Introduction to Artificial Intelligence - Old Questions

Bayesian networks are a type of probabilistic graphical model that uses Bayesian inference for probability computations.

• Bayesian Network is a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph.
• Nodes in the graph represent the random variables and the directed edges between nodes represent conditional dependencies.
• The edge exists between nodes if there exists conditional probability i.e. a link from X to Y means Y is dependent of X.
• Each nodes are labelled with probability.

E.g.

P(x) = 0.5

P(y/x) = 0.7

P(z) = 0.8

P(u/y) = 0.47

Inference with Bayesian Network:

        Using a Bayesian network to compute probabilities is called inference in Bayesian network.

The first task is to compute the posterior probability distribution for the query variable X, given some assignment of values e to the set of evidence variable E = E₁,......., E_n and the hidden variables are Y = Y₁,.....Y_n. From the full joint probability distribution we can answer the query P(X/e) by computing

        P(x/e) = αP(X, e) = αΣ_Y(X, e, Y)

A Bayesian network gives a complete representation of the full joint distribution, specifically, the terms P(X, e, Y) can be written as products of conditional probabilities from the network.

        Therefore, a query can be answered using a Bayesian network by computing sums of products of conditional probabilities from the network.