First-order integer programming for MAP problems
This work addresses the efficiency and scalability of MAP inference in statistical relational learning, but it appears incremental as it builds on existing first-order MIP syntax and semantics.
The paper tackles the problem of finding the most probable (MAP) model in statistical relational learning frameworks like Markov logic and Problog by developing mfoilp, a first-order mixed integer programming approach that preserves useful first-order structure lost in traditional grounded-out methods, focusing on implementation and algorithmic issues.
Finding the most probable (MAP) model in SRL frameworks such as Markov logic and Problog can, in principle, be solved by encoding the problem as a `grounded-out' mixed integer program (MIP). However, useful first-order structure disappears in this process motivating the development of first-order MIP approaches. Here we present mfoilp, one such approach. Since the syntax and semantics of mfoilp is essentially the same as existing approaches we focus here mainly on implementation and algorithmic issues. We start with the (conceptually) simple problem of using a logic program to generate a MIP instance before considering more ambitious exploitation of first-order representations.