{"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/optimal-cleaning-for-singular-values-of-cross","title":"Optimal cleaning for singular values of cross-covariance matrices","arxiv_id":"1901.05543","date":"2019-01-16","proceeding":null,"authors":["Florent Benaych-Georges","Jean-Philippe Bouchaud","Marc Potters"],"abstract":"We give a new algorithm for the estimation of the cross-covariance matrix $\\mathbb{E} XY'$ of two large dimensional signals $X\\in\\mathbb{R}^n$, $Y\\in \\mathbb{R}^p$ in the context where the number $T$ of observations of the pair $(X,Y)$ is large but $n/T$ and $p/T$ are not supposed to be small. In the asymptotic regime where $n,p,T$ are large, with high probability, this algorithm is optimal for the Frobenius norm among rotationally invariant estimators, i.e. estimators derived from the empirical estimator by cleaning the singular values, while letting singular vectors unchanged.","url_abs":"https://arxiv.org/abs/1901.05543v6","url_pdf":"https://arxiv.org/pdf/1901.05543v6.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":"optimal-cleaning-for-singular-values-of-cross","repo_url":"https://github.com/CFMTech/Optimal_cleaning_for_singular_values_of_cross-covariance_matrices","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}