Gaussian Process Learning via Fisher Scoring of Vecchia's Approximation
This work provides a computational improvement for fitting nonstationary Gaussian process models to large spatial and spatial-temporal datasets, which is incremental but beneficial for practitioners in fields like oceanography.
The authors tackled the problem of efficiently optimizing parameters for Gaussian process models with Vecchia's approximation by deriving a single-pass algorithm for computing gradient and Fisher information, enabling faster and more accurate fitting, especially for covariance functions with many parameters, as demonstrated in numerical examples and an Argo ocean temperature dataset.
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 are more accurate and much faster 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.