Ideal reformulation of belief networks

The intelligent reformulation or restructuring of a be­ lief network can greatly increase the efficiency of in­ ference. However, time expended for reformulation is not available for performing inference. Thus, un­ der 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 ap­ plied to reformulation and time used for inference. We shall describe first general principles for comput­ ing 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 re­ sults of our empirical study of the problem of deter­ mining the ideal amount of time to devote to search­ ing 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 net­ works. 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. •This work was su pported by Rockwell International Sci­ ence Center and the National Science Foundation under Grant IRI-8703710.