{"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/measuring-association-with-wasserstein","title":"Measuring association with Wasserstein distances","arxiv_id":"2102.00356","date":"2021-01-31","proceeding":null,"authors":["Johannes Wiesel"],"abstract":"Let $\\pi\\in \\Pi(\\mu,\\nu)$ be a coupling between two probability measures $\\mu$ and $\\nu$ on a Polish space. In this article we propose and study a class of nonparametric measures of association between $\\mu$ and $\\nu$, which we call Wasserstein correlation coefficients. These coefficients are based on the Wasserstein distance between $\\nu$ and the disintegration $\\pi_{x_1}$ of $\\pi$ with respect to the first coordinate. We also establish basic statistical properties of this new class of measures: we develop a statistical theory for strongly consistent estimators and determine their convergence rate in the case of compactly supported measures $\\mu$ and $\\nu$. Throughout our analysis we make use of the so-called adapted/bicausal Wasserstein distance, in particular we rely on results established in [Backhoff, Bartl, Beiglb\\\"ock, Wiesel. Estimating processes in adapted Wasserstein distance. 2020]. Our approach applies to probability laws on general Polish spaces.","url_abs":"https://arxiv.org/abs/2102.00356v3","url_pdf":"https://arxiv.org/pdf/2102.00356v3.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"measuring-association-with-wasserstein","repo_url":"https://github.com/johanneswiesel/Wasserstein-correlation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2102.00356","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}