11 citations · 40 across the 18 of their papers we have counts for
5 papers · 1 filter
Multilevel Bayesian Quadrature
Kaiyu Li, Daniel Giles, Toni Karvonen +2
Multilevel Monte Carlo is a key tool for approximating integrals involving expensive scientific models. The idea is to use approximations of the integrand to construct an estimator…
Orthonormal Expansions for Translation-Invariant Kernels
Filip Tronarp, Toni Karvonen
We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of …
Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed
Toni Karvonen, Chris J. Oates
Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select…
Asymptotic Bounds for Smoothness Parameter Estimates in Gaussian Process Interpolation
Toni Karvonen
It is common to model a deterministic response function, such as the output of a computer experiment, as a Gaussian process with a Matérn covariance kernel. The smoothness paramete…
Error analysis for a statistical finite element method
Toni Karvonen, Fehmi Cirak, Mark Girolami
The recently proposed statistical finite element (statFEM) approach synthesises measurement data with finite element models and allows for making predictions about the unknown true…