Continuous Relaxation of MAP Inference: A Nonconvex Perspective

TL;DR

This paper introduces a nonconvex continuous relaxation for MAP inference in discrete MRFs, demonstrating its tightness and proposing an ADMM-based solution that outperforms existing methods.

Contribution

It presents a novel nonconvex relaxation approach for MAP inference, along with an ADMM-based algorithm that achieves superior performance on real-world problems.

Findings

Relaxation is tight for arbitrary MRFs

ADMM-based method outperforms other nonconvex relaxations

Proposed approach compares favorably with state-of-the-art algorithms

Abstract

In this paper, we study a nonconvex continuous relaxation of MAP inference in discrete Markov random fields (MRFs). We show that for arbitrary MRFs, this relaxation is tight, and a discrete stationary point of it can be easily reached by a simple block coordinate descent algorithm. In addition, we study the resolution of this relaxation using popular gradient methods, and further propose a more effective solution using a multilinear decomposition framework based on the alternating direction method of multipliers (ADMM). Experiments on many real-world problems demonstrate that the proposed ADMM significantly outperforms other nonconvex relaxation based methods, and compares favorably with state of the art MRF optimization algorithms in different settings.