Incremental Region Selection for Mini-Bucket Elimination Bounds

Abstract

Region choice is a key issue for many approximate inference bounds. Mini-bucket elimination avoids the space and time complexity of exact inference by using a top-down partitioning approach that mimics the construction of a junction tree and aims to minimize the number of regions subject to a bound on their size; however, these methods rarely take into account functions’ values. In contrast, message passing algorithms often use “cluster pursuit” methods to select regions, a bottom-up approach in which a predefined set of clusters (such as triplets) is scored and incrementally added. In this work, we develop a hybrid approach that balances the advantages of both perspectives, providing larger regions chosen in an intelligent, energy-based way. Our method is applicable to bounds on a variety of inference tasks, and we demonstrate its power empirically on a broad array of problem types.