Continuous Relaxation of MAP Inference: A Nonconvex Perspective
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.
Cite
Text
Lê-Huu and Paragios. "Continuous Relaxation of MAP Inference: A Nonconvex Perspective." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018. doi:10.1109/CVPR.2018.00580Markdown
[Lê-Huu and Paragios. "Continuous Relaxation of MAP Inference: A Nonconvex Perspective." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018.](https://mlanthology.org/cvpr/2018/lehuu2018cvpr-continuous/) doi:10.1109/CVPR.2018.00580BibTeX
@inproceedings{lehuu2018cvpr-continuous,
title = {{Continuous Relaxation of MAP Inference: A Nonconvex Perspective}},
author = {Lê-Huu, D. Khuê and Paragios, Nikos},
booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
year = {2018},
doi = {10.1109/CVPR.2018.00580},
url = {https://mlanthology.org/cvpr/2018/lehuu2018cvpr-continuous/}
}