{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/near-linear-time-approximation-algorithms-for","title":"Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration","arxiv_id":"1705.09634","date":"2017-05-26","proceeding":"NeurIPS 2017 12","authors":["Jason Altschuler","Jonathan Weed","Philippe Rigollet"],"abstract":"Computing optimal transport distances such as the earth mover's distance is a\nfundamental problem in machine learning, statistics, and computer vision.\nDespite the recent introduction of several algorithms with good empirical\nperformance, it is unknown whether general optimal transport distances can be\napproximated in near-linear time. This paper demonstrates that this ambitious\ngoal is in fact achieved by Cuturi's Sinkhorn Distances. This result relies on\na new analysis of Sinkhorn iteration, which also directly suggests a new greedy\ncoordinate descent algorithm, Greenkhorn, with the same theoretical guarantees.\nNumerical simulations illustrate that Greenkhorn significantly outperforms the\nclassical Sinkhorn algorithm in practice.","url_abs":"http://arxiv.org/abs/1705.09634v2","url_pdf":"http://arxiv.org/pdf/1705.09634v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"near-linear-time-approximation-algorithms-for","repo_url":"https://github.com/shuge-mit/mot_project","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1705.09634","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}