toothache  toothache catch  catch catch  catch cavity  cavity Joint PDF

Structure and Semantics of BN draw causal nodes first draw directed edges to effects (“direct causes”) links encode conditional probability tables (CPT over parents) fewer parameters than full joint PDF absence of link is related to independence

child is cond.dep. on parent: P(B|A) parent is cond.dep. on child: –P(A|B)=P(B|A)P(A)/P(B) what about when one node is not an ancestor of the other? e.g. siblings ABAB A and B are only conditionally independent given C

simple trees poly-trees (singly connected, one path between any pair of nodes) “cyclic” (using undirected edges) – much harder to do computations explaining away: P(sprinkler | wetGrass) = 0.43 P(sprinkler | wetGrass,rain) = 0.19

A Bayesian network approach to threat valuation with application to an air defense scenario, Johansson and Falkman

Lumiere – Office Assistant

Inference Tasks posterior: P(Xi|{Zi}) –Zi observed vars, with unobserved variables Yi, marginalized out –prediction vs. diagnosis –evidence combination is crucial –handling unobserved variables is crucial all marginals: P(Ai) – like priors, but for interior nodes too subjoint: P(A,B) boolean queries most-probable explanation: –argmax{Yi} P(Yi U Zi) – state with highest joint probability

(see slides 4-10 in for discussion of Enumeration and VariableElimination)

from: Inference in Bayesian Networks, D’Ambrosio full joint PDF: sub-joint conditional (normalized):

Belief Propagation (this figure happens to come from see also: wiki, Ch. 8 in Bishop PR&ML