• Probabilistic (Bayesian) representations of
knowledge have had a major impact on AI
– contrast with symbolic/logical knowledge bases
– necessity to handle uncertainty in real world apps
– recent advances allow scaling up to larger networks
• Example applications of Bayesian networks
– HCI: inferring intent in conversation/action, plan
recognition, intelligent tutoring
– vision – image interpretation, de-noising
– control – variables that influence flight
– medicine
– economics
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
• types of independence
– A is indep of non-descendants given parents
– Markov blanket
– d-separation – all paths between A and B are
“blocked”
– useful for determining if obtaining knowledge of B
would change belief about A
• 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
A and B are only conditionally independent given C
A
B
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
• Compact representations of CPT
– Noisy-Or
– prob. version of: cold  flu  malaria  fever
– only have to represent 3 numbers (“strengths”)
instead of 8
Network Engineering for Complex
Belief Networks, Mahoney and Laskey
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 http://aima.eecs.berkeley.edu/slides-pdf/chapter14b.pdf
for discussion of Enumeration and VariableElimination)
Inference in Bayesian Networks, D’Ambrosio
Belief Propagation
(this figure happens to come from http://www.pr-owl.org/basics/bn.php)
see also: wiki, Ch. 8 in Bishop PR&ML