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A Novel Methodology for Processing Probabilistic Knowledge Bases Under Maximum Entropy

Probabilistic reasoning under the so-called principle of maximum entropy is a viable and convenient alternative to Bayesian networks, relieving the user from providing complete (local) probabilistic information and observing rigorous conditional independence assumptions. In this paper, we present a novel approach to performing computational MaxEnt reasoning that makes use of symbolic computations instead of graph-based techniques. Given a probabilistic knowledge base, we encode the MaxEnt optimization problem into a system of polynomial equations, and then apply Grobner basis theory to find MaxEnt inferences as solutions to the polynomials. We illustrate our approach with an example of a knowledge base that represents findings on fraud detection in enterprises.