#### 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

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

#### Advantages of BN

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