# Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

arXiv: https://arxiv.org/abs/1406.7343 · HTML: https://mlsanity.com/paper/1406.7343/

## Key facts

- Cited by 72 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2014.

## Built on by (most cited first, 30 of 72)

- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Posterior and Computational Uncertainty in Gaussian Processes](https://mlsanity.com/paper/2205.15449/) (2022)
- [Positional Encoder Graph Neural Networks for Geographic Data](https://mlsanity.com/paper/2111.10144/) (2021)
- [Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networks](https://mlsanity.com/paper/2105.04554/) (2021)
- [Bias-Free Scalable Gaussian Processes via Randomized Truncations](https://mlsanity.com/paper/2102.06695/) (2021)
- [Neural networks for geospatial data](https://mlsanity.com/paper/2304.09157/) (2023)
- [Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference](https://mlsanity.com/paper/2411.01036/) (2024)
- [MuyGPs: Scalable Gaussian Process Hyperparameter Estimation Using Local Cross-Validation](https://mlsanity.com/paper/2104.14581/) (2021)
- [Variational Nearest Neighbor Gaussian Process](https://mlsanity.com/paper/2202.01694/) (2022)
- [Scalable Gaussian-process regression and variable selection using Vecchia approximations](https://mlsanity.com/paper/2202.12981/) (2022)
- [Correlated Product of Experts for Sparse Gaussian Process Regression](https://mlsanity.com/paper/2112.09519/) (2021)
- [Physics-Informed Variational State-Space Gaussian Processes](https://mlsanity.com/paper/2409.13876/) (2024)
- [Scalable Cross Validation Losses for Gaussian Process Models](https://mlsanity.com/paper/2105.11535/) (2021)
- [Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models](https://mlsanity.com/paper/2310.12000/) (2023)
- [Leveraging Locality and Robustness to Achieve Massively Scalable Gaussian Process Regression](https://mlsanity.com/paper/2306.14731/) (2023)
- [Lightweight Distributed Gaussian Process Regression for Online Machine Learning](https://mlsanity.com/paper/2105.04738/) (2021)
- [Fully Decentralized, Scalable Gaussian Processes for Multi-Agent Federated Learning](https://mlsanity.com/paper/2203.02865/) (2022)
- [Variational sparse inverse Cholesky approximation for latent Gaussian processes via double Kullback-Leibler minimization](https://mlsanity.com/paper/2301.13303/) (2023)
- [Iterative Methods for Full-Scale Gaussian Process Approximations for Large Spatial Data](https://mlsanity.com/paper/2405.14492/) (2024)
- [Scalable Spatiotemporally Varying Coefficient Modelling with Bayesian Kernelized Tensor Regression](https://mlsanity.com/paper/2109.00046/) (2021)
- [Stein's method for marginals on large graphical models](https://mlsanity.com/paper/2410.11771/) (2024)
- [Neighbour-Driven Gaussian Process Variational Autoencoders for Scalable Structured Latent Modelling](https://mlsanity.com/paper/2505.16481/) (2025)
- [Transformer with Koopman-Enhanced Graph Convolutional Network for Spatiotemporal Dynamics Forecasting](https://mlsanity.com/paper/2507.03855/) (2025)
- [Modeling massive highly-multivariate nonstationary spatial data with the basis graphical lasso](https://mlsanity.com/paper/2101.02404/) (2021)
- [Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Regression Framework](https://mlsanity.com/paper/2109.04447/) (2021)
- [Nearest neighbor empirical processes](https://mlsanity.com/paper/2110.15083/) (2021)
- [Incorporating Prior Knowledge into Neural Networks through an Implicit Composite Kernel](https://mlsanity.com/paper/2205.07384/) (2022)
- [Bayesian Complementary Kernelized Learning for Multidimensional Spatiotemporal Data](https://mlsanity.com/paper/2208.09978/) (2022)
- [Contraction rates for conjugate gradient and Lanczos approximate posteriors in Gaussian process regression](https://mlsanity.com/paper/2406.12678/) (2024)
- [A Spatio-Temporal Machine Learning Model for Mortgage Credit Risk: Default Probabilities and Loan Portfolios](https://mlsanity.com/paper/2410.02846/) (2024)

## Abstract (arXiv)

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This manuscript develops a class of highly scalable Nearest Neighbor Gaussian Process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive United States Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods.