Lecture 19 Bayesian Networks III

#notes#cs471

Recap §

Recap: Independence in a BN §

Active / Inactive Paths: Question: Are X and Y conditionally independent given evidence variables {Z}

• Yes, if X and Y are “d-separated” by Z
• Consider all (undirected) paths from X to Y
• No active paths = independence

A path is active if each triple is active.

Recap: Inference §

Inference: Calculating some useful quantity from a joint probability distribution.

Inference by Enumeration

• General Case:
  • Evidence Variables: $E_1...E_k=e_1...e_k$
  • Query* Variable: $Q$
  • Hidden Variables: $H_1...H_r$
• We Want: $P(Q|e_1...e_k)$

1. Select entries consistent with evidence
2. Sum out h to get joint of query and evidence
3. Normalize