Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration
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6792-near-linear-time-approximation-algorithms-for-optimal-transport-via-sinkhorn-iteration.pdf
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Author(s)
Altschuler, Jason Max
Weed, Jonathan
Rigollet, Philippe
Date Issued
February 2018
Journal
Advances in Neural Information Processing Systems
Publisher
Neural Information Processing Systems Foundation
Citation
Altschuler, Jason, Jonathan Weed and Philippe Rigollet. "Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration." Advances in Neural Information Processing Systems 30 (NIPS 2017): 1961-1971.
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://dx.doi.org/
