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Since exact probabilistic inference is intractable in general for largemultiply connected belief nets, approximate methods are required. A promisingapproach is to use heuristic search among hypotheses (instantiations of thenetwork) to find the most probable ones, as in the TopN algorithm. Search isbased on the relative probabilities of hypotheses which are efficient tocompute. Given upper and lower bounds on the relative probability of partialhypotheses, it is possible to obtain bounds on the absolute probabilities ofhypotheses. Best-first search aimed at reducing the maximum error progressivelynarrows the bounds as more hypotheses are examined. Here, qualitativeprobabilistic analysis is employed to obtain bounds on the relative probabilityof partial hypotheses for the BN20 class of networks networks and ageneralization replacing the noisy OR assumption by negative synergy. Theapproach is illustrated by application to a very large belief network, QMR-BN,which is a reformulation of the Internist-1 system for diagnosis in internalmedicine.

Search-based Methods to Bound Diagnostic Probabilities in Very Large Belief Nets