Chapter 4 - BELIEF UPDATING BY NETWORK PROPAGATION

Abstract

In a large class of networks, coherent and stable probabilistic reasoning can be accomplished by local propagation mechanisms, keeping the weights on the links constant throughout the process. This is done by characterizing the belief in a proposition by a list of parameters, each representing the degree of support the host proposition obtains from one of its neighbors. Maintaining such a record of the sources of belief facilitates local updating of beliefs and that the network relaxes to a stable equilibrium, consistent with the axioms of probability theory, in time proportional to the network diameter. Such a record of parameters is also postulated as a mechanism that permits people to retrace rationales and assemble explanations for currently held beliefs. The impact of each new piece of evidence is viewed as a perturbation that propagates through the network via message-passing between neighboring variables, with minimal external supervision. These objectives can be fully realized with causal trees, that is, Bayesian networks in which each node has at most one parent. The chapter discusses several approaches to achieving autonomous propagation in multiply connected networks and presents an extension of the inferential repertoire of Bayesian networks to include answering Boolean queries under propositional constraints.