BayesNet Enumeration

reachtarunhere · reachtarunhere · commit a121360ce740 · 2016-07-07T03:23:28.000+05:30
diff --git a/probability.ipynb b/probability.ipynb
@@ -609,6 +609,75 @@
    "source": [
     "burglary.variable_node('Alarm').cpt"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Exact Inference in Bayesian Networks\n",
+    "\n",
+    "A Bayes Network is a more compact representation of the full joint distribution and like full joint distributions allows us to do inference i.e. answer questions about probability distributions of random variables given some evidence.\n",
+    "\n",
+    "Exact algorithms don't scale well for larger networks. Approximate algorithms are explained in the next section.\n",
+    "\n",
+    "### Inference by Enumeration\n",
+    "\n",
+    "We apply techniques similar to those used for **enumerate_joint_ask** and **enumerate_joint** to draw inference from Bayesian Networks. **enumeration_ask** and **enumerate_all** implement the algorithm described in **Figure 14.9** of the book."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%psource enumerate_all"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**enumerate__all** recursively evaluates a general form of the **Equation 14.4** in the book.\n",
+    "\n",
+    "$$\\textbf{P}(X | \\textbf{e}) = α \\textbf{P}(X, \\textbf{e}) = α \\sum_{y} \\textbf{P}(X, \\textbf{e}, \\textbf{y})$$ \n",
+    "\n",
+    "such that **P(X, e, y)** is written in the form of product of conditional probabilities **P(variable | parents(variable))** from the Bayesian Network.\n",
+    "\n",
+    "**enumeration_ask** calls **enumerate_all** on each value of query variable **X** and finally normalizes them. \n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%psource enumeration_ask"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let us solve the problem of finding out **P(Burglary=True | JohnCalls=True, MaryCalls=True)** using the **burglary** network.**enumeration_ask** takes three arguments **X** = variable name, **e** = Evidence (in form a dict like previously explained), **bn** = The Bayes Net to do inference on."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "ans_dist = enumeration_ask('Burglary', {'JohnCalls': True, 'MaryCalls': True}, burglary)\n",
+    "ans_dist[True]"
+   ]
   }
  ],
  "metadata": {
