Maximum A Posteriori Inference in Sum-Product Networks

2018-02-08

Proceedings of the AAAI Conference on Artificial Intelligence, 32

Volume

Thirty-Second AAAI Conference on Artificial Intelligence 2018

AAAI Technical Track: Knowledge Representation and Reasoning

Sum-product networks (SPNs) are a class of probabilistic graphical models that allow tractable marginal inference. However, the maximum a posteriori (MAP) inference in SPNs is NP-hard. We investigate MAP inference in SPNs from both theoretical and algorithmic perspectives. For the theoretical part, we reduce general MAP inference to its special case without evidence and hidden variables; we also show that it is NP-hard to approximate the MAP problem to 2nε for fixed 0 ≤ ε < 1, where n is the input size. For the algorithmic part, we first present an exact MAP solver that runs reasonably fast and could handle SPNs with up to 1k variables and 150k arcs in our experiments. We then present a new approximate MAP solver with a good balance between speed and accuracy, and our comprehensive experiments on real-world datasets show that it has better overall performance than existing approximate solvers.

10.1609/aaai.v32i1.11550