Sampling-based Nystr\"om Approximation and Kernel Quadrature
Numerical Analysis
2023-05-24 v3 Machine Learning
Numerical Analysis
Machine Learning
Abstract
We analyze the Nystr\"om approximation of a positive definite kernel associated with a probability measure. We first prove an improved error bound for the conventional Nystr\"om approximation with i.i.d. sampling and singular-value decomposition in the continuous regime; the proof techniques are borrowed from statistical learning theory. We further introduce a refined selection of subspaces in Nystr\"om approximation with theoretical guarantees that is applicable to non-i.i.d. landmark points. Finally, we discuss their application to convex kernel quadrature and give novel theoretical guarantees as well as numerical observations.
Cite
@article{arxiv.2301.09517,
title = {Sampling-based Nystr\"om Approximation and Kernel Quadrature},
author = {Satoshi Hayakawa and Harald Oberhauser and Terry Lyons},
journal= {arXiv preprint arXiv:2301.09517},
year = {2023}
}
Comments
22 pages, ICML 2023 camera-ready version. Typos fixed