Solving Marginal MAP Exactly by Probabilistic Circuit Transformations

Probabilistic circuits (PCs) are a class of tractable probabilistic models that allow efficient, often linear-time, inference of queries such as marginals and most probable explanations (MPE). However, marginal MAP, which is central to many decision-making problems, remains a hard query for PCs unless they satisfy highly restrictive structural constraints. In this paper, we develop a pruning algorithm that removes parts of the PC that are irrelevant to a marginal MAP query, shrinking the PC while maintaining the correct solution. This pruning technique is so effective that we are able to build a marginal MAP solver based solely on iteratively transforming the circuit -- no search is required. We empirically demonstrate the efficacy of our approach on real-world datasets.