Most Relevant Explanation in Bayesian Networks

TL;DR

This paper introduces the Most Relevant Explanation (MRE) method for Bayesian networks, which automatically identifies concise, relevant explanations by maximizing the generalized Bayes factor, effectively balancing simplicity and informativeness.

Contribution

The paper proposes MRE, a novel approach that uses generalized Bayes factor and conditional Bayes factor to automatically select relevant variables and generate diverse, high-quality explanations in Bayesian networks.

Findings

MRE effectively prunes less relevant variables from explanations.

MRE captures the explaining-away phenomenon in Bayesian networks.

Case studies show MRE produces concise, precise explanations.

Abstract

A major inference task in Bayesian networks is explaining why some variables are observed in their particular states using a set of target variables. Existing methods for solving this problem often generate explanations that are either too simple (underspecified) or too complex (overspecified). In this paper, we introduce a method called Most Relevant Explanation (MRE) which finds a partial instantiation of the target variables that maximizes the generalized Bayes factor (GBF) as the best explanation for the given evidence. Our study shows that GBF has several theoretical properties that enable MRE to automatically identify the most relevant target variables in forming its explanation. In particular, conditional Bayes factor (CBF), defined as the GBF of a new explanation conditioned on an existing explanation, provides a soft measure on the degree of relevance of the variables in the new explanation in explaining the evidence given the existing explanation. As a result, MRE is able to automatically prune less relevant variables from its explanation. We also show that CBF is able to capture well the explaining-away phenomenon that is often represented in Bayesian networks. Moreover, we define two dominance relations between the candidate solutions and use the relations to generalize MRE to find a set of top explanations that is both diverse and representative. Case studies on several benchmark diagnostic Bayesian networks show that MRE is often able to find explanatory hypotheses that are not only precise but also concise.