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

TL;DR

This paper introduces a Bayesian autoregressive method for optimizing hyperparameters of temporal Matérn kernel Gaussian processes, improving efficiency and accuracy over traditional methods.

Contribution

It proposes a novel recursive Bayesian estimation approach for hyperparameter optimization in Gaussian processes, outperforming existing techniques like marginal likelihood maximization and HMC sampling.

Findings

Outperforms marginal likelihood optimization in runtime and accuracy

Surpasses Hamiltonian Monte Carlo in efficiency and root mean square error

Demonstrates effectiveness in Gaussian process regression tasks

Abstract

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.