Efficient MAP Inference for Statistical Relational Models through Hybrid Metaheuristics

Abstract

Statistical Relational Models are state-of-the-art representation formalisms at the intersection of logical and statistical machine learning. One of the most promising models is Markov Logic (ML) which combines Markov networks (MNs) and first-order logic by attaching weights to first-order formulas and using these as templates for features of MNs. MAP inference in ML is the task of finding the most likely state of a set of output variables given the state of the input variables and this problem is NP-hard. In this paper we present an algorithm for this inference task based on the Iterated Local Search (ILS) and Robust Tabu Search (RoTS) metaheuristics. The algorithm performs a biased sampling of the set of local optima by using RoTS as a local search procedure and repetitively jumping in the search space through a perturbation operator, focusing the search not on the full space of solutions but on a smaller subspace defined by the solutions that are locally optimal for the optimization engine. We show through extensive experiments in real-world domains that it improves over the state-of-the-art algorithm in terms of solution quality and inference time.