# On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces

arXiv: https://arxiv.org/abs/2504.13623 · HTML: https://mlsanity.com/paper/2504.13623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 17 references that are in the map.
- First posted on arXiv 18 Apr 2025.

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

- [Reproducing Kernel Hilbert Spaces Cannot Contain all Continuous Functions on a Compact Metric Space](https://mlsanity.com/paper/2002.03171/) (2020)
- [Dimensionality Reduction and Wasserstein Stability for Kernel Regression](https://mlsanity.com/paper/2203.09347/) (2022)

## Abstract (arXiv)

We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the input data. We first prove error estimates in the kernel's RKHS norm. This leads us to new results concerning uniform convergence of kernel regression on compact domains. For Lipschitz continuous and H"older continuous kernels, we prove convergence rates.