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.
