{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T09:51:12Z","timestamp":1747216272993,"version":"3.40.5"},"reference-count":0,"publisher":"IOS Press","isbn-type":[{"type":"print","value":"9781643684369"},{"type":"electronic","value":"9781643684376"}],"license":[{"start":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T00:00:00Z","timestamp":1695859200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,9,28]]},"abstract":"<jats:p>We suggest a simple Gaussian mixture model for data generation that complies with Feldman\u2019s long tail theory (2020). We demonstrate that a linear classifier cannot decrease the generalization error below a certain level in the proposed model, whereas a nonlinear classifier with a memorization capacity can. This confirms that for long-tailed distributions, rare training examples must be considered for optimal generalization to new data. Finally, we show that the performance gap between linear and nonlinear models can be lessened as the tail becomes shorter in the subpopulation frequency distribution, as confirmed by experiments on synthetic and real data.<\/jats:p>","DOI":"10.3233\/faia230260","type":"book-chapter","created":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T08:59:55Z","timestamp":1695977995000},"source":"Crossref","is-referenced-by-count":0,"title":["Long-Tail Theory Under Gaussian Mixtures"],"prefix":"10.3233","author":[{"given":"Arman","family":"Bolatov","sequence":"first","affiliation":[{"name":"Department of Computer Science, School of Engineering and Digital Sciences, Nazarbayev University, Kabanbay Batyr 53, Astana, Kazakhstan, 010000"}]},{"given":"Maxat","family":"Tezekbayev","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Kabanbay Batyr 53, Astana, Kazakhstan, 010000"}]},{"given":"Igor","family":"Melnykov","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN, USA"}]},{"given":"Artur","family":"Pak","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Kabanbay Batyr 53, Astana, Kazakhstan, 010000"}]},{"given":"Vassilina","family":"Nikoulina","sequence":"additional","affiliation":[{"name":"NAVER LABS Europe, 6-8 chemin de Maupertuis, 38240 Meylan, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0095-9409","authenticated-orcid":false,"given":"Zhenisbek","family":"Assylbekov","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne, IN, USA"}]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","ECAI 2023"],"original-title":[],"link":[{"URL":"https:\/\/ebooks.iospress.nl\/pdf\/doi\/10.3233\/FAIA230260","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T08:59:57Z","timestamp":1695977997000},"score":1,"resource":{"primary":{"URL":"https:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA230260"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,28]]},"ISBN":["9781643684369","9781643684376"],"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia230260","relation":{},"ISSN":["0922-6389","1879-8314"],"issn-type":[{"type":"print","value":"0922-6389"},{"type":"electronic","value":"1879-8314"}],"subject":[],"published":{"date-parts":[[2023,9,28]]}}}