Kernel Quadrature with Randomly Pivoted Cholesky

Ethan Nicholas Epperly, Elvira Moreno Ferreira

Keywords: kernel quadrature, Nyström approximation, reproducing kernel Hilbert space, randomly pivoted Cholesky

TL;DR: We develop new kernel quadrature schemes based on the randomly pivoted Cholesky sampling algorithm

Abstract: This paper presents new quadrature rules for functions in a reproducing kernel Hilbert space using nodes drawn by a sampling algorithm known as randomly pivoted Cholesky. The resulting computational procedure compares favorably to previous kernel quadrature methods, which either achieve low accuracy or require solving a computationally challenging sampling problem. Theoretical and numerical results show that randomly pivoted Cholesky is fast and achieves comparable quadrature error rates to more computationally expensive quadrature schemes based on continuous volume sampling, thinning, and recombination. Randomly pivoted Cholesky is easily adapted to complicated geometries with arbitrary kernels, unlocking new potential for kernel quadrature.

Submission Number: 9321