.legend()\n    plt.xlabel(\"Number of samples\")\n    plt.ylabel(\"Entropy [bits]\")"
+        "# list of estimators to compare\nmetrics = {\n    \"GC\": get_entropy(\"gc\"),\n    \"Gaussian\": get_entropy(\"gauss\"),\n    \"KNN-3\": get_entropy(\"knn\", k=3),\n    \"Kernel\": get_entropy(\"kernel\"),\n}\n\n# number of samples to simulate data\nn_samples = np.geomspace(20, 1000, 15).astype(int)\n\n# number of repetitions to estimate the percentile interval\nn_repeat = 10\n\n\n# plotting function\ndef plot(h_x, h_theoric):\n    \"\"\"Plotting function.\"\"\"\n    for n_m, metric_name in enumerate(h_x.keys()):\n        # get the entropies\n        x = h_x[metric_name]\n\n        # get the color\n        color = f\"C{n_m}\"\n\n        # estimate lower and upper bounds of the [5, 95]th percentile interval\n        x_low, x_high = np.percentile(x, [5, 95], axis=0)\n\n        # plot the entropy as a function of the number of samples and interval\n        plt.plot(n_samples, x.mean(0), color=color, lw=2, label=metric_name)\n        plt.fill_between(n_samples, x_low, x_high, color=color, alpha=0.2)\n\n    # plot the theoretical value\n    plt.axhline(\n        h_theoric, linestyle=\"--\", color=\"k\", label=\"Theoretical entropy\"\n    )\n    plt.legend()\n    plt.xlabel(\"Number of samples\")\n    plt.ylabel(\"Entropy [bits]\")"
       ]
     },
     {

diff --git a/_images/sphx_glr_plot_bootstrapping_001.png b/_images/sphx_glr_plot_bootstrapping_001.png
diff --git a/_images/sphx_glr_plot_bootstrapping_002.png b/_images/sphx_glr_plot_bootstrapping_002.png
diff --git a/_images/sphx_glr_plot_bootstrapping_003.png b/_images/sphx_glr_plot_bootstrapping_003.png
diff --git a/_images/sphx_glr_plot_bootstrapping_thumb.png b/_images/sphx_glr_plot_bootstrapping_thumb.png
diff --git a/_images/sphx_glr_plot_entropies_001.png b/_images/sphx_glr_plot_entropies_001.png
diff --git a/_images/sphx_glr_plot_entropies_002.png b/_images/sphx_glr_plot_entropies_002.png
diff --git a/_images/sphx_glr_plot_entropies_003.png b/_images/sphx_glr_plot_entropies_003.png
diff --git a/_images/sphx_glr_plot_entropies_thumb.png b/_images/sphx_glr_plot_entropies_thumb.png
diff --git a/_images/sphx_glr_plot_infotopo_001.png b/_images/sphx_glr_plot_infotopo_001.png
diff --git a/_images/sphx_glr_plot_infotopo_002.png b/_images/sphx_glr_plot_infotopo_002.png
diff --git a/_images/sphx_glr_plot_infotopo_thumb.png b/_images/sphx_glr_plot_infotopo_thumb.png
diff --git a/_images/sphx_glr_plot_inspect_results_001.png b/_images/sphx_glr_plot_inspect_results_001.png
diff --git a/_images/sphx_glr_plot_ml_vs_it_003.png b/_images/sphx_glr_plot_ml_vs_it_003.png
diff --git a/_images/sphx_glr_plot_oinfo_001.png b/_images/sphx_glr_plot_oinfo_001.png
diff --git a/_images/sphx_glr_plot_oinfo_thumb.png b/_images/sphx_glr_plot_oinfo_thumb.png
diff --git a/_images/sphx_glr_plot_rsi_001.png b/_images/sphx_glr_plot_rsi_001.png
diff --git a/_images/sphx_glr_plot_rsi_thumb.png b/_images/sphx_glr_plot_rsi_thumb.png
diff --git a/_images/sphx_glr_plot_sim_red_syn_001.png b/_images/sphx_glr_plot_sim_red_syn_001.png
diff --git a/_images/sphx_glr_plot_sim_red_syn_002.png b/_images/sphx_glr_plot_sim_red_syn_002.png
diff --git a/_images/sphx_glr_plot_sim_red_syn_thumb.png b/_images/sphx_glr_plot_sim_red_syn_thumb.png
diff --git a/_modules/hoi/core/combinatory.html b/_modules/hoi/core/combinatory.html
@@ -254,10 +254,10 @@
 <li class="toctree-l2 has-children"><a class="reference internal" href="../../../api/api_core.html"><code class="docutils literal notranslate"><span class="pre">hoi.core</span></code></a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.get_entropy.html">hoi.core.get_entropy</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_gc.html">hoi.core.entropy_gc</a></li>
+<li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_gauss.html">hoi.core.entropy_gauss</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_bin.html">hoi.core.entropy_bin</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_knn.html">hoi.core.entropy_knn</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_kernel.html">hoi.core.entropy_kernel</a></li>
-<li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.copnorm_nd.html">hoi.core.copnorm_nd</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.prepare_for_it.html">hoi.core.prepare_for_it</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.get_mi.html">hoi.core.get_mi</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.combinations.html">hoi.core.combinations</a></li>

diff --git a/_modules/hoi/core/entropies.html b/_modules/hoi/core/entropies.html
diff --git a/_modules/hoi/core/mi.html b/_modules/hoi/core/mi.html
@@ -254,10 +254,10 @@
 <li class="toctree-l2 has-children"><a class="reference internal" href="../../../api/api_core.html"><code class="docutils literal notranslate"><span class="pre">hoi.core</span></code></a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.get_entropy.html">hoi.core.get_entropy</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_gc.html">hoi.core.entropy_gc</a></li>
+<li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_gauss.html">hoi.core.entropy_gauss</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_bin.html">hoi.core.entropy_bin</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_knn.html">hoi.core.entropy_knn</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_kernel.html">hoi.core.entropy_kernel</a></li>
-<li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.copnorm_nd.html">hoi.core.copnorm_nd</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.prepare_for_it.html">hoi.core.prepare_for_it</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.get_mi.html">hoi.core.get_mi</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.combinations.html">hoi.core.combinations</a></li>
@@ -377,7 +377,7 @@ <h1>Source code for hoi.core.mi</h1><div class="highlight"><pre>
 <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">from</span> <span class="nn">jax.scipy.special</span> <span class="kn">import</span> <span class="n">digamma</span> <span class="k">as</span> <span class="n">psi</span>
 
-<span class="kn">from</span> <span class="nn">hoi.core.entropies</span> <span class="kn">import</span> <span class="n">get_entropy</span>
+<span class="kn">from</span> <span class="nn">hoi.core.entropies</span> <span class="kn">import</span> <span class="n">get_entropy</span><span class="p">,</span> <span class="n">preproc_gc_2d</span>
 <span class="kn">from</span> <span class="nn">hoi.utils.logging</span> <span class="kn">import</span> <span class="n">logger</span>
 
 <span class="c1">###############################################################################</span>
@@ -407,6 +407,8 @@ <h1>Source code for hoi.core.mi</h1><div class="highlight"><pre>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="k">if</span> <span class="n">method</span> <span class="o">==</span> <span class="s2">&quot;gc&quot;</span><span class="p">:</span>
         <span class="k">return</span> <span class="n">partial</span><span class="p">(</span><span class="n">mi_gc</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+    <span class="k">elif</span> <span class="n">method</span> <span class="o">==</span> <span class="s2">&quot;gauss&quot;</span><span class="p">:</span>
+        <span class="k">return</span> <span class="n">mi_gauss</span>
     <span class="k">elif</span> <span class="n">method</span> <span class="o">==</span> <span class="s2">&quot;knn&quot;</span><span class="p">:</span>
         <span class="k">return</span> <span class="n">partial</span><span class="p">(</span><span class="n">mi_knn</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
     <span class="k">elif</span> <span class="nb">callable</span><span class="p">(</span><span class="n">method</span><span class="p">):</span>
@@ -510,7 +512,10 @@ <h1>Source code for hoi.core.mi</h1><div class="highlight"><pre>
 
 <span class="nd">@partial</span><span class="p">(</span><span class="n">jax</span><span class="o">.</span><span class="n">jit</span><span class="p">,</span> <span class="n">static_argnums</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
 <span class="k">def</span> <span class="nf">mi_gc</span><span class="p">(</span>
-    <span class="n">x</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">biascorrect</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span> <span class="n">demean</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span>
+    <span class="n">x</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">,</span>
+    <span class="n">y</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">,</span>
+    <span class="n">biascorrect</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
+    <span class="n">copnorm</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
 <span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;Mutual information (MI) between two Gaussian variables in bits.</span>
 
@@ -522,8 +527,8 @@ <h1>Source code for hoi.core.mi</h1><div class="highlight"><pre>
 <span class="sd">        (n_features_y, n_samples)</span>
 <span class="sd">    biascorrect : bool | False</span>
 <span class="sd">        Specifies whether bias correction should be applied to the estimated MI</span>
-<span class="sd">    demean : bool | False</span>
-<span class="sd">        Specifies whether the input data have to be demeaned</span>
+<span class="sd">    copnorm : bool | True</span>
+<span class="sd">        Apply gaussian copula normalization</span>
 
 
 <span class="sd">    Returns</span>
@@ -537,8 +542,8 @@ <h1>Source code for hoi.core.mi</h1><div class="highlight"><pre>
 
     <span class="c1"># joint variable</span>
     <span class="n">xy</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">))</span>
-    <span class="k">if</span> <span class="n">demean</span><span class="p">:</span>
-        <span class="n">xy</span> <span class="o">=</span> <span class="n">xy</span> <span class="o">-</span> <span class="n">xy</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)[:,</span> <span class="n">jnp</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span>
+    <span class="k">if</span> <span class="n">copnorm</span><span class="p">:</span>
+        <span class="n">xy</span> <span class="o">=</span> <span class="n">preproc_gc_2d</span><span class="p">(</span><span class="n">xy</span><span class="p">)</span>
     <span class="n">cxy</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">xy</span><span class="p">,</span> <span class="n">xy</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">/</span> <span class="nb">float</span><span class="p">(</span><span class="n">n_samples</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
     <span class="c1"># submatrices of joint covariance</span>
     <span class="n">cx</span> <span class="o">=</span> <span class="n">cxy</span><span class="p">[:</span><span class="n">n_features_x</span><span class="p">,</span> <span class="p">:</span><span class="n">n_features_x</span><span class="p">]</span>
@@ -573,6 +578,31 @@ <h1>Source code for hoi.core.mi</h1><div class="highlight"><pre>
     <span class="k">return</span> <span class="n">i</span>
 
 
+<span class="c1">###############################################################################</span>
+<span class="c1">###############################################################################</span>
+<span class="c1">#                       GAUSSIAN MUTUAL INFORMATION</span>
+<span class="c1">###############################################################################</span>
+<span class="c1">###############################################################################</span>
+
+
+<span class="k">def</span> <span class="nf">mi_gauss</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;Mutual information (MI) between two Gaussian variables in bits.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    x, y : array_like</span>
+<span class="sd">        Arrays to consider for computing the Mutual Information. The two input</span>
+<span class="sd">        variables x and y should have a shape of (n_features_x, n_samples) and</span>
+<span class="sd">        (n_features_y, n_samples)</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    i : float</span>
+<span class="sd">        Information shared by x and y (in bits)</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="n">mi_gc</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">biascorrect</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">copnorm</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
+
+
 <span class="c1">###############################################################################</span>
 <span class="c1">###############################################################################</span>
 <span class="c1">#                         KNN MUTUAL INFORMATION</span>

diff --git a/_modules/hoi/metrics/dtc.html b/_modules/hoi/metrics/dtc.html
@@ -254,10 +254,10 @@
 <li class="toctree-l2 has-children"><a class="reference internal" href="../../../api/api_core.html"><code class="docutils literal notranslate"><span class="pre">hoi.core</span></code></a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.get_entropy.html">hoi.core.get_entropy</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_gc.html">hoi.core.entropy_gc</a></li>
+<li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_gauss.html">hoi.core.entropy_gauss</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_bin.html">hoi.core.entropy_bin</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_knn.html">hoi.core.entropy_knn</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.entropy_kernel.html">hoi.core.entropy_kernel</a></li>
-<li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.copnorm_nd.html">hoi.core.copnorm_nd</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.prepare_for_it.html">hoi.core.prepare_for_it</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.get_mi.html">hoi.core.get_mi</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../../../api/generated/hoi.core.combinations.html">hoi.core.combinations</a></li>
@@ -463,6 +463,7 @@ <h1>Source code for hoi.metrics.dtc</h1><div class="highlight"><pre>
 
 <span class="sd">                * &#39;gc&#39;: gaussian copula entropy [default]. See</span>
 <span class="sd">                  :func:`hoi.core.entropy_gc`</span>
+<span class="sd">                * &#39;gauss&#39;: gaussian entropy. See :func:`hoi.core.entropy_gauss`</span>
 <span class="sd">                * &#39;binning&#39;: binning-based estimator of entropy. Note that to</span>
 <span class="sd">                  use this estimator, the data have be to discretized. See</span>
 <span class="sd">                  :func:`hoi.core.entropy_bin`</span>