Uncertainty quantification for sparse spectral variational approximations in Gaussian process regression

Dennis Nieman, Botond Szabo, Harry van Zanten

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)2250-2288
Number of pages39
JournalElectronic Journal of Statistics
Volume17
Issue number2
Early online date4 Oct 2023
DOIs
Publication statusPublished - 2023

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© 2023, Institute of Mathematical Statistics. All rights reserved.

Keywords

  • Bayesian asymptotics
  • inducing variables method
  • nonparametric regression
  • uncertainty quantification
  • Variational Bayes

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