Approximating probabilistic inference in Bayesian belief networks

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 ρ=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. Such a stochastic simulation algorithm, D-BNRAS, which is a randomized approximation scheme is presented. To analyze the run time, belief networks are parameterized, by the dependence value D _ξ, which is a measure of the cumulative strengths of the belief network dependencies given background evidence ξ. This parameterization defines the class of f-dependence networks. The run time of D-BNRAS is polynomial when f is a polynomial function. Thus, the results prove the existence of a class of belief networks for which inference approximation is polynomial and, hence, provably faster than any exact algorithm