Sampling-based Nyström Approximation and Kernel Quadrature

Satoshi Hayakawa; Harald Oberhauser; Terry Lyons

ICML 2023poster10 citations

Sampling-based Nyström Approximation and Kernel Quadrature

Satoshi Hayakawa, Harald Oberhauser, Terry Lyons

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.

BibTeX

@inproceedings{icml2023_samplingbasednys,
  title = {Sampling-based Nyström Approximation and Kernel Quadrature},
  author = {Satoshi Hayakawa and Harald Oberhauser and Terry Lyons},
  booktitle = {ICML 2023},
  year = {2023}
}