Bayesian autoregression to optimize temporal Matérn kernel Gaussian process hyperparameters

Wouter M. Kouw
Proceedings of the First International Conference on Probabilistic Numerics, PMLR 271:122-130, 2025.

Abstract

Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Matérn kernel temporal Gaussian processes with respect to the kernel covariance function’s hyperparameters. It is based on casting the optimization problem as a recursive Bayesian estimation procedure for the parameters of an autoregressive model. We demonstrate that the proposed procedure outperforms maximizing the marginal likelihood as well as Hamiltonian Monte Carlo sampling, both in terms of runtime and ultimate root mean square error in Gaussian process regression.

Cite this Paper

BibTeX
@InProceedings{pmlr-v271-kouw25a, title = {{B}ayesian autoregression to optimize temporal {M}atérn kernel {G}aussian process hyperparameters}, author = {Kouw, Wouter M.}, booktitle = {Proceedings of the First International Conference on Probabilistic Numerics}, pages = {122--130}, year = {2025}, editor = {Kanagawa, Motonobu and Cockayne, Jon and Gessner, Alexandra and Hennig, Philipp}, volume = {271}, series = {Proceedings of Machine Learning Research}, month = {01--03 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v271/main/assets/kouw25a/kouw25a.pdf}, url = {https://proceedings.mlr.press/v271/kouw25a.html}, abstract = {Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Matérn kernel temporal Gaussian processes with respect to the kernel covariance function’s hyperparameters. It is based on casting the optimization problem as a recursive Bayesian estimation procedure for the parameters of an autoregressive model. We demonstrate that the proposed procedure outperforms maximizing the marginal likelihood as well as Hamiltonian Monte Carlo sampling, both in terms of runtime and ultimate root mean square error in Gaussian process regression.} }
Endnote
%0 Conference Paper %T Bayesian autoregression to optimize temporal Matérn kernel Gaussian process hyperparameters %A Wouter M. Kouw %B Proceedings of the First International Conference on Probabilistic Numerics %C Proceedings of Machine Learning Research %D 2025 %E Motonobu Kanagawa %E Jon Cockayne %E Alexandra Gessner %E Philipp Hennig %F pmlr-v271-kouw25a %I PMLR %P 122--130 %U https://proceedings.mlr.press/v271/kouw25a.html %V 271 %X Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Matérn kernel temporal Gaussian processes with respect to the kernel covariance function’s hyperparameters. It is based on casting the optimization problem as a recursive Bayesian estimation procedure for the parameters of an autoregressive model. We demonstrate that the proposed procedure outperforms maximizing the marginal likelihood as well as Hamiltonian Monte Carlo sampling, both in terms of runtime and ultimate root mean square error in Gaussian process regression.
APA
Kouw, W.M.. (2025). Bayesian autoregression to optimize temporal Matérn kernel Gaussian process hyperparameters. Proceedings of the First International Conference on Probabilistic Numerics, in Proceedings of Machine Learning Research 271:122-130 Available from https://proceedings.mlr.press/v271/kouw25a.html.

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