Most Relevant Explanation in Bayesian Networks

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.

💡 Research Summary

Bayesian networks are powerful tools for representing probabilistic dependencies among variables, yet a central inference task remains: given observed evidence, why do certain target variables take the states they do? Traditional approaches such as MAP (Maximum A Posteriori) or MPE (Most Probable Explanation) produce full assignments that are often either overly simplistic—leaving out important causes—or overly complex—burdening the user with irrelevant details. This paper introduces a novel framework called Most Relevant Explanation (MRE) that directly addresses this “explain‑why” problem by searching for a partial instantiation of the target variables that best accounts for the evidence.

The cornerstone of MRE is the Generalized Bayes Factor (GBF), defined as

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