{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T17:20:49Z","timestamp":1787764849307,"version":"build-2784847793"},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,8,7]],"date-time":"2023-08-07T00:00:00Z","timestamp":1691366400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,5,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether kernel interpolation can generalize well, since it may help us understand the \u2018benign overfitting phenomenon\u2019 reported in the literature on deep networks. In this paper, under mild conditions, we show that, for any \u03b5&amp;gt;0, the generalization error of kernel interpolation is lower bounded by \u03a9(n\u2212\u03b5). In other words, the kernel interpolation generalizes poorly for a large class of kernels. As a direct corollary, we can show that overfitted wide neural networks defined on the sphere generalize poorly.<\/jats:p>","DOI":"10.1093\/biomet\/asad048","type":"journal-article","created":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T12:26:26Z","timestamp":1691151986000},"page":"715-722","source":"Crossref","is-referenced-by-count":3,"title":["Kernel interpolation generalizes poorly"],"prefix":"10.1093","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9497-0379","authenticated-orcid":false,"given":"Yicheng","family":"Li","sequence":"first","affiliation":[{"name":"Center for Statistical Science, Department of Industrial Engineering, Tsinghua University , 30 Shuangqing Road , Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3478-140X","authenticated-orcid":false,"given":"Haobo","family":"Zhang","sequence":"additional","affiliation":[{"name":"Center for Statistical Science, Department of Industrial Engineering, Tsinghua University , 30 Shuangqing Road , Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qian","family":"Lin","sequence":"additional","affiliation":[{"name":"Center for Statistical Science, Department of Industrial Engineering, Tsinghua University , 30 Shuangqing Road , Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,8,7]]},"reference":[{"key":"2024051307572186000_asad048-B1","volume-title":"Sobolev Spaces","author":"Adams","year":"2003"},{"key":"2024051307572186000_asad048-B2","author":"Allen-Zhu","year":"2019"},{"key":"2024051307572186000_asad048-B3","author":"Beaglehole","year":"2022"},{"key":"2024051307572186000_asad048-B4","doi-asserted-by":"crossref","first-page":"15849","DOI":"10.1073\/pnas.1903070116","article-title":"Reconciling modern machine-learning practice and the classical bias-variance trade-off","volume":"116","author":"Belkin","year":"2019","journal-title":"Proc. Nat. Acad. Sci"},{"key":"2024051307572186000_asad048-B5","author":"Bietti","year":"2021"},{"key":"2024051307572186000_asad048-B6","first-page":"12893","volume-title":"Proc. 33rd Int. Conf. Neural Info. Proces. Syst","author":"Bietti","year":"2019"},{"key":"2024051307572186000_asad048-B7","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1007\/s10208-017-9359-7","article-title":"Optimal rates for regularization of statistical inverse learning problems","volume":"18","author":"Blanchard","year":"2018","journal-title":"Foundat. Comp. Math"},{"key":"2024051307572186000_asad048-B8","first-page":"1","volume-title":"Proc. 35th Ann. Conf. Learn. Theory","author":"Buchholz","year":"2022"},{"key":"2024051307572186000_asad048-B9","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10208-006-0196-8","article-title":"Optimal rates for the regularized least-squares algorithm","volume":"7","author":"Caponnetto","year":"2007","journal-title":"Foundat. Comp. Math"},{"key":"2024051307572186000_asad048-B10","volume-title":"Support Vector Machines. Information Science and Statistics","author":"Christmann","year":"2008"},{"key":"2024051307572186000_asad048-B11","author":"Du","year":"2019"},{"key":"2024051307572186000_asad048-B12","first-page":"1","article-title":"Sobolev norm learning rates for regularized least-squares algorithms","volume":"21","author":"Fischer","year":"2020","journal-title":"J. Mach. Learn. Res"},{"key":"2024051307572186000_asad048-B13","author":"Ghorbani","year":"2020"},{"key":"2024051307572186000_asad048-B14","author":"Ghosh","year":"2021"},{"key":"2024051307572186000_asad048-B15","doi-asserted-by":"crossref","DOI":"10.1007\/b97848","volume-title":"A Distribution-Free Theory of Nonparametric Regression","author":"Gy\u00f6rfi","year":"2002"},{"key":"2024051307572186000_asad048-B16","first-page":"8580","volume-title":"Proc. 32nd Int. Conf. Neural Info. Proces. Syst., S. Bengio","author":"Jacot","year":"2018"},{"key":"2024051307572186000_asad048-B17","author":"Lai","year":"2023"},{"key":"2024051307572186000_asad048-B18","first-page":"8572","volume-title":"Proc. 33rd Int. Conf. Neural Info. Proces. Syst","author":"Lee","year":"2019"},{"key":"2024051307572186000_asad048-B19","author":"Li","year":"2023"},{"key":"2024051307572186000_asad048-B20","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1214\/19-AOS1849","article-title":"Just interpolate: kernel \u2018ridgeless\u2019 regression can generalize","volume":"48","author":"Liang","year":"2020","journal-title":"Ann. Statist."},{"key":"2024051307572186000_asad048-B21","first-page":"2683","author":"Liang","year":"2020"},{"key":"2024051307572186000_asad048-B22","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1002\/cpa.22008","article-title":"The generalization error of random features regression: precise asymptotics and the double descent curve","volume":"75","author":"Mei","year":"2022","journal-title":"Commun. Pure Appl. Math"},{"key":"2024051307572186000_asad048-B23","author":"Neyshabur","year":"2015"},{"key":"2024051307572186000_asad048-B24","first-page":"2595","author":"Rakhlin","year":"2019"},{"key":"2024051307572186000_asad048-B25","first-page":"290","volume-title":"Proc. 13th Int. Conf. Neural Info. Proces. Syst","author":"Smola","year":"2000"},{"key":"2024051307572186000_asad048-B26","author":"Steinwart","year":"2009"},{"key":"2024051307572186000_asad048-B27","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s00365-012-9153-3","article-title":"Mercer\u2019s theorem on general domains: on the interaction between measures, kernels, and RKHSs","volume":"35","author":"Steinwart","year":"2012","journal-title":"Constr. Approx"},{"key":"2024051307572186000_asad048-B28","volume-title":"The Nature of Statistical Learning Theory","author":"Vapnik","year":"1999"},{"key":"2024051307572186000_asad048-B29","doi-asserted-by":"crossref","DOI":"10.1017\/9781108627771","volume-title":"High-Dimensional Statistics: A Non-Asymptotic Viewpoint","author":"Wainwright","year":"2019"},{"key":"2024051307572186000_asad048-B30","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511617539","volume-title":"Scattered Data Approximation","author":"Wendland","year":"2004"},{"key":"2024051307572186000_asad048-B31","author":"Zhang","year":"2017"},{"key":"2024051307572186000_asad048-B32","author":"Zhang","year":"2023"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asad048\/53028367\/asad048.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/111\/2\/715\/57467427\/asad048.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/111\/2\/715\/57467427\/asad048.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T08:14:46Z","timestamp":1715588086000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/111\/2\/715\/7238206"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,7]]},"references-count":32,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,8,7]]},"published-print":{"date-parts":[[2024,5,13]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asad048","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,6,1]]},"published":{"date-parts":[[2023,8,7]]}}}