Open Access
2023 Uncertainty quantification for sparse spectral variational approximations in Gaussian process regression
Dennis Nieman, Botond Szabo, Harry van Zanten
Author Affiliations +
Electron. J. Statist. 17(2): 2250-2288 (2023). DOI: 10.1214/23-EJS2155


We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and limitations for the frequentist coverage of the resulting variational credible sets. We also derive sufficient and necessary lower bounds for the number of inducing variables required to achieve minimax posterior contraction rates. The implications of these results are demonstrated for different choices of priors. In a numerical analysis we consider a wider range of inducing variable methods and observe similar phenomena beyond the scope of our theoretical findings.

Funding Statement

Co-funded by the European Union (ERC, BigBayesUQ, project number: 101041064). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.


Download Citation

Dennis Nieman. Botond Szabo. Harry van Zanten. "Uncertainty quantification for sparse spectral variational approximations in Gaussian process regression." Electron. J. Statist. 17 (2) 2250 - 2288, 2023.


Received: 1 December 2022; Published: 2023
First available in Project Euclid: 4 October 2023

arXiv: 2212.11031
MathSciNet: MR4649981
Digital Object Identifier: 10.1214/23-EJS2155

Primary: 62G20
Secondary: 62G05 , 62G08 , 62G15

Keywords: Bayesian asymptotics , inducing variables method , Nonparametric regression , uncertainty quantification , variational Bayes

Vol.17 • No. 2 • 2023
Back to Top