# Non-asymptotic confidence regions on RKHS. The Paley-Wiener and standard Sobolev space cases

arXiv: https://arxiv.org/abs/2507.06657 · HTML: https://mlsanity.com/paper/2507.06657/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Builds on (most cited first, 4 of 4)

- [Nonparametric, Nonasymptotic Confidence Bands with Paley-Wiener Kernels for Band-Limited Functions](https://mlsanity.com/paper/2206.13629/) (2022)
- [Improving Kernel-Based Nonasymptotic Simultaneous Confidence Bands](https://mlsanity.com/paper/2401.15791/) (2024)
- [Gaussian process interpolation with conformal prediction: methods and comparative analysis](https://mlsanity.com/paper/2407.08271/) (2024)
- [Scalable and adaptive prediction bands with kernel sum-of-squares](https://mlsanity.com/paper/2505.21039/) (2025)

## Built on by (most cited first, 1 of 1)

- [MiNCE: Nonparametric, Strongly Consistent Confidence Envelopes for Band-Limited Functions and their Smoothed Spectra](https://mlsanity.com/paper/2609.09436/) (2026)

## Abstract (arXiv)

We consider the problem of constructing a global, probabilistic, and non-asymptotic confidence region for an unknown function observed on a random design. The unknown function is assumed to lie in a reproducing kernel Hilbert space (RKHS). We show that this construction can be reduced to accurately estimating the RKHS norm of the unknown function. Our analysis primarily focuses both on the Paley-Wiener and on the standard Sobolev space settings.