When Kernel Ridge Regression Meets the H\"older-Zygmund Class: Minimax Optimality and Failure of Properness

Abstract:We study kernel ridge regression for nonparametric regression over the Hölder-Zygmund class. Using an RKHS equivalent to a Sobolev space of smoothness s+d/2, we prove that misspecified KRR attains the minimax L2 rate n^{-2s/(2s+d)}. We also show that properness fails in the Hölder-Zygmund norm: even for the zero regression function with Gaussian noise, the expected squared Hölder-Zygmund norm of the KRR noise component grows as log n.

Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST)

arXiv:2607.26065 [stat.ML]

(or arXiv:2607.26065v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2607.26065 Focus to learn more arXiv-issued DOI via DataCite

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