# Bayesian autoregression to optimize temporal Mat'ern kernel Gaussian process hyperparameters

arXiv: https://arxiv.org/abs/2508.09792 · HTML: https://mlsanity.com/paper/2508.09792/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 13 Aug 2025.

## Builds on (most cited first, 6 of 6)

- [Probabilistic Line Searches for Stochastic Optimization](https://mlsanity.com/paper/1502.02846/) (2015)
- [Preconditioning for Scalable Gaussian Process Hyperparameter Optimization](https://mlsanity.com/paper/2107.00243/) (2021)
- [Optimization, fast and slow: optimally switching between local and Bayesian optimization](https://mlsanity.com/paper/1805.08610/) (2018)
- [Marginalizing Gaussian Process Hyperparameters using Sequential Monte Carlo](https://mlsanity.com/paper/1502.01908/) (2015)
- [GaussianProcesses.jl: A Nonparametric Bayes package for the Julia Language](https://mlsanity.com/paper/1812.09064/) (2018)
- [Information-seeking polynomial NARX model-predictive control through expected free energy minimization](https://mlsanity.com/paper/2312.15046/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Factor Graph Approach to Scalable Multi-Output Gaussian Process Regression](https://mlsanity.com/paper/2608.11917/) (2026)

## Abstract (arXiv)

Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Mat'ern 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.