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

arXiv 2607.26065 ↗First posted 19 Jun 2026stat.ML cs.LG math.STcited by 0

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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.

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

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References · 2

  1. 2023On the Optimality of Misspecified Spectral Algorithmscited by 28
  2. 2022Benign overfitting and adaptive nonparametric regressioncited by 3

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