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

arXiv: https://arxiv.org/abs/1905.08374 · HTML: https://mlsanity.com/paper/1905.08374/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2019.

## Built on by (most cited first, 10 of 10)

- [Scalable Gaussian-process regression and variable selection using Vecchia approximations](https://mlsanity.com/paper/2202.12981/) (2022)
- [Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models](https://mlsanity.com/paper/2310.12000/) (2023)
- [Gaussian Process Inference Using Mini-batch Stochastic Gradient Descent: Convergence Guarantees and Empirical Benefits](https://mlsanity.com/paper/2111.10461/) (2021)
- [A Spatio-Temporal Machine Learning Model for Mortgage Credit Risk: Default Probabilities and Loan Portfolios](https://mlsanity.com/paper/2410.02846/) (2024)
- [Modelling wildland fire burn severity in California using a spatial Super Learner approach](https://mlsanity.com/paper/2311.16187/) (2023)
- [Implementation and Analysis of GPU Algorithms for Vecchia Approximation](https://mlsanity.com/paper/2407.02740/) (2024)
- [STACI: Spatio-Temporal Aleatoric Conformal Inference](https://mlsanity.com/paper/2505.21658/) (2025)
- [When the whole is greater than the sum of its parts: Scaling black-box inference to large data settings through divide-and-conquer](https://mlsanity.com/paper/2412.20323/) (2024)
- [Vecchia-Inducing-Points Full-Scale Approximations for Gaussian Processes](https://mlsanity.com/paper/2507.05064/) (2025)
- [Fast Gaussian process inference by exact Mat'ern kernel decomposition](https://mlsanity.com/paper/2508.01864/) (2025)

## Abstract (arXiv)

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.