Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration
Jason Altschuler, Jonathan Niles-Weed, Philippe Rigollet
Abstract
Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance, it is unknown whether general optimal transport distances can be approximated in near-linear time. This paper demonstrates that this ambitious goal is in fact achieved by Cuturi's Sinkhorn Distances. This result relies on a new analysis of Sinkhorn iterations, which also directly suggests a new greedy coordinate descent algorithm Greenkhorn with the same theoretical guarantees. Numerical simulations illustrate that Greenkhorn significantly outperforms the classical Sinkhorn algorithm in practice.
BibTeX
@inproceedings{NIPS2017_491442df,
author = {Altschuler, Jason and Niles-Weed, Jonathan and Rigollet, Philippe},
booktitle = {Advances in Neural Information Processing Systems},
editor = {I. Guyon and U. Von Luxburg and S. Bengio and H. Wallach and R. Fergus and S. Vishwanathan and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration},
url = {https://proceedings.neurips.cc/paper_files/paper/2017/file/491442df5f88c6aa018e86dac21d3606-Paper.pdf},
volume = {30},
year = {2017}
}