核插值的泛化性很差

IF 2.4 2区 数学 Q2 BIOLOGY
Biometrika Pub Date : 2023-08-07 DOI:10.1093/biomet/asad048
Yicheng Li, Haobo Zhang, Qian Lin
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引用次数: 5

摘要

最近核回归研究复兴中最有趣的问题之一可能是核插值是否可以很好地泛化,因为它可以帮助我们理解深度网络文献中报道的“良性过拟合现象”。在温和条件下,我们证明了对于任意ε>0,核插值的泛化误差下界为Ω(n−ε)。换句话说,对于大量的核,核插值的泛化效果很差。作为一个直接推论,我们可以证明在球上定义的过拟合宽神经网络泛化效果很差。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Kernel interpolation generalizes poorly
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.
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来源期刊
Biometrika
Biometrika 生物-生物学
CiteScore
5.50
自引率
3.70%
发文量
56
审稿时长
6-12 weeks
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.
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