Belief Network

A belief network is a DAG in which

• nodes represent random variables
• edges represent conditional dependencies
• CPT denotes how each node depend on its parents

BN = DAG + CPTs

Constructing a BN

1. Choose random variables
2. Choose ordering of the nodes (best is to start with root cases, then what they influence)
3. While there are variables left
   1. Add a node X to BN
   2. Set the parents of X to be the minimal set satisfying X
   3. Define CPT P(X|Parents(Xi)

Advantages of BN

1. More compact representation of joint distributions (originally 2^k for k values, O(n 2^k) with BN)
2. Clean separation of qualitative vs quantitative knowledge; DAG encodes (conditional independence), CPTs encode numerical influences.