1. Example applications of Bayesian networks
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

2. 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

4. 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

5. 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 B
A and B are only conditionally independent given C

6. poly-trees (singly connected, one path between any pair of nodes)
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

7. Compact representations of CPT
Noisy-Or
prob. version of: cold  flu  malaria  fever
only have to represent 3 numbers (“strengths”) instead of 8

9. Network Engineering for Complex
Belief Networks, Mahoney and Laskey

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

11. Lumiere – Office Assistant

12. 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

13. (see slides 4-10 in http://aima. eecs. berkeley
for discussion of Enumeration and VariableElimination)

14. Inference in Bayesian Networks, D’Ambrosio

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