Sample calculation for Simple Bayesian Network

Pim-Mostert · Oct 4, 2024 · d0adfda · d0adfda
1 parent 242caa3
commit d0adfda
Showing 1 changed file with 29 additions and 23 deletions.
diff --git a/docs/SimpleBayesianNetwork.ipynb b/docs/SimpleBayesianNetwork.ipynb
@@ -61,7 +61,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 37,
    "metadata": {},
    "outputs": [
     {
@@ -72,7 +72,7 @@
        "       [0.33333333, 0.66666667]])"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 37,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -185,45 +185,51 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 38,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([0.11764706, 0.88235294])"
+       "array([[0.11764706, 0.88235294],\n",
+       "       [0.8       , 0.2       ],\n",
+       "       [0.33333333, 0.66666667]])"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 38,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "Y_hat = 0\n",
+    "P_QxY = np.zeros((3, 2))\n",
     "\n",
-    "# Upwards\n",
-    "d3 = (np.arange(3) == Y_hat).astype(float)\n",
-    "a3 = d3\n",
-    "b2 = (P_YxQ * a3[None, :]).sum(axis=1)\n",
-    "a1 = b2\n",
+    "# For each possible input value\n",
+    "for Y_hat in [0, 1, 2]:\n",
+    "    # Messages upwards\n",
+    "    d3 = (np.arange(3) == Y_hat).astype(float)\n",
+    "    a3 = d3\n",
+    "    b2 = (P_YxQ * a3[None, :]).sum(axis=1)\n",
+    "    a1 = b2\n",
     "\n",
-    "# Downards\n",
-    "b1 = P_Q\n",
-    "a2 = b1\n",
-    "b3 = (P_YxQ * a2[:, None]).sum(axis=0)\n",
-    "\n",
-    "\n",
-    "# maak netjes\n",
-    "a1 * b1 / (a1 * b1).sum()"
+    "    # Messages downwards\n",
+    "    b1 = P_Q\n",
+    "    a2 = b1\n",
+    "    b3 = (P_YxQ * a2[:, None]).sum(axis=0)\n",
+    "    \n",
+    "    # Calculate P_Q\n",
+    "    P_QxY[Y_hat, :] = a1 * b1 / (a1 * b1).sum()\n",
+    "    \n",
+    "P_QxY\n",
+    "    "
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "source": [
+    "These values match with the ones calculated naively, showing the correctness of the algorithm."
+   ]
   }
  ],
  "metadata": {