Published on Tue Jul 20 2021

Positively Weighted Kernel Quadrature via Subsampling

Satoshi Hayakawa, Harald Oberhauser, Terry Lyons

We study kernel quadrature rules with positive weights for probability measures on general domains. Our theoretical analysis combines the spectral properties of the kernel with random sampling of points. This results in effective algorithms to construct kernel quadRature rules.

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Abstract

We study kernel quadrature rules with positive weights for probability measures on general domains. Our theoretical analysis combines the spectral properties of the kernel with random sampling of points. This results in effective algorithms to construct kernel quadrature rules with positive weights and small worst-case error. Besides additional robustness, our numerical experiments indicate that this can achieve fast convergence rates that compete with the optimal bounds in well-known examples.