To implement the inference Burglary P(B| j,⥗m) in alarm problem by using Variable Elimination method in Python.
Step 1: Define the Bayesian Network structure for alarm problem with 5 random variables, Burglary,Earthquake,John Call,Mary Call and Alarm.
Step 2: Define the Conditional Probability Distributions (CPDs) for each variable using the TabularCPD class from the pgmpy library.
Step 3: Add the CPDs to the network.
Step 4: Initialize the inference engine using the VariableElimination class from the pgmpy library.
Step 5: Define the evidence (observed variables) and query variables.
Step 6: Perform exact inference using the defined evidence and query variables.
Step 7: Print the results.
!pip install pgmpy
from pgmpy.models import BayesianNetwork
from pgmpy.factors.discrete import TabularCPD
from pgmpy.inference import VariableElimination
# Define the network structure
network = BayesianNetwork([('Burglary', 'Alarm'),
('Earthquake', 'Alarm'),
('Alarm', 'JohnCalls'),
('Alarm', 'MaryCalls')])
# Define the Conditional Probability Distributions (CPDs)
cpd_burglary = TabularCPD(variable='Burglary', variable_card=2, values=[[0.999], [0.001]])
cpd_earthquake = TabularCPD(variable='Earthquake', variable_card=2, values=[[0.998], [0.002]])
cpd_alarm = TabularCPD(variable='Alarm', variable_card=2,
values=[[0.999, 0.71, 0.06, 0.05],
[0.001, 0.29, 0.94, 0.95]],
evidence=['Burglary', 'Earthquake'],
evidence_card=[2, 2])
cpd_john_calls = TabularCPD(variable='JohnCalls', variable_card=2,
values=[[0.95, 0.1],
[0.05, 0.9]],
evidence=['Alarm'],
evidence_card=[2])
cpd_mary_calls = TabularCPD(variable='MaryCalls', variable_card=2,
values=[[0.99, 0.01],
[0.01, 0.99]],
evidence=['Alarm'],
evidence_card=[2])
# Add CPDs to the network
network.add_cpds(cpd_burglary, cpd_earthquake, cpd_alarm, cpd_john_calls, cpd_mary_calls)
# Initialize the inference engine
inference = VariableElimination(network)
# Perform exact inference
evidence = {'JohnCalls': 1, 'MaryCalls': 0}
query_variable = 'Burglary'
result = inference.query(variables=[query_variable], evidence=evidence)
print(result)
Thus, Bayesian Inference was successfully determined using Variable Elimination Method
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