First-order integer programming for MAP problems

TL;DR

The paper introduces mfoilp, a first-order MIP approach for MAP problems in SRL frameworks, focusing on implementation and algorithmic issues to better exploit first-order structures.

Contribution

It presents mfoilp, a novel first-order MIP method for MAP inference, emphasizing implementation details and algorithmic strategies.

Findings

mfoilp effectively encodes MAP problems as first-order MIPs

The approach maintains the syntax and semantics of existing methods

Implementation insights improve exploitation of first-order structures

Abstract

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.