Uniform convergence for Gaussian kernel ridge regression

• URL: http://arxiv.org/abs/2508.11274v2
• Date: Thu, 11 Sep 2025 09:19:48 GMT
• Title: Uniform convergence for Gaussian kernel ridge regression
• Authors: Paul Dommel, Rajmadan Lakshmanan,
• Abstract summary: This paper establishes the first convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyper in both the uniform and the $2$-norm.<n>The results provide new theoretical justification for the use of Gaussian KRR with fixed hypers in nonparametric regression.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper establishes the first polynomial convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyperparameter in both the uniform and the $L^{2}$-norm. The uniform convergence result closes a gap in the theoretical understanding of KRR with the Gaussian kernel, where no such rates were previously known. In addition, we prove a polynomial $L^{2}$-convergence rate in the case, where the Gaussian kernel's width parameter is fixed. This also contributes to the broader understanding of smooth kernels, for which previously only sub-polynomial $L^{2}$-rates were known in similar settings. Together, these results provide new theoretical justification for the use of Gaussian KRR with fixed hyperparameters in nonparametric regression.

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