[Probability] Belief Network

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


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.