Continuous Relaxation of MAP Inference: A Nonconvex Perspective
This addresses the computational bottleneck of MAP inference in MRFs for computer vision and machine learning applications, representing an incremental improvement over existing relaxation methods.
The paper tackles the problem of MAP inference in discrete Markov random fields by proposing a nonconvex continuous relaxation that is proven tight for arbitrary MRFs, with a simple block coordinate descent algorithm reaching discrete stationary points. Experiments show that their ADMM-based solution significantly outperforms other nonconvex methods and compares favorably with state-of-the-art MRF optimization algorithms.
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.