Generating Bayesian Networks from Probability Logic Knowledge Bases

TL;DR

This paper introduces a method to automatically generate Bayesian networks from first-order probability logic knowledge bases, ensuring probabilistic completeness and correctness for inference tasks.

Contribution

It defines a subset of probability logic suitable for Bayesian network representation and presents an algorithm for dynamic network generation from knowledge bases.

Findings

The method guarantees the generated network contains all necessary probabilistic information.

The concept of d-separation is extended to knowledge bases to ensure independence.

The network generation algorithm is proven correct for inference tasks.

Abstract

We present a method for dynamically generating 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 discrete-valued nodes. We impose constraints on the form of the sentences that guarantee that the knowledge base contains all the probabilistic information necessary to generate 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 generation algorithm that, given an inference 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.