Sampling-Based Nyström Approximation and Kernel Quadrature
Abstract
We analyze the Nyström approximation of a positive definite kernel associated with a probability measure. We first prove an improved error bound for the conventional Nyström 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 Nyström 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
Text
Hayakawa et al. "Sampling-Based Nyström Approximation and Kernel Quadrature." International Conference on Machine Learning, 2023.Markdown
[Hayakawa et al. "Sampling-Based Nyström Approximation and Kernel Quadrature." International Conference on Machine Learning, 2023.](https://mlanthology.org/icml/2023/hayakawa2023icml-samplingbased/)BibTeX
@inproceedings{hayakawa2023icml-samplingbased,
title = {{Sampling-Based Nyström Approximation and Kernel Quadrature}},
author = {Hayakawa, Satoshi and Oberhauser, Harald and Lyons, Terry},
booktitle = {International Conference on Machine Learning},
year = {2023},
pages = {12678-12699},
volume = {202},
url = {https://mlanthology.org/icml/2023/hayakawa2023icml-samplingbased/}
}