{"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/agnostic-estimation-of-mean-and-covariance","title":"Agnostic Estimation of Mean and Covariance","arxiv_id":"1604.06968","date":"2016-04-24","proceeding":null,"authors":["Kevin A. Lai","Anup B. Rao","Santosh Vempala"],"abstract":"We consider the problem of estimating the mean and covariance of a\ndistribution from iid samples in $\\mathbb{R}^n$, in the presence of an $\\eta$\nfraction of malicious noise; this is in contrast to much recent work where the\nnoise itself is assumed to be from a distribution of known type. The agnostic\nproblem includes many interesting special cases, e.g., learning the parameters\nof a single Gaussian (or finding the best-fit Gaussian) when $\\eta$ fraction of\ndata is adversarially corrupted, agnostically learning a mixture of Gaussians,\nagnostic ICA, etc. We present polynomial-time algorithms to estimate the mean\nand covariance with error guarantees in terms of information-theoretic lower\nbounds. As a corollary, we also obtain an agnostic algorithm for Singular Value\nDecomposition.","url_abs":"http://arxiv.org/abs/1604.06968v2","url_pdf":"http://arxiv.org/pdf/1604.06968v2.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":"agnostic-estimation-of-mean-and-covariance","repo_url":"https://github.com/kal2000/AgnosticMeanAndCovarianceCode","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"agnostic-estimation-of-mean-and-covariance","repo_url":"https://github.com/hoonose/robust-filter","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"ica","method_name":"ICA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1604.06968","atlas_url":"https://app.syntology.ai/?focus=1604.06968","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}