Representing belief function knowledge with graphical models

Abstract

Belief function theory is an appropriate framework to model different forms of knowledge including probabilistic knowledge. One simple and efficient way to reason under uncertainty, is the use of compact graphical models, namely directed acyclic graphs. Therefore naturally, a question crosses the mind: If we deal with Bayesian belief knowledge does the network collapse into a Bayesian network? This paper attempts to answer this question by analyzing different forms of belief function networks defined with conditional beliefs defined either with a unique conditional distribution for all parents or a single conditional distribution for each single parent. We also propose a new method for the deconditionalization process to compute the joint distribution. © 2011 Springer-Verlag.