On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces

Armin Iske

Session: General

Keywords: Kernel regression, irregular sampling, reproducing kernel Hilbert spaces

TL;DR: We prove convergence of kernel regression from irregular samples under minimalistic conditions on both the kernel and the samples.

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 Hölder continuous kernels, we prove convergence rates.

Submission Number: 29