{"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/random-matrix-improved-estimation-of-the","title":"Random Matrix-Improved Estimation of the Wasserstein Distance between two Centered Gaussian Distributions","arxiv_id":"1903.03447","date":"2019-03-08","proceeding":null,"authors":["Malik Tiomoko","Romain Couillet"],"abstract":"This article proposes a method to consistently estimate functionals\n$\\frac1p\\sum_{i=1}^pf(\\lambda_i(C_1C_2))$ of the eigenvalues of the product of\ntwo covariance matrices $C_1,C_2\\in\\mathbb{R}^{p\\times p}$ based on the\nempirical estimates $\\lambda_i(\\hat C_1\\hat C_2)$ ($\\hat\nC_a=\\frac1{n_a}\\sum_{i=1}^{n_a} x_i^{(a)}x_i^{(a){{\\sf T}}}$), when the size\n$p$ and number $n_a$ of the (zero mean) samples $x_i^{(a)}$ are similar. As a\ncorollary, a consistent estimate of the Wasserstein distance (related to the\ncase $f(t)=\\sqrt{t}$) between centered Gaussian distributions is derived.\n  The new estimate is shown to largely outperform the classical sample\ncovariance-based `plug-in' estimator. Based on this finding, a practical\napplication to covariance estimation is then devised which demonstrates\npotentially significant performance gains with respect to state-of-the-art\nalternatives.","url_abs":"http://arxiv.org/abs/1903.03447v1","url_pdf":"http://arxiv.org/pdf/1903.03447v1.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":"random-matrix-improved-estimation-of-the","repo_url":"https://github.com/maliktiomoko/RMTWasserstein","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}