Bayesian autoregression to optimize temporal Matérn kernel Gaussian process hyperparameters
This work addresses a specific computational bottleneck in Gaussian process modeling for temporal data, offering an incremental improvement in optimization efficiency.
The paper tackles the problem of optimizing hyperparameters for Matérn kernel temporal Gaussian processes by proposing a Bayesian autoregression method, which outperforms marginal likelihood maximization and Hamiltonian Monte Carlo in runtime and root mean square error.
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.