{"title":"核插值的泛化性很差","authors":"Yicheng Li, Haobo Zhang, Qian Lin","doi":"10.1093/biomet/asad048","DOIUrl":null,"url":null,"abstract":"Summary 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 ‘benign overfitting phenomenon’ reported in the literature on deep networks. In this paper, under mild conditions, we show that, for any ε>0, the generalization error of kernel interpolation is lower bounded by Ω(n−ε). 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.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Kernel interpolation generalizes poorly\",\"authors\":\"Yicheng Li, Haobo Zhang, Qian Lin\",\"doi\":\"10.1093/biomet/asad048\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary 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 ‘benign overfitting phenomenon’ reported in the literature on deep networks. In this paper, under mild conditions, we show that, for any ε>0, the generalization error of kernel interpolation is lower bounded by Ω(n−ε). 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.\",\"PeriodicalId\":9001,\"journal\":{\"name\":\"Biometrika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2023-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Biometrika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/biomet/asad048\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"BIOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Biometrika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/biomet/asad048","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"BIOLOGY","Score":null,"Total":0}
Summary 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 ‘benign overfitting phenomenon’ reported in the literature on deep networks. In this paper, under mild conditions, we show that, for any ε>0, the generalization error of kernel interpolation is lower bounded by Ω(n−ε). 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.
期刊介绍:
Biometrika is primarily a journal of statistics in which emphasis is placed on papers containing original theoretical contributions of direct or potential value in applications. From time to time, papers in bordering fields are also published.