Temporal Gaussian Process Regression in Logarithmic Time

Adrien Corenflos*, Zheng Zhao, Simo Sarkka

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

1 Citation (Scopus)


The aim of this article is to present a novel parallelization method for temporal Gaussian process (GP) regression problems. The method allows for solving GP regression problems in logarithmic O(\log N) time, where N stands for the number of observations and test points. Our approach uses the state-space representation of GPs which, in its original form, allows for linear O(N) time GP regression by leveraging Kalman filtering and smoothing methods. By using a recently proposed parallelization method for Bayesian filters and smoothers, we are able to reduce the linear computational complexity of the temporal GP regression problems into logarithmic span complexity. This ensures logarithmic time complexity when parallel hardware such as a graphics processing unit (GPU) are employed. We experimentally show the computational benefits of our approach on simulated and real datasets via our open-source implementation leveraging the GPflow framework.

Original languageEnglish
Title of host publication2022 25th International Conference on Information Fusion, FUSION 2022
Number of pages5
ISBN (Electronic)978-1-7377497-2-1
Publication statusPublished - 2022
MoE publication typeA4 Conference publication
EventInternational Conference on Information Fusion - Linkoping, Sweden
Duration: 4 Jul 20227 Jul 2022
Conference number: 25


ConferenceInternational Conference on Information Fusion
Abbreviated titleFUSION


  • Gaussian process
  • Kalman filter and smoother
  • logarithmic time
  • parallelization
  • state space


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