The phase diagram of kernel interpolation in large dimensions

Haobo Zhang, Weihao Lu and Qian Lin

Biometrika, 2025, vol. 112, issue 1, 242-52

Abstract: SummaryThe generalization ability of kernel interpolation in large dimensions, ie,for some , 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 . Consequently, we obtain thephase diagram of large-dimensional kernel interpolation, ie, we determine the regions in theplane where the kernel interpolation is minimax optimal, suboptimal and inconsistent.

Keywords: Benign overfitting; High dimension; Kernel interpolation; Lower bound; Minimax optimality (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asae057 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:112:y:2025:i:1:p:242-52.

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().