Inference in Polytrees with Sets of Probabilities

Inferences in directed acyclic graphs associated with probability intervals and sets of probabil­ ities are NP-hard, even for polytrees. We pro­ pose: I) an improvement on Tessem's AIR algo­ rithm for inferences on polytrees associated with probability intervals; 2) a new algorithm for ap­ proximate 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 gener­ ate 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 sev­ eral orders of magnitude.