Paper · arXiv
When Kernel Ridge Regression Meets the Hölder-Zygmund Class: Minimax Optimality and Failure of Properness
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.
| Authors | Yuxuan Hou |
|---|---|
| Primary category | stat.ML |
| Published | 19 June 2026 |
| Last updated at source | 19 June 2026 |
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