Solving M-Modes in Loopy Graphs Using Tree Decompositions
; Proceedings of the Ninth International Conference on Probabilistic Graphical Models, PMLR 72:145-156, 2018.
M-Modes is the problem of finding the top M labelings of a graphical model that are locally optimal. The state-of-the-art M-Modes algorithm is a heuristic search method that finds global modes by incrementally concatenating MAP solutions in local neighborhoods. The search method also relies on the guidance of a heuristic function to explore the most promising parts of the search space. However, due to the difficulty of coordinating mode search, heuristic function calculation and local MAP computation in general loopy graphs, the method was only implemented and tested on special graphical models such as trees or submodular grid graphs. This paper provides a more general implementation of the search method based on tree decompositions that is applicable to general loopy graphs. A tree decomposition allows a sequence of local subgraphs to be mapped to a set of sub-trees sweeping through the tree decomposition, thus enabling a smooth and efficient transition back and forth between mode search, heuristic functio