On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces
Machine Learning
2025-04-21 v1 Machine Learning
Numerical Analysis
Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2504.13623,
title = {On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces},
author = {Armin Iske},
journal= {arXiv preprint arXiv:2504.13623},
year = {2025}
}