Hybrid algorithms for approximate belief updating in Bayes nets

Abstract

Belief updating in Bayes nets, a well-known computationally hard problem, has recently been approximated by several deterministic algorithms and by various randomized approximation algorithms. Deterministic algorithms usually provide probability bounds, but have an exponential runtime. Some randomized schemes have a polynomial runtime, but provide only probability estimates. Randomized algorithms that accumulate high-probability partial instantiations, resulting in probability bounds, are presented. Some of these algorithms are also sampling algorithms. Specifically, a variant of backward sampling, used both as a sampling algorithm and as a randomized enumeration algorithm, is introduced and evaluated. An implicit assumption made in prior work, for both sampling and accumulation algorithms, that query nodes must be instantiated in all the samples, is relaxed. Genetic algorithms can be used as an alternate search component for high-probability instantiations; several methods of applying them to belief updating are presented.