10 Mar 2004
CS 3243 - Uncertainty
21
Conditional
independence contd.
nWrite out full joint distribution using chain
rule:
P(Toothache, Catch, Cavity)
= P(Toothache | Catch, Cavity) P(Catch, Cavity)
= P(Toothache | Catch, Cavity) P(Catch | Cavity) P(Cavity)
= P(Toothache | Cavity) P(Catch | Cavity) P(Cavity)
I.e., 2 + 2 + 1 = 5 independent numbers
nIn most cases, the
use of conditional independence reduces the size of the representation of the joint
distribution from exponential
in n to linear in n.
nConditional
independence is our most basic and robust form of knowledge about uncertain environments.