{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T16:08:41Z","timestamp":1792685321331,"version":"4.5.0"},"reference-count":49,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,5,10]],"date-time":"2023-05-10T00:00:00Z","timestamp":1683676800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100031323","name":"Heilbronn Institute for Mathematical Research","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100031323","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000883","name":"University of Bristol","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000883","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,2,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Many modern datasets are collected automatically and are thus easily contaminated by outliers. This has led to a renewed interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the data. However, most robust estimation methods are designed for a specific model. Notably, many methods were proposed recently to obtain robust estimators in linear models, or generalized linear models, and a few were developed for very specific settings, for example beta regression or sample selection models. In this paper we develop a new approach for robust estimation in arbitrary regression models, based on maximum mean discrepancy minimization. We build two estimators that are both proven to be robust to Huber-type contamination. For one of them, we obtain a non-asymptotic error bound and show that it is also robust to adversarial contamination, but this estimator is computationally more expensive to use in practice than the other one. As a by-product of our theoretical analysis of the proposed estimators, we derive new results on kernel conditional mean embedding of distributions that are of independent interest.<\/jats:p>","DOI":"10.1093\/biomet\/asad031","type":"journal-article","created":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T02:52:29Z","timestamp":1683773549000},"page":"71-92","source":"Crossref","is-referenced-by-count":10,"title":["Universal robust regression via maximum mean discrepancy"],"prefix":"10.1093","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4249-7337","authenticated-orcid":false,"given":"P","family":"Alquier","sequence":"first","affiliation":[{"name":"ESSEC Business School, Asia-Pacific Campus , 5 Nepal Park , 139408","place":["Singapore"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M","family":"Gerber","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Bristol , Woodland Road , Bristol BS8 1UG,","place":["U.K"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,5,10]]},"reference":[{"key":"2026042015154002300_asad031-B1","doi-asserted-by":"crossref","first-page":"920","DOI":"10.1111\/biom.12212","article-title":"Robust inference in the negative binomial regression model with an application to falls data","volume":"70","author":"Aeberhard","year":"2014","journal-title":"Biometrics"},{"key":"2026042015154002300_asad031-B2","doi-asserted-by":"crossref","first-page":"2117","DOI":"10.1214\/18-AOS1742","article-title":"Estimation bounds and sharp oracle inequalities of regularized procedures with Lipschitz loss functions","volume":"47","author":"Alquier","year":"2019","journal-title":"Ann. 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