Journal of the Association for Computing Machinery, Vol. 43, No. 3, May 1996, pp. 399–430.

On Linear Potential Functions for Approximating Bayesian Computations

EUGENE SANTOS, JR.

Abstract. Probabilistic reasoning suffers from NP-hard implementations. In particular, the amount of probabilistic information necessary to the computations is often overwhelming. For example, the size of conditional probability tables in Bayesian networks has long been a limiting factor in the general use of these networks.

We present a new approach for manipulating the probabilistic information given. This approach avoids being overwhelmed by essentially compressing the information using approximation functions called linear potential functions. We can potentially reduce the information from a combinatorial amount to roughly linear in the number of random variable assignments. Furthermore, we can compute these functions through closed form equations. As it turns out, our approximation method is quite general and may be applied to other data compression problems.

Categories and Subject Descriptors. E.4 [Coding and Information Theory]; G.1.2 [Numerical Analysis]: Approximation; G.1.6 [Numerical Analysis]: Optimization; I.2.3 [Artificial Intelligence]: Deduction and Theorem Proving; I.5 [Pattern Recognition]

General Terms. Algorithms, Design, Experimentation, Theory

Additional Key words and Phrases. Artificial intelligence, data compaction and compression, integer programming, least squares approximation, pattern recognition, probabilistic reasoning, uncertainty

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