Positively Weighted Kernel Quadrature via Subsampling
Abstract
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules using only access to i.i.d. samples from the underlying measure and evaluation of the kernel and that result in a small worst-case error. In addition to our theoretical results and the benefits resulting from convex weights, our experiments indicate that this construction can compete with the optimal bounds in well-known examples.
Cite
Text
Hayakawa et al. "Positively Weighted Kernel Quadrature via Subsampling." Neural Information Processing Systems, 2022.Markdown
[Hayakawa et al. "Positively Weighted Kernel Quadrature via Subsampling." Neural Information Processing Systems, 2022.](https://mlanthology.org/neurips/2022/hayakawa2022neurips-positively/)BibTeX
@inproceedings{hayakawa2022neurips-positively,
title = {{Positively Weighted Kernel Quadrature via Subsampling}},
author = {Hayakawa, Satoshi and Oberhauser, Harald and Lyons, Terry},
booktitle = {Neural Information Processing Systems},
year = {2022},
url = {https://mlanthology.org/neurips/2022/hayakawa2022neurips-positively/}
}