A belief network comprises a graphical representation of dependencies between variables of a domain and a set of conditional probabilities associated with each dependency. Unless P=NP, an efficient, exact algorithm does not exist to compute probabilistic inference in belief networks. Stochastic simulation methods, which often improve run times, provide an alternative to exact inference algorithms. We present such a stochastic simulation algorithm 2)-BNRAS that is a randomized approximation scheme. To analyze the run time, we parameterize belief networks by the dependence value P E , which is a measure of the cumulative strengths of the belief network dependencies given background evidence E. This parameterization defines the class of f-dependence networks. The run time of 2)-BNRAS is polynomial when f is a polynomial function. Thus, the results of this paper prove the existence of a class of belief networks for which inference approximation is polynomial and, hence, provably faster than any exact algorithm.
Researchers in decision analysis and artificial intelligence (AI) have used Bayesian belief networks to build probabilistic expert systems. Using standard methods drawn from the theory of computational complexity, workers in the field have shown that the problem of probabilistic inference in belief networks is difficult and almost certainly intractable. We have developed a randomized approximation scheme, BN-RAS, for doing probabilistic inference in belief networks. The algorithm can, in many circumstances, perform efficient approximate inference in large and richly interconnected models. Unlike previously described stochastic algorithms for probabilistic inference, the randomized approximation scheme (ras) computes a priori bounds on running time by analyzing the structure and contents of the belief network. In this article, we describe BN-RAS precisely and analyze its performance mathematically.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.