# Vecchia approximations of Gaussian-process predictions

arXiv: https://arxiv.org/abs/1805.03309 · HTML: https://mlsanity.com/paper/1805.03309/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2018.

## Built on by (most cited first, 21 of 21)

- [Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes](https://mlsanity.com/paper/2304.01294/) (2023)
- [Structured Neural Networks for Density Estimation and Causal Inference](https://mlsanity.com/paper/2311.02221/) (2023)
- [Scalable Bayesian Optimization Using Vecchia Approximations of Gaussian Processes](https://mlsanity.com/paper/2203.01459/) (2022)
- [Scalable Gaussian-process regression and variable selection using Vecchia approximations](https://mlsanity.com/paper/2202.12981/) (2022)
- [Scalable Bayesian Optimization via Focalized Sparse Gaussian Processes](https://mlsanity.com/paper/2412.20375/) (2024)
- [Correlated Product of Experts for Sparse Gaussian Process Regression](https://mlsanity.com/paper/2112.09519/) (2021)
- [Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models](https://mlsanity.com/paper/2310.12000/) (2023)
- [Voronoi Candidates for Bayesian Optimization](https://mlsanity.com/paper/2402.04922/) (2024)
- [Gaussian Process Inference Using Mini-batch Stochastic Gradient Descent: Convergence Guarantees and Empirical Benefits](https://mlsanity.com/paper/2111.10461/) (2021)
- [All Emulators are Wrong, Many are Useful, and Some are More Useful Than Others: A Reproducible Comparison of Computer Model Surrogates](https://mlsanity.com/paper/2512.09060/) (2025)
- [Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Regression Framework](https://mlsanity.com/paper/2109.04447/) (2021)
- [Contraction rates for conjugate gradient and Lanczos approximate posteriors in Gaussian process regression](https://mlsanity.com/paper/2406.12678/) (2024)
- [Fast Gaussian Process Approximations for Autocorrelated Data](https://mlsanity.com/paper/2512.02925/) (2025)
- [Scalable Model-Based Gaussian Process Clustering](https://mlsanity.com/paper/2309.07882/) (2023)
- [Modelling wildland fire burn severity in California using a spatial Super Learner approach](https://mlsanity.com/paper/2311.16187/) (2023)
- [Learning non-Gaussian spatial distributions via Bayesian transport maps with parametric shrinkage](https://mlsanity.com/paper/2409.19208/) (2024)
- [Effect Decomposition of Functional-Output Computer Experiments via Orthogonal Additive Gaussian Processes](https://mlsanity.com/paper/2506.12701/) (2025)
- [Vecchia-Inducing-Points Full-Scale Approximations for Gaussian Processes](https://mlsanity.com/paper/2507.05064/) (2025)
- [Scalable Derivative Gaussian Processes via Exact Gradient Reduction](https://mlsanity.com/paper/2606.02909/) (2026)
- [GraphGP: Scalable Gaussian Processes with Vecchia's Approximation](https://mlsanity.com/paper/2606.11402/) (2026)
- [Spectrally Deconfounded Gradient Boosting](https://mlsanity.com/paper/2607.09371/) (2026)

## Abstract (arXiv)

Gaussian processes (GPs) are highly flexible function estimators used for geospatial analysis, nonparametric regression, and machine learning, but they are computationally infeasible for large datasets. Vecchia approximations of GPs have been used to enable fast evaluation of the likelihood for parameter inference. Here, we study Vecchia approximations of spatial predictions at observed and unobserved locations, including obtaining joint predictive distributions at large sets of locations. We consider a general Vecchia framework for GP predictions, which contains some novel and some existing special cases. We study the accuracy and computational properties of these approaches theoretically and numerically, proving that our new methods exhibit linear computational complexity in the total number of spatial locations. We show that certain choices within the framework can have a strong effect on uncertainty quantification and computational cost, which leads to specific recommendations on which methods are most suitable for various settings. We also apply our methods to a satellite dataset of chlorophyll fluorescence, showing that the new methods are faster or more accurate than existing methods, and reduce unrealistic artifacts in prediction maps.