Exact MAP-Inference by Confining Combinatorial Search With LP Relaxation

2018-02-08

Proceedings of the AAAI Conference on Artificial Intelligence, 32

Volume

Thirty-Second AAAI Conference on Artificial Intelligence 2018

Main Track: Search and Constraint Satisfaction

We consider the MAP-inference problem for graphical models, which is a valued constraint satisfaction problem defined on real numbers with a natural summation operation. We propose a family of relaxations (different from the famous Sherali-Adams hierarchy), which naturally define lower bounds for its optimum. This family always contains a tight relaxation and we give an algorithm able to find it and therefore, solve the initial non-relaxed NP-hard problem. The relaxations we consider decompose the original problem into two non-overlapping parts: an easy LP-tight part and a difficult one. For the latter part a combinatorial solver must be used. As we show in our experiments, in a number of applications the second, difficult part constitutes only a small fraction of the whole problem. This property allows to significantly reduce the computational time of the combinatorial solver and therefore solve problems which were out of reach before.

10.1609/aaai.v32i1.12202