Title: Branch and Bound Search for Exact MAP Inference in Credal Networks
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: probabilistic reasoning, credal networks, search, MAP inference

Abstract: Credal networks extend Bayesian networks by incorporating imprecise probabilities through convex sets of probability distributions known as credal sets. MAP inference in credal networks, which seeks the most probable variable assignment given evidence, becomes inherently more difficult than in Bayesian networks because it involves computations over a complex joint credal set. In this paper, we introduce two tasks called \emph{maximax} and \emph{maximin} MAP, and develop depth-first branch-and-bound search algorithms for solving them \emph{exactly}. The algorithms exploit problem decomposition by exploring an AND/OR search space and use a partitioning-based heuristic function enhanced with a cost-shifting scheme to effectively guide the search. Our experimental results obtained on both random and realistic credal networks clearly demonstrate the effectiveness of the proposed algorithms as they scale to large and complex problem instances.

TL;DR: The paper presents new branch and bound search algorithms for exact MAP inference in credal networks