Tighter relaxations for MAP-MRF optimization via Singleton Arc Consistency

2026-05-13

AI Summary

This work addresses the NP-hard maximum a posteriori (MAP) inference problem in discrete-variable Markov random fields (MRFs) by proposing an improved linear programming (LP) relaxation approach. The key innovation lies in introducing a cluster identification mechanism based on Singleton Arc Consistency (SAC) to replace conventional strategies that rely on frustrated cycle detection. This enables more effective discovery of high-order constraints and facilitates iterative tightening of the LP relaxation. Experimental results demonstrate that the proposed method achieves significantly tighter relaxations compared to the classical approach of Sontag et al. (UAI 2012).

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/.

Problem

• MAP-MRF
• discrete optimization
• LP relaxation
• Singleton Arc Consistency
• NP-hard

Innovation

• MAP-MRF
• Singleton Arc Consistency
• LP relaxation tightening
• cluster identification
• discrete optimization