{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:43:42Z","timestamp":1753875822648,"version":"3.41.2"},"reference-count":37,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2024,11,9]],"date-time":"2024-11-09T00:00:00Z","timestamp":1731110400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,1,16]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>The generalization ability of kernel interpolation in large dimensions, ie, $ n\\asymp d^{\\gamma} $ for some $ \\gamma \\gt 0 $, could be one of the most interesting problems in the recent renaissance of kernel regression, since it may help us understand the so-called benign overfitting phenomenon reported in the neural networks literature. Focusing on the inner product kernel on the unit sphere, we fully characterize the exact order of both the variance and the bias of large-dimensional kernel interpolation under various source conditions $ s\\geqslant 0 $. Consequently, we obtain the $ (s,\\gamma) $ phase diagram of large-dimensional kernel interpolation, ie, we determine the regions in the $ (s,\\gamma) $ plane where the kernel interpolation is minimax optimal, suboptimal and inconsistent.<\/jats:p>","DOI":"10.1093\/biomet\/asae057","type":"journal-article","created":{"date-parts":[[2024,11,9]],"date-time":"2024-11-09T15:06:18Z","timestamp":1731164778000},"source":"Crossref","is-referenced-by-count":0,"title":["The phase diagram of kernel interpolation in large dimensions"],"prefix":"10.1093","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3478-140X","authenticated-orcid":false,"given":"Haobo","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, Tsinghua University , 100084 Beijing,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weihao","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Tsinghua University , 100084 Beijing,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qian","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Tsinghua University , 100084 Beijing,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,11,9]]},"reference":[{"volume-title":"11th Int. 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