# Vecchia-Laplace approximations of generalized Gaussian processes for big non-Gaussian spatial data

arXiv: https://arxiv.org/abs/1906.07828 · HTML: https://mlsanity.com/paper/1906.07828/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2019.

## Built on by (most cited first, 4 of 4)

- [Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models](https://mlsanity.com/paper/2310.12000/) (2023)
- [Variational sparse inverse Cholesky approximation for latent Gaussian processes via double Kullback-Leibler minimization](https://mlsanity.com/paper/2301.13303/) (2023)
- [Learning non-Gaussian spatial distributions via Bayesian transport maps with parametric shrinkage](https://mlsanity.com/paper/2409.19208/) (2024)
- [On the Laplace Approximation as Model Selection Criterion for Gaussian Processes](https://mlsanity.com/paper/2403.09215/) (2024)

## Abstract (arXiv)

Generalized Gaussian processes (GGPs) are highly flexible models that combine latent GPs with potentially non-Gaussian likelihoods from the exponential family. GGPs can be used in a variety of settings, including GP classification, nonparametric count regression, modeling non-Gaussian spatial data, and analyzing point patterns. However, inference for GGPs can be analytically intractable, and large datasets pose computational challenges due to the inversion of the GP covariance matrix. We propose a Vecchia-Laplace approximation for GGPs, which combines a Laplace approximation to the non-Gaussian likelihood with a computationally efficient Vecchia approximation to the GP, resulting in a simple, general, scalable, and accurate methodology. We provide numerical studies and comparisons on simulated and real spatial data. Our methods are implemented in a freely available R package.