Bayesian autoregression to optimize temporal Matérn-kernel Gaussian process hyperparameters

Abstract

We present a probabilistic numerical procedure for optimizing Matérn-class 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. The recursive nature means that there is an initial value that should improve after every update, much like iterative local optimization techniques. We demonstrate that the proposed procedure outperforms the standard maximum marginal likelihood-based approach in both runtime and ultimate root mean square error in Gaussian process regression.