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Probabilistic (Bayesian) representations of knowledge have had a major impact on AI

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

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Probabilistic (Bayesian) representations of knowledge have had a major impact on AI

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  1. 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

  3. 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

  4. A B • 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

  5. 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

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

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

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

  9. Lumiere – Office Assistant

  10. 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

  11. (see slides 4-10 in http://aima.eecs.berkeley.edu/slides-pdf/chapter14b.pdf for discussion of Enumeration and VariableElimination)

  12. Inference in Bayesian Networks, D’Ambrosio

  13. 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

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