11 citations · 40 across the 18 of their papers we have counts for
7 papers · 1 filter
Wasserstein bounds for non-linear Gaussian filters
Toni Karvonen, Simo Särkkä
Most Kalman filters for non-linear systems, such as the unscented Kalman filter, are based on Gaussian approximations. We use Poincaré inequalities to bound the Wasserstein distanc…
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…
Scale estimation and rate-unbiasedness for Gaussian processes under smoothness misspecification
Toni Karvonen, François Bachoc
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covari…
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…
On the positivity and magnitudes of Bayesian quadrature weights
Toni Karvonen, Motonobu Kanagawa, Simo Särkkä
This article reviews and studies the properties of Bayesian quadrature weights, which strongly affect stability and robustness of the quadrature rule. Specifically, we investigate…