# Gaussian Process Learning via Fisher Scoring of Vecchia's Approximation

## TL;DR

This paper introduces a fast, accurate Fisher scoring method for Gaussian process models using Vecchia's approximation, enabling efficient fitting of complex nonstationary models to large spatial datasets.

## Contribution

It develops a single pass algorithm for gradient and Fisher information computation, improving optimization speed and accuracy over existing methods.

## Key findings

- More accurate parameter estimation.
- Significantly faster optimization process.
- Effective for large spatial-temporal datasets.

## Abstract

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.