3 citations · 3 across the 2 of their papers we have counts for
10 papers
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…
Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering and Smoothing
Zheng Zhao, Toni Karvonen, Roland Hostettler +1
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an Itô stochastic differ…
Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions
Toni Karvonen, George Wynne, Filip Tronarp +2
Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically ne…
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…