# Implementation and Analysis of GPU Algorithms for Vecchia Approximation

arXiv: https://arxiv.org/abs/2407.02740 · HTML: https://mlsanity.com/paper/2407.02740/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 3 Jul 2024.

## Builds on (most cited first, 14 of 14)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [A Framework for Interdomain and Multioutput Gaussian Processes](https://mlsanity.com/paper/2003.01115/) (2020)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Sparse Cholesky factorization by Kullback-Leibler minimization](https://mlsanity.com/paper/2004.14455/) (2020)
- [Permutation and Grouping Methods for Sharpening Gaussian Process Approximations](https://mlsanity.com/paper/1609.05372/) (2016)
- [Gaussian variational approximation with sparse precision matrices](https://mlsanity.com/paper/1605.05622/) (2016)
- [The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still running](https://mlsanity.com/paper/2111.01084/) (2021)
- [Gaussian Process Learning via Fisher Scoring of Vecchia's Approximation](https://mlsanity.com/paper/1905.08374/) (2019)
- [ExaGeoStat: A High Performance Unified Software for Geostatistics on Manycore Systems](https://mlsanity.com/paper/1708.02835/) (2017)
- [Massively parallel approximate Gaussian process regression](https://mlsanity.com/paper/1310.5182/) (2013)
- [Gaussian Process Models with Parallelization and GPU acceleration](https://mlsanity.com/paper/1410.4984/) (2014)
- [GPU-Accelerated Vecchia Approximations of Gaussian Processes for Geospatial Data using Batched Matrix Computations](https://mlsanity.com/paper/2403.07412/) (2024)

## Built on by (most cited first, 1 of 1)

- [GraphGP: Scalable Gaussian Processes with Vecchia's Approximation](https://mlsanity.com/paper/2606.11402/) (2026)

## Abstract (arXiv)

Gaussian Processes have become an indispensable part of the spatial statistician's toolbox but are unsuitable for analyzing large dataset because of the significant time and memory needed to fit the associated model exactly. Vecchia Approximation is widely used to reduce the computational complexity and can be calculated with embarrassingly parallel algorithms. While multi-core software has been developed for Vecchia Approximation, such as the GpGp R package, software designed to run on graphics processing units (GPU) is lacking, despite the tremendous success GPUs have had in statistics and machine learning. We compare three different ways to implement Vecchia Approximation on a GPU: two of which are similar to methods used for other Gaussian Process approximations and one that is new. The impact of memory type on performance is investigated and the final method is optimized accordingly. We show that our new method outperforms the other two and then present it in the GpGpU R package. We compare GpGpU to existing multi-core and GPU-accelerated software by fitting Gaussian Process models on various datasets, including a large spatial-temporal dataset of n>106 points collected from an earth-observing satellite. Our results show that GpGpU achieves faster runtimes and better predictive accuracy.