Approximations in Bayesian Belief Universe for Knowledge Based Systems

TL;DR

This paper introduces an approximation method for Bayesian belief networks that reduces computational complexity by excluding rare cases, with proven bounds on errors and empirical validation on real-world systems.

Contribution

It proposes a novel approximation scheme for CPNs that improves efficiency by exploiting sparseness, with error bounds and empirical testing included.

Findings

Significant reduction in computational resources used

Error bounds established for the approximation method

Empirical results demonstrate effectiveness on real-world CPNs

Abstract

When expert systems based on causal probabilistic networks (CPNs) reach a certain size and complexity, 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 representation 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, reports on empirical studies of applying the approximation scheme to a real-world CPN are given.