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Importance Sampling in Bayesian Networks: An Influence-Based Approximation Strategy for Importance Functions

One of the main problems of importance sampling in Bayesian networks is representation of the importance function, which should ideally be as close as possible to the posterior joint distribution. Typically, we represent an importance function as a factorization, i.e., product of conditional probability tables (CPTs). Given diagnostic evidence, we do not have explicit forms for the CPTs in the networks. We first derive the exact form for the CPTs of the optimal importance function. Since the calculation is hard, we usually only use their approximations. We review several popular strategies and point out their limitations. Based on an analysis of the influence of evidence, we propose a method for approximating the exact form of importance function by explicitly modeling the most important additional dependence relations introduced by evidence. Our experimental results show that the new approximation strategy offers an immediate improvement in the quality of the importance function.