11 citations · 40 across the 18 of their papers we have counts for
7 papers · 1 filter
Black Box Probabilistic Numerics
Onur Teymur, Christopher N. Foley, Philip G. Breen +2
Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quanti…
Integration in reproducing kernel Hilbert spaces of Gaussian kernels
Toni Karvonen, Chris J. Oates, Mark Girolami
The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numer…
Sampling based approximation of linear functionals in Reproducing Kernel Hilbert Spaces
Gabriele Santin, Toni Karvonen, Bernard Haasdonk
In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature r…
Kernel-based interpolation at approximate Fekete points
Toni Karvonen, Simo Särkkä, Ken'ichiro Tanaka
We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion…
Worst-case optimal approximation with increasingly flat Gaussian kernels
Toni Karvonen, Simo Särkkä
We study worst-case optimal approximation of positive linear functionals in reproducing kernel Hilbert spaces induced by increasingly flat Gaussian kernels. This provides a new per…
Gaussian kernel quadrature at scaled Gauss-Hermite nodes
Toni Karvonen, Simo Särkkä
This article derives an accurate, explicit, and numerically stable approximation to the kernel quadrature weights in one dimension and on tensor product grids when the kernel and i…
Fully symmetric kernel quadrature
Toni Karvonen, Simo Särkkä
Kernel quadratures and other kernel-based approximation methods typically suffer from prohibitive cubic time and quadratic space complexity in the number of function evaluations. T…