Gaussian process learning via Fisher scoring of Vecchia's approximation

We derive a single-pass algorithm for computing the gradient and Fisher information of Vecchia's Gaussian process loglikelihood approximation, which provides a computationally efficient means for applying the Fisher scoring algorithm for maximizing the loglikelihood. The advantages of the optimization techniques are demonstrated in numerical examples and in an application to Argo ocean temperature data. The new methods find the maximum likelihood estimates much faster and more reliably than an optimization method that uses only function evaluations, especially when the covariance function has many parameters. This allows practitioners to fit nonstationary models to large spatial and spatial-temporal datasets.

Automated summary

In this study, a single-pass algorithm was proposed for computing the gradient and Fisher information of Vecchia's Gaussian process loglikelihood approximation, providing an efficient means for applying the Fisher scoring algorithm for maximizing the loglikelihood. The advantages of the optimization techniques were demonstrated in numerical examples and an application to Argo ocean temperature data, showing that the new methods can find maximum likelihood estimates faster and more reliably, especially when the covariance function has many parameters. This enables practitioners to fit nonstationary models to large spatial and spatial-temporal datasets.