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

TL;DR

This paper introduces an influence-based approximation method for importance sampling in Bayesian networks, explicitly modeling evidence-induced dependencies to improve the accuracy of importance functions.

Contribution

It proposes a novel influence-based strategy to better approximate importance functions by capturing evidence-driven dependencies, addressing limitations of existing methods.

Findings

Improved importance function quality with the new approximation strategy

Explicit modeling of evidence-induced dependencies enhances sampling accuracy

Experimental results demonstrate immediate benefits over traditional approaches

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 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.