Evaluating exact and approximate algorithms for integer linear programming formulations of MAP inference

Abstract

Structured prediction tasks involve an inference step which allows for producing coherent label assignments to the output structure. This can be achieved by constraining the output using prior knowledge about the domain. This paradigm is called Constrained Conditional Models; and it involves augmenting the learning of conditional models with declarative constraints. The MAP inference problem in CCM framework can be solved by formulating an Integer Linear Programming problem. This ILP formulation is generally relaxed to an Linear Programming problem by dropping the integrality constraints and making it tractable. In this work, we evaluate other approximate inference algorithms for the MAP estimate for structured prediction task in the CCM framework. We model the constrained structured prediction problem as a factor graph and use different graphical models based algorithms. We evaluate these methods for the quality of their solution and the computation time over some NLP tasks with varying complexity. For large-scale problems, the tradeoff between inference time and the approximateness of the solution is a crucial aspect. Furthermore, these inference solvers are provided as black-box implementations in Saul, which is a declarative programming language for structured prediction tasks.