The phase diagram of kernel interpolation in large dimensions
成果类型：
Article
署名作者：
Zhang, Haobo; Lu, Weihao; Lin, Qian
署名单位：
Tsinghua University
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asae057
发表日期：
2025
关键词：
摘要：
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.