Importance Sampling in Bayesian Networks: An Influence-Based Approximation Strategy for Importance Functions
This work addresses a specific bottleneck in Bayesian inference for researchers and practitioners, offering an incremental improvement over existing approximation strategies.
The paper tackles the problem of approximating importance functions in Bayesian networks for importance sampling, proposing a method that models key dependence relations introduced by evidence, which leads to improved quality in the importance function.
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.