Continuous Relaxation of MAP Inference: A Nonconvex Perspective

International audience; 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 multi-pliers (ADMM). Experiments on many real-world problems demonstrate that the proposed ADMM significantly outper-forms other nonconvex relaxation based methods, and compares favorably with state of the art MRF optimization algorithms in different settings.