# Scaled Vecchia approximation for fast computer-model emulation

arXiv: https://arxiv.org/abs/2005.00386 · HTML: https://mlsanity.com/paper/2005.00386/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2020.

## Built on by (most cited first, 15 of 15)

- [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)
- [Sensitivity Prewarping for Local Surrogate Modeling](https://mlsanity.com/paper/2101.06296/) (2021)
- [Variational sparse inverse Cholesky approximation for latent Gaussian processes via double Kullback-Leibler minimization](https://mlsanity.com/paper/2301.13303/) (2023)
- [Vecchia Gaussian Process Ensembles on Internal Representations of Deep Neural Networks](https://mlsanity.com/paper/2305.17063/) (2023)
- [Sampling from Gaussian Processes: A Tutorial and Applications in Global Sensitivity Analysis and Optimization](https://mlsanity.com/paper/2507.14746/) (2025)
- [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)
- [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)
- [Correspondence of NNGP Kernel and the Matern Kernel](https://mlsanity.com/paper/2410.08311/) (2024)
- [Gaussian Processes Sampling with Sparse Grids under Additive Schwarz Preconditioner](https://mlsanity.com/paper/2408.00206/) (2024)
- [Aggregation Models with Optimal Weights for Distributed Gaussian Processes](https://mlsanity.com/paper/2408.00955/) (2024)
- [Scalable Derivative Gaussian Processes via Exact Gradient Reduction](https://mlsanity.com/paper/2606.02909/) (2026)
- [GNet: A scalable and flexible Gaussian process network with nonparametric neurons](https://mlsanity.com/paper/2607.10735/) (2026)
- [Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matrices](https://mlsanity.com/paper/2609.30348/) (2026)

## Abstract (arXiv)

Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments, enabling interpolation between input settings, but direct GP inference is computationally infeasible for large datasets. We adapt and extend a powerful class of GP methods from spatial statistics to enable the scalable analysis and emulation of large computer experiments. Specifically, we apply Vecchia's ordered conditional approximation in a transformed input space, with each input scaled according to how strongly it relates to the computer-model response. The scaling is learned from the data, by estimating parameters in the GP covariance function using Fisher scoring. Our methods are highly scalable, enabling estimation, joint prediction and simulation in near-linear time in the number of model runs. In several numerical examples, our approach substantially outperformed existing methods.