Discrete Bayesian Networks: The Exact Posterior Marginal Distributions

TL;DR

This paper introduces exact algorithms for computing marginal probabilities in Bayesian networks, including the border algorithm, a revised polytree algorithm, and a parentless polytree method, improving inference efficiency.

Contribution

It presents novel algorithms that convert any Bayesian network into a form enabling efficient exact marginal probability computation, regardless of network size.

Findings

The parentless polytree method makes inference complexity independent of network size.

The border algorithm effectively converts BNs into directed chains for easier inference.

The revised polytree algorithm adapts existing methods within the new framework.

Abstract

In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a directed chain. For the polytrees, we then present in details, with some modifications and within the border algorithm framework, the "revised polytree algorithm" by Peot & Shachter (1991). Finally, we present our "parentless polytree method," which, coupled with the border algorithm, converts any Bayesian network into a polytree, rendering the complexity of our inferences independent of the size of network, and linear with the number of its evidence and query variables. All quantities in this paper have probabilistic interpretations.