{"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/robust-estimators-in-high-dimensions-without","title":"Robust Estimators in High Dimensions without the Computational Intractability","arxiv_id":"1604.06443","date":"2016-04-21","proceeding":null,"authors":["Ilias Diakonikolas","Gautam Kamath","Daniel Kane","Jerry Li","Ankur Moitra","Alistair Stewart"],"abstract":"We study high-dimensional distribution learning in an agnostic setting where\nan adversary is allowed to arbitrarily corrupt an $\\varepsilon$-fraction of the\nsamples. Such questions have a rich history spanning statistics, machine\nlearning and theoretical computer science. Even in the most basic settings, the\nonly known approaches are either computationally inefficient or lose\ndimension-dependent factors in their error guarantees. This raises the\nfollowing question:Is high-dimensional agnostic distribution learning even\npossible, algorithmically?\n  In this work, we obtain the first computationally efficient algorithms with\ndimension-independent error guarantees for agnostically learning several\nfundamental classes of high-dimensional distributions: (1) a single Gaussian,\n(2) a product distribution on the hypercube, (3) mixtures of two product\ndistributions (under a natural balancedness condition), and (4) mixtures of\nspherical Gaussians. Our algorithms achieve error that is independent of the\ndimension, and in many cases scales nearly-linearly with the fraction of\nadversarially corrupted samples. Moreover, we develop a general recipe for\ndetecting and correcting corruptions in high-dimensions, that may be applicable\nto many other problems.","url_abs":"http://arxiv.org/abs/1604.06443v2","url_pdf":"http://arxiv.org/pdf/1604.06443v2.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":"robust-estimators-in-high-dimensions-without","repo_url":"https://github.com/AlexisAyme/estimateurs-robustes","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"robust-estimators-in-high-dimensions-without","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":[{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1604.06443","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}