Ideal Reformulation of Belief Networks

TL;DR

This paper explores how to optimally allocate time between reformulating belief networks and performing inference, proposing general principles and empirically studying clustering search methods to improve efficiency under time constraints.

Contribution

It introduces a framework for determining the ideal resource partition in belief network reformulation and inference, supported by empirical analysis of heuristic search methods.

Findings

Optimal resource partitioning principles for belief networks.

Empirical results on heuristic search for clustering in belief networks.

System for selecting ideal reformulation time based on performance models.

Abstract

The intelligent reformulation or restructuring of a belief network can greatly increase the efficiency of inference. However, time expended for reformulation is not available for performing inference. Thus, under time pressure, there is a tradeoff between the time dedicated to reformulating the network and the time applied to the implementation of a solution. We investigate this partition of resources into time applied to reformulation and time used for inference. We shall describe first general principles for computing the ideal partition of resources under uncertainty. These principles have applicability to a wide variety of problems that can be divided into interdependent phases of problem solving. After, we shall present results of our empirical study of the problem of determining the ideal amount of time to devote to searching for clusters in belief networks. In this work, we acquired and made use of probability distributions that characterize (1) the performance of alternative heuristic search methods for reformulating a network instance into a set of cliques, and (2) the time for executing inference procedures on various belief networks. Given a preference model describing the value of a solution as a function of the delay required for its computation, the system selects an ideal time to devote to reformulation.