Implementation and Analysis of GPU Algorithms for Vecchia Approximation

TL;DR

This paper introduces a new GPU implementation of Vecchia Approximation for Gaussian Processes, significantly improving computational speed and accuracy for large spatial datasets, including over a million points.

Contribution

A novel GPU-based method for Vecchia Approximation is developed, optimized, and integrated into the GpGpU R package, outperforming existing software in speed and accuracy.

Findings

New GPU method outperforms existing approaches

Achieves faster runtimes on large datasets

Provides better predictive accuracy

Abstract

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 $n>10^6$ points collected from an earth-observing satellite. Our results show that GpGpU achieves faster runtimes and better predictive accuracy.