# Two Reformulation Approaches to Maximum-A-Posteriori Inference in Sum-Product Networks

Denis Deratani Mauá, Heitor Reis Ribeiro, Gustavo Perez Katague, Alessandro Antonucci

January 2020
### Abstract

Sum-product networks are expressive efficient probabilistic graphical models that allow for tractable marginal inference. Many tasks however require the computation of maximum-a-posteriori configurations, an NP-Hard problem for such models. To date there have been very few proposals for computing maximum-a-posteriori configurations in sum-product networks. This is in sharp difference with other probabilistic frameworks such as Bayesian networks and random Markov fields, where the problem is also NP-hard. In this work we propose two approaches to reformulate maximum-a-posteriori inference as other combinatorial optimization problems with widely available solvers. The first approach casts the problem as a similar inference problem in Bayesian networks, overcoming some limitations of previous similar translations. In addition to making available the toolset of maximum-a-posteriori inference on Bayesian networks to sum-product networks, our reformulation also provides further insight into the connections of these two classes of models. The second approach casts the problem as a mixed-integer linear program, for which there exists very efficient solvers. This allows such inferences to be enriched with integer-linear constraints, increasing the expressivity of the models. We compare our reformulation approaches in a large collection of problems, and against state-of-the-art approaches. The results show that reformulation approaches are competitive.

Publication

*Proceedings of the Tenth International Conference on Probabilistic Graphical Models*