CSE 150 Lecture Notes - Lecture 4: Directed Acyclic Graph, Conditional Independence, Product Rule

• School: UCSD
• Department: Computer Science & Engineering
• Course: CSE 150
• Professor: Lawrence Saul

Document Summary

= p(b) p(e|b) p(a|b, e) p(j|a, b, e) p(m|a, b, e, j) These tables are called conditional probability tables (cpts) P(b = 1, e = 0, a = 1, j = 1, m = 0) = p(b=1) p(e=0) p(a = 1|b = 1, e = 0) p(j = 1|a = 1) p(m = 0|a = 1) Any query can be answered from joint probabilities! From product rule: p(b=1|a=1) = p(b=1, a=1) / p(a=1) ratio of unconditional probs. P(b=1,a=1) = (e,j,m) p(b=1, a=1, e = e, j = j, m = m) = (b,e,j,m) p(b = b, e = e, a = 1, j = j, m = m) Let {x 1 , , x n } be n discrete random vars. If all x i {0,1} are binary, then to specify joint p(x 1 = x 1 , , x n = x n ) requires o(2 n ) numbers!