Generating Bayesian Networks from Probability Logic Knowledge Bases

Peter Haddawy Department of Electrical Engineering and Computer Science University of Wisconsin­Milwaukee PO Box 784 Milwaukee, WI 53201

Abstract

We present a method for dynamically gen­ erating Bayesian networks from knowledge bases consisting of first­order probability logic sentences. We present a subset of proba­ bility logic sufficient for representing the class of Bayesian networks with discrete­valued nodes. We impose constraints on the form of the sentences that guarantee that the knowl­ edge base contains all the probabilistic infor­ mation necessary to generate a network. We define the concept of d­separation for knowl­ edge bases and prove that a knowledge base with independence conditions defined by d­ separation is a complete specification of a probability distribution. We present a net­ work generation algorithm that, given an in­ ference problem in the form of a query Q and a set of evidence E, generates a network to compute P (Q|E). We prove the algorithm to be correct.