On the Robustness of Most Probable Explanations

In Bayesian networks, a Most Probable Explanation (MPE) is a complete variable instantiation with the highest probability given the current evidence. In this paper, we discuss the problem of finding robustness conditions of the MPE under single parameter changes. Specifically, we ask the question: How much change in a single network parameter can we afford to apply while keeping the MPE unchanged? We will describe a procedure, which is the first of its kind, that computes this answer for all parameters in the Bayesian network in time O(n exp(w)), where n is the number of network variables and w is its treewidth.