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

Changhe Yuan, Marek J. Druzdzel

Abstract

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 distributions (CPDs). Given diagnostic evidence, we do not have explicit forms for the CPDs in the networks; Their calculation is also hard, because it is practically equivalent to exact inference in the networks. Therefore, we usually only use their approximations, whose quality is critical to the performance of importance sampling. We first review several popular approximation strategies for the CPDs and point out their limitations. After that, based on an analysis of the influence of evidence in Bayesian networks, we propose a method for approximating the exact form of importance function by explicitly modelling some of the 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.

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Bibtex

@inproceedings{Yuan05c,
AUTHOR = "C. Yuan and M. J. Druzdzel",
TITLE = "Importance Sampling in {B}ayesian Networks: An Influence-Based Approximation Strategy for Importance Functions",
YEAR = "2005",
BOOKTITLE = {Proceedings of the 21th Annual Conference on Uncertainty in Artificial Intelligence (UAI--05)},
}