Ideal Reformulation of Belief Networks

John Breese and Eric Horvitz

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The intelligent reformulation or restructuring of a belief network can greatly increasethe 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 searchmethods 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 toreformulation.

In: Proceedings of Sixth Conference on Uncertainty in Artificial Intelligence, Cambridge, MA, Association for Uncertainty in Artificial Intelligence, Mountain View, CA. July 1990. pp 64-72.

Keywords: Decision-theoretic control, Bayesian networks, bounded optimal systems, bounded optimality, decision-theoretic control of computation, metareasoning, rationality under bounded resources, probabilistic inference.

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