Principled Construction of Minimal Bayesian Networks from Probability Logic Knowledge Bases

We present a method for dynamically constructing Bayesian networks from knowledge bases consisting of first-order probability logic sentences. We present a subset of probability 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 knowledge base contains all the probabilistic information necessary to construct a network. We define the concept of d-separation for knowledge 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 network construction algorithm that, given an inference problem in the form of a query Q and a set of evidence E, constructs the smallest network to compute P (QjE). We prove the algorithm to be correct. Submitted to Journal of AI Research 1 Introduction The flexibility of Bayesian networks for representing probabilistic dependencies and the ..