Error Bounds and the Asymptotic Setting in Kernel-Based Approximation
Title | Error Bounds and the Asymptotic Setting in Kernel-Based Approximation |
Publication Type | Journal Article |
Year of Publication | 2022 |
Authors | Karvonen, T |
Journal | Dolomites Research Notes on Approximation |
Volume | 15 |
Issue | 3 |
Pagination | 65-77 |
Date Published | 10/2022 |
Publisher | Padova University Press |
Place Published | Padova, IT |
ISSN Number | 2035-6803 |
Abstract | We use ideas from Gaussian process regression to derive computable error bounds that can be used as stopping criteria in kernel-based approximation. The proposed bounds are based on maximum likelihood estimation and cross-validation of a kernel scale parameter and take the form of a product of the scale parameter estimate and the worst-case approximation error in the reproducing kernel Hilbert space induced by the kernel. We also use known results on the so-called asymptotic setting to argue that such worst-case type error bounds are not necessarily conservative. |
URL | https://drna.padovauniversitypress.it/2022/3/7 |
DOI | 10.14658/pupj-drna-2022-3-7 |