Bayesian autoregression to optimize temporal Matérn kernel Gaussian process hyperparameters

Wouter M. Kouw
8/13/2025
cs.LGeess.SPstat.ML

No official code found. Best implementation: biaslab/ProbNum2025-BARGPhparams (1 star, MIT, last commit 2025-07-18).

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.

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Code Implementations(1)

biaslab/ProbNum2025-BARGPhparamsCommunity70%
MIT

Bayesian autoregression to optimize temporal Mat´ern-kernel Gaussian process hyperparameters

10Julia, Jupyter NotebookJul 17, 20251 years agoMIT

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Cite this paper

@article{kouw2025bayesian,
  title  = {Bayesian autoregression to optimize temporal Matérn kernel Gaussian process hyperparameters},
  author = {Wouter M. Kouw},
  year   = {2025},
  eprint = {2508.09792},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2508.09792v1}
}

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