Uniform convergence for Gaussian kernel ridge regression

2025/08/15 by Dommel, Paul, Lakshmanan, Rajmadan
#FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · doi:10.48550/arxiv.2508.11274

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 L²-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 L²-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 L²-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.

Citations

• On the Approximation of Kernel functions
• Convex Risk Measures based on Divergence
• A Short Note on the Comparison of Interpolation Widths, Entropy Numbers,\n and Kolmogorov Widths
• Less is More: Nyström Computational Regularization

Related

• A Comprehensive Analysis on the Learning Curve in Kernel Ridge Regression
• A Geometrical Analysis of Kernel Ridge Regression and its Applications
• Convergence of Gaussian process regression: Optimality, robustness, and relationship with kernel ridge regression
• Sharp Asymptotics of Kernel Ridge Regression Beyond the Linear Regime
• When Kernel Ridge Regression Meets the Hölder-Zygmund Class: Minimax Optimality and Failure of Properness