kiran03-jagadeesh / ex-3--aai

NAME : Kiran J

REGISTER NO : 212221240022

EX. NO.3

DATE: 07.02.2023

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:

• Define the Bayesian network structure using the BayesianNetwork class from pgmpy.models.
• Define Conditional Probability Distributions (CPDs) for each variable using the TabularCPD class.
• Add the CPDs to the network.

Step 2: Printing Bayesian Network Structure:

• Print the structure of the Bayesian network using the print(network) statement.

Step 3: Graph Visualization:

• Import the necessary libraries (networkx and matplotlib).
• Create a directed graph using networkx.DiGraph().
• Define the nodes and edges of the graph.
• Add nodes and edges to the graph.
• Optionally, define positions for the nodes.
• Use nx.draw() to visualize the graph using matplotlib.

Step 4: Gibbs Sampling and MCMC:

• Initialize Gibbs Sampling for MCMC using the GibbsSampling class and provide the Bayesian network.
• Set the number of samples to be generated using num_samples.

Step 5: Perform MCMC Sampling:

• Use the sample() method of the GibbsSampling instance to perform MCMC sampling.
• Store the generated samples in the samples variable.

Step 6: Approximate Probability Calculation:

• Specify the variable for which you want to calculate the approximate probabilities (query_variable).
• Use .value_counts(normalize=True) on the samples of the query_variable to calculate approximate probabilities.

Step 7:Print Approximate Probabilities:

• Print the calculated approximate probabilities for the specified query_variable.

Program:

!pip install pgmpy

from pgmpy.models import BayesianNetwork
from pgmpy.factors.discrete import TabularCPD
from pgmpy.sampling import GibbsSampling

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

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, 0.911]],evidence=['Alarm'], evidence_card=[2])
cpd_mary_calls = TabularCPD (variable='MaryCalls', variable_card=2,values=[[0.99, 0.3], [0.01, 0.711]],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)
# Print the Bayesian network structure 
print("Bayesian Network Structure: ") 
print (network)

!pip install nx
import networkx as nx

# 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 positions for nodes (optional)
pos = {
    'Burglary': (0, 0),
    'Earthquake':(2, 0),
    'Alarm' : (1, -2),
    'JohnCalls': (0, -4),
    'MaryCalls' : (2, 4)
}
# Draw the graph
nx.draw(G, pos, with_labels=True, node_size=1500,node_color='skyblue', font_size=10,font_weight='bold', arrowsize=20)
import matplotlib.pyplot as plt
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
# Perform MCMC 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("\nApproximate Probabilities of {}:".format (query_variable))
print (query_result)

Output:

Bayesian Network Structure :

Graph :

Approximate Probabilities of Burglary:

Result:

Thus, Gibb's Sampling( Approximate Inference method) is succuessfully implemented using python.