Tighter relaxations for MAP-MRF optimization via Singleton Arc Consistency

TL;DR

This paper introduces a new technique for tightening LP relaxations in MAP-MRF inference by using Singleton Arc Consistency, outperforming previous methods like frustrated cycle search.

Contribution

The authors propose a novel cluster identification method based on Singleton Arc Consistency for better LP relaxation tightening in MAP-MRF inference.

Findings

The new technique outperforms previous frustrated cycle search methods.

Experimental results demonstrate improved relaxation tightening.

Code is available at https://github.com/vnk-ist/MAP-MRF/.

Abstract

We consider the MAP-MRF inference task, that is, minimizing a function of discrete variables represented as a sum of unary and pairwise terms. A prominent approach for tackling this NP-hard problem in practice is to solve its natural LP relaxation and then iteratively tighten the relaxation by adding clusters. Based on some theoretical observations, we propose a new technique for identifying such clusters. It works by running the Singleton Arc Consistency algorithm in a certain CSP instance. Experimental results indicate that the new tightening technique outperforms the previous approach by [Sontag et al. UAI 2012] that searches for frustrated cycles. Our code will be made available at https://github.com/vnk-ist/MAP-MRF/.