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

arXiv: https://arxiv.org/abs/2607.26065 · HTML: https://mlsanity.com/paper/2607.26065/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 7 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Builds on (most cited first, 2 of 2)

- [On the Optimality of Misspecified Spectral Algorithms](https://mlsanity.com/paper/2303.14942/) (2023)
- [Benign overfitting and adaptive nonparametric regression](https://mlsanity.com/paper/2206.13347/) (2022)

## Abstract (arXiv)

We study kernel ridge regression for nonparametric regression over the H"older-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 H"older-Zygmund norm: even for the zero regression function with Gaussian noise, the expected squared H"older-Zygmund norm of the KRR noise component grows as log n.