update description causal updating

ComputationalPsychiatry · Nov 22, 2024 · 09c80c0 · 09c80c0
1 parent 8756223
commit 09c80c0
Showing 1 changed file with 6 additions and 16 deletions.
diff --git a/docs/source/notebooks/Example_4_Causal.ipynb b/docs/source/notebooks/Example_4_Causal.ipynb
@@ -721,7 +721,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 538,
+   "execution_count": null,
    "id": "45c8cbfa",
    "metadata": {},
    "outputs": [],
@@ -736,27 +736,19 @@
     "    r\"\"\"\n",
     "Causal coupling strength update.\n",
     "\n",
-    "The causal coupling strength \\( w_{ij} \\) is updated in three steps:\n",
+    "The causal coupling strength \\( w_{ij} \\) is updated as follows:\n",
     "\n",
-    "1. **Precision-weighted prediction error**:\n",
-    "   \n",
-    "   .. math::\n",
-    "       \\Delta_j = \\pi_j \\cdot \\epsilon_j\n",
-    "\n",
-    "   where:\n",
-    "   - \\( \\pi_j \\) is the precision of the child node.\n",
-    "   - \\( \\epsilon_j = y_j - \\hat{y}_j \\) is the prediction error, defined as the difference between the observed value \\( y_j \\) and the predicted value \\( \\hat{y}_j \\).\n",
-    "\n",
-    "2. **Raw update**:\n",
+    "1. **Raw update**:\n",
     "   \n",
     "   .. math::\n",
     "       w_{ij}^{t} = w_{ij}^{t-1} + \\eta \\cdot \\Delta_j \\cdot \\mu_i\n",
     "\n",
     "   where:\n",
     "   - \\( \\eta \\) is the learning rate.\n",
     "   - \\( \\mu_i \\) is the parent's expected mean.\n",
+    "   - \\( \\Delta_j \\) is the precision-weighted PE.\n",
     "\n",
-    "3. **Rescaling with Sigmoid-like Transformation**:\n",
+    "2. **Rescaling with Sigmoid-like transformation**:\n",
     "   \n",
     "   .. math::\n",
     "       w_{ij} = \\frac{x^\\text{temperature}}{x^\\text{temperature} + (1 - x)^\\text{temperature}}\n",
@@ -844,7 +836,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 541,
+   "execution_count": null,
    "id": "9f8a053b",
    "metadata": {},
    "outputs": [
@@ -909,7 +901,6 @@
     "\n",
     "axs.plot(\n",
     "    causal_hgf.node_trajectories[1][\"temp\"]['value_prediction_error'], \n",
-    "  #  colour = \"blue\", \n",
     "    linestyle=\"--\", \n",
     "    linewidth=1.0, \n",
     "    label=\"PE child\"\n",
@@ -920,7 +911,6 @@
     "\n",
     "axs.plot(\n",
     "    causal_hgf.node_trajectories[0]['mean'], \n",
-    "  #  colour = \"green\", \n",
     "    linestyle=\"-\", \n",
     "    linewidth=1.0, \n",
     "    label=\"Mean parent\"\n",