Approximations in Bayesian Belief Universe for Knowledge Based Systems

When expert systems based on causal probabilistic networks (CPNs) reach a certai n size and complex­ ity, the "combinatorial explosion monster" tends to be present. We propose an approximation scheme that identifies rarely occurring cases and excludes these from being processed as ordinary cases in a CPN-based expert system. Depending on the topology and the probability distributions of the CPN, the numbers (representing probabilities of state combinations) in the underlying numerical rep­ resentation can become very small. Annihilating these numbers and utilizing the resulting sparseness through data structuring techniques often results in several orders of magnitude of improvement in the consumption of computer resources. Bounds on the errors introduced into a CPN-based expert system through approximations are established. Finally, re­ ports on empirical studies of applying the approxi­ mation scheme to a real-world CPN are given.