Ex-No.4 Implementation of Approximate Inference in Bayesian Networks

Aim :

To construct a python program to implement approximate inference using Gibbs Sampling.

Algorithm:

Step 1: Bayesian Network Definition and CPDs:
(i) Define the Bayesian network structure using the BayesianNetwork class from pgmpy.models.
(ii) Define Conditional Probability Distributions (CPDs) for each variable using the TabularCPD class.
(iii) Add the CPDs to the network.

Step 2: Printing Bayesian Network Structure:
(i) Print the structure of the Bayesian network using the print(network) statement.

Step 3: Graph Visualization:
(i)Import the necessary libraries (networkx and matplotlib).
(ii)Create a directed graph using networkx.DiGraph().
(iii)Define the nodes and edges of the graph.
(iv)Add nodes and edges to the graph.
(v) Optionally, define positions for the nodes.
(vi) Use nx.draw() to visualize the graph using matplotlib.

Step 4: Gibbs Sampling and MCMC:
(i) Initialize Gibbs Sampling for MCMC using the GibbsSampling class and provide the Bayesian network.
(ii)Set the number of samples to be generated using num_samples.
Step 5: Perform MCMC Sampling:
(i)Use the sample() method of the GibbsSampling instance to perform MCMC sampling.
(ii)Store the generated samples in the samples variable.
Step 6: Approximate Probability Calculation:
(i) Specify the variable for which you want to calculate the approximate probabilities (query_variable).
(ii)Use .value_counts(normalize=True) on the samples of the query_variable to calculate approximate probabilities.
Step 7:Print Approximate Probabilities: (i) Print the calculated approximate probabilities for the specified query_variable.

Program :

NAME:- Gunaseelan G
REG NO:- 212221230031

Import the necessary libraries

from pgmpy.models import BayesianNetwork
from pgmpy.factors.discrete import TabularCPD
from pgmpy.sampling import GibbsSampling
import networkx as nx
import matplotlib.pyplot as plt

Define the Bayesians network Structure

network=BayesianNetwork([('Burglary','Alarm'),
                         ('Earthquake','Alarm'),
                         ('Alarm','JohnCalls'),
                         ('Alarm','MaryCalls')])

Define the conditional Probability Distractions(CPDs)

cpd_burglay=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=[[0.99,0.3],[0.01,0.7]],evidence=['Alarm'],evidence_card=[2])

Add CPDs to the network

network.add_cpds(cpd_burglay,cpd_earthquake,cpd_alarm,cpd_john_calls,cpd_mary_calls)

Print the Bayesian network structure

print("Bayesian Network Structure:")
print(network)

Create a Directed Graph

G=nx.DiGraph()

Define nodes and Edges

nodes=['Burglary', 'Earthquake', 'Alarm',' JohnCalls',' MaryCalls']
edges=[('Burglary','Alarm'),('Earthquake','Alarm'),('Alarm','JohnCalls'),('Alarm','MaryCalls')]

Add nodes and Edges to the Graph

G.add_nodes_from(nodes)
G.add_edges_from(edges)

Set the positions from nodes

pos={'Burglary':(0,0),'Earthquake':(2,0),'Alarm':(1,-2),'JohnCalls':(0,-4),'MaryCalls':(2,-4)}

Draw the network

nx.draw(G,pos,with_labels=True,node_size=1500,node_color='skyblue',font_size=10,font_weight='bold',arrowsize=20)
plt.title("Bayesian Network:alarm Problem")
plt.show()

Initialize Gibbs Sampling for MCMC

gibbs_sampler=GibbsSampling(network)

Set the number of samples

num_samples=10000

Perfrom MNMC sampling

samples=gibbs_sampler.sample(size=num_samples)

Calculate approximate probabilities based on the samples

query_variable='Burglary'
query_result=samples[query_variable].value_counts(normalize=True)

Print the approximate probabilities

print('\n Approximate probabilities of {}:'.format(query_variable))
print(query_result)

Output :

Result :

Thus, an Approximate method of interference computation is implemented using Gibbs Sampling in Python

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