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.

Most Relevant Explanation: Properties, Algorithms, and Evaluations

Most Relevant Explanation (MRE) is a method for finding multivariate explanations for given evidence in Bayesian networks [12]. This paper studies the theoretical properties of MRE and develops an algorithm for finding multiple top MRE solutions. Our study shows that MRE relies on an implicit soft relevance measure in automatically identifying the most relevant target variables and pruning less relevant variables from an explanation. The soft measure also enables MRE to capture the intuitive phenomenon of explaining away encoded in Bayesian networks. Furthermore, our study shows that the solution space of MRE has a special lattice structure which yields interesting dominance relations among the solutions. A K-MRE algorithm based on these dominance relations is developed for generating a set of top solutions that are more representative. Our empirical results show that MRE methods are promising approaches for explanation in Bayesian networks.