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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Inference in Discrete Bayesian Network"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this notebook, we show a simple example for doing Exact inference in Bayesian Networks using pgmpy. We will be using the Asia network (http://www.bnlearn.com/bnrepository/#asia) for this example."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step 1: Define the model."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Fetch the asia model from the bnlearn repository\n",
"\n",
"from pgmpy.utils import get_example_model\n",
"\n",
"asia_model = get_example_model(\"asia\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Nodes: ['asia', 'tub', 'smoke', 'lung', 'bronc', 'either', 'xray', 'dysp']\n",
"Edges: [('asia', 'tub'), ('tub', 'either'), ('smoke', 'lung'), ('smoke', 'bronc'), ('lung', 'either'), ('bronc', 'dysp'), ('either', 'xray'), ('either', 'dysp')]\n"
]
},
{
"data": {
"text/plain": [
"[<TabularCPD representing P(asia:2) at 0x7f08a40e6a90>,\n",
" <TabularCPD representing P(bronc:2 | smoke:2) at 0x7f08a40e6dc0>,\n",
" <TabularCPD representing P(dysp:2 | bronc:2, either:2) at 0x7f08a40fa730>,\n",
" <TabularCPD representing P(either:2 | lung:2, tub:2) at 0x7f08a40fa100>,\n",
" <TabularCPD representing P(lung:2 | smoke:2) at 0x7f08a40fa790>,\n",
" <TabularCPD representing P(smoke:2) at 0x7f08a40fa5e0>,\n",
" <TabularCPD representing P(tub:2 | asia:2) at 0x7f08a40fac40>,\n",
" <TabularCPD representing P(xray:2 | either:2) at 0x7f08a40fab80>]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"print(\"Nodes: \", asia_model.nodes())\n",
"print(\"Edges: \", asia_model.edges())\n",
"asia_model.get_cpds()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you would like to create a model from scratch, please refer to the Creating Bayesian Networks notebook: https://github.com/pgmpy/pgmpy/blob/dev/examples/Creating%20a%20Bayesian%20Network.ipynb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step 2: Initialize the inference class"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Currently, pgmpy support two algorithms for inference: 1. Variable Elimination and, 2. Belief Propagation. Both of these are exact inference algorithms. The following example uses `VariableElimination` but `BeliefPropagation` has an identifcal API, so all the methods show below would also work for `BeliefPropagation`."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Initializing the VariableElimination class\n",
"\n",
"from pgmpy.inference import VariableElimination\n",
"\n",
"asia_infer = VariableElimination(asia_model)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step 3: Doing Inference using hard evidence"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Finding Elimination Order: : : 0it [00:00, ?it/s]\n",
"0it [00:00, ?it/s]\u001b[A\n",
"\n",
"0it [00:00, ?it/s]\u001b[A\n",
"Finding Elimination Order: : : 0it [00:00, ?it/s]\u001b[A\n",
"\n",
"0it [00:00, ?it/s]\u001b[A\u001b[A\n",
"\n",
"\n",
"0it [00:00, ?it/s]\u001b[A\u001b[A\n",
"\n",
"Finding Elimination Order: : : 0it [00:00, ?it/s]\u001b[A\u001b[A\n",
"\n",
"\n",
"0it [00:00, ?it/s]\u001b[A\u001b[A\u001b[A"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"+------------+--------------+\n",
"| bronc | phi(bronc) |\n",
"+============+==============+\n",
"| bronc(yes) | 0.3000 |\n",
"+------------+--------------+\n",
"| bronc(no) | 0.7000 |\n",
"+------------+--------------+\n",
"+------------+-----------+-------------------+\n",
"| bronc | asia | phi(bronc,asia) |\n",
"+============+===========+===================+\n",
"| bronc(yes) | asia(yes) | 0.0060 |\n",
"+------------+-----------+-------------------+\n",
"| bronc(yes) | asia(no) | 0.5940 |\n",
"+------------+-----------+-------------------+\n",
"| bronc(no) | asia(yes) | 0.0040 |\n",
"+------------+-----------+-------------------+\n",
"| bronc(no) | asia(no) | 0.3960 |\n",
"+------------+-----------+-------------------+\n",
"+------------+--------------+\n",
"| bronc | phi(bronc) |\n",
"+============+==============+\n",
"| bronc(yes) | 0.3000 |\n",
"+------------+--------------+\n",
"| bronc(no) | 0.7000 |\n",
"+------------+--------------+\n",
"+-----------+-------------+\n",
"| asia | phi(asia) |\n",
"+===========+=============+\n",
"| asia(yes) | 0.0100 |\n",
"+-----------+-------------+\n",
"| asia(no) | 0.9900 |\n",
"+-----------+-------------+\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"# Computing the probability of bronc given smoke=no.\n",
"q = asia_infer.query(variables=[\"bronc\"], evidence={\"smoke\": \"no\"})\n",
"print(q)\n",
"\n",
"# Computing the joint probability of bronc and asia given smoke=yes\n",
"q = asia_infer.query(variables=[\"bronc\", \"asia\"], evidence={\"smoke\": \"yes\"})\n",
"print(q)\n",
"\n",
"# Computing the probabilities (not joint) of bronc and asia given smoke=no\n",
"q = asia_infer.query(variables=[\"bronc\", \"asia\"], evidence={\"smoke\": \"no\"}, joint=False)\n",
"for factor in q.values():\n",
" print(factor)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n",
"\n",
"\n",
"0it [00:00, ?it/s]\u001b[A\u001b[A\u001b[A\n",
"\n",
"\n",
"Finding Elimination Order: : : 0it [00:00, ?it/s]\u001b[A\u001b[A\u001b[A\n",
"\n",
"\n",
"\n",
"0it [00:00, ?it/s]\u001b[A\u001b[A\u001b[A\u001b[A\n",
"\n",
"\n",
"\n",
"\n",
"0it [00:00, ?it/s]\u001b[A\u001b[A\u001b[A\u001b[A\n",
"\n",
"\n",
"\n",
"Finding Elimination Order: : : 0it [00:00, ?it/s]\u001b[A\u001b[A\u001b[A\u001b[A\n",
"\n",
"\n",
"\n",
"\n",
"0it [00:00, ?it/s]\u001b[A\u001b[A\u001b[A\u001b[A\u001b[A"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'bronc': 'no'}\n",
"{'bronc': 'yes', 'asia': 'no'}\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"# Computing the MAP of bronc given smoke=no.\n",
"q = asia_infer.map_query(variables=[\"bronc\"], evidence={\"smoke\": \"no\"})\n",
"print(q)\n",
"\n",
"# Computing the MAP of bronc and asia given smoke=yes\n",
"q = asia_infer.map_query(variables=[\"bronc\", \"asia\"], evidence={\"smoke\": \"yes\"})\n",
"print(q)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step 5: Inference using virtual evidence"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Finding Elimination Order: : : 0it [00:04, ?it/s]\n",
"Finding Elimination Order: : : 0it [00:04, ?it/s]\n",
"Finding Elimination Order: : : 0it [00:02, ?it/s]\n",
"Finding Elimination Order: : : 0it [00:02, ?it/s]\n",
"\n",
"0it [00:00, ?it/s]\u001b[A\n",
"Finding Elimination Order: : : 0it [00:00, ?it/s]\u001b[A\n",
"\n",
"0it [00:00, ?it/s]\u001b[A\u001b[A"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"+------------+--------------+\n",
"| bronc | phi(bronc) |\n",
"+============+==============+\n",
"| bronc(yes) | 0.3000 |\n",
"+------------+--------------+\n",
"| bronc(no) | 0.7000 |\n",
"+------------+--------------+\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"from pgmpy.factors.discrete import TabularCPD\n",
"\n",
"# Get state name, which ensure lung evidence has same state names as asia_model\n",
"state_names = asia_model.get_cpds('lung').state_names\n",
"\n",
"lung_virt_evidence = TabularCPD(variable=\"lung\", variable_card=2, values=[[0.4], [0.6]],state_names=state_names)\n",
"\n",
"# Query with hard evidence smoke = no and virtual evidence lung = [0.4, 0.6]\n",
"q = asia_infer.query(\n",
" variables=[\"bronc\"], evidence={\"smoke\": \"no\"}, virtual_evidence=[lung_virt_evidence]\n",
")\n",
"print(q)\n",
"\n",
"# Query with hard evidence smoke = no and virtual evidences lung = [0.4, 0.6] and bronc = [0.3, 0.7]\n",
"lung_virt_evidence = TabularCPD(variable=\"lung\", variable_card=2, values=[[0.4], [0.7]])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"+-----------+------------+-----------+\n",
"| smoke | smoke(yes) | smoke(no) |\n",
"+-----------+------------+-----------+\n",
"| lung(yes) | 0.1 | 0.01 |\n",
"+-----------+------------+-----------+\n",
"| lung(no) | 0.9 | 0.99 |\n",
"+-----------+------------+-----------+\n"
]
}
],
"source": [
"print(asia_model.get_cpds(\"lung\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step 4: Troubleshooting for slow inference"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the case of large models, or models in which variables have a lot of states, inference can be quite slow. Some of the ways to deal with it are:\n",
"\n",
"1. Reduce the number of states of variables by combining states together.\n",
"2. Try a different elimination order by specifying `elimination_order` argument. Possible options are: MinFill, MinNeighbors, MinWeight, WeightedMinFill. \n",
"3. Try a custom elimination order: The implemented heuristics for computing the elimination order might not be efficient in every case. If you can think of a more efficient order, you can also pass it as a list to the `elimination_order` argument.\n",
"4. If it is still too slow, try using approximate inference using sampling algorithms."
]
}
],
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