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.
