Exact Algorithms for MRE Inference

Most Relevant Explanation (MRE) is an inference task in Bayesian networks that finds the most relevant partial instantiation of target variables as an explanation for given evidence by maximizing the Generalized Bayes Factor (GBF). No exact algorithm has been developed for solving MRE previously. This paper fills the void and introduces Breadth-First Branch-and-Bound (BFBnB) MRE algorithms based on two novel upper bounds on GBF. One bound is calculated by decomposing the computation of the score to a set of Markov blankets of subsets of evidence variables. Furthermore, another improved Markov blanket bound is proposed based on two new ideas. One is to split the Markov blankets that are too large by converting auxiliary nodes into pseudo-targets. The other is to perform summation instead of maximization on some of the targets in each Markov blanket. Our empirical evaluations show that the proposed BFBnB algorithms make exact MRE inference tractable in Bayesian networks that could not be solved previously.