Inference in polytrees with sets of probabilities

Authors:
Jose Carlos Ferreira da Rocha;Fabio Gagliardi Cozmanl;Cassio Polpo de Campos
Affiliations:
Escola Politécnica, Univ. de São Paulo, São Paulo, SP and Univ. Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil;Escola Politécnica, Univ. de São Paulo, São Paulo, SP, Brazil;Escola Politécnica, Univ. de São Paulo, São Paulo, SP and Pontifícia Universidade Católica, São Paulo, SP, Brazil
Venue:
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Year:
2002

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Abstract

Inferences in directed acyclic graphs associated with probability intervals and sets of probabilities are NP-hard, even for polytrees. We propose: 1) an improvement on Tessem's A/R algorithm for inferences on polytrees associated with probability intervals; 2) a new algorithm for approximate inferences based on local search; 3) branch-and-bound algorithms that combine the previous techniques. The first two algorithms produce complementary approximate solutions, while branch-and-bound procedures can generate either exact or approximate solutions. We report improvements on existing techniques for inference with probability sets and intervals, in some cases reducing computational effort by several orders of magnitude.