Block Vecchia Approximation for Scalable and Efficient Gaussian Process Computations

TL;DR

This paper introduces block Vecchia, a GPU-accelerated approximation method for Gaussian Processes that improves scalability and efficiency in large geospatial datasets by evaluating multivariate conditional distributions.

Contribution

The study proposes block Vecchia, a novel approximation technique using multivariate conditionals with K-means clustering, and develops a GPU framework to enhance computational efficiency.

Findings

Significantly reduces likelihood evaluations compared to classical Vecchia.

Achieves high accuracy with large block counts and random ordering.

Successfully applied to large-scale real datasets with over a million points.

Abstract

Gaussian Processes (GPs) are vital for modeling and predicting irregularly-spaced, large geospatial datasets. However, their computations often pose significant challenges in large-scale applications. One popular method to approximate GPs is the Vecchia approximation, which approximates the full likelihood via a series of conditional probabilities. The classical Vecchia approximation uses univariate conditional distributions, which leads to redundant evaluations and memory burdens. To address this challenge, our study introduces block Vecchia, which evaluates each multivariate conditional distribution of a block of observations, with blocks formed using the K-means algorithm. The proposed GPU framework for the block Vecchia uses varying batched linear algebra operations to compute multivariate conditional distributions concurrently, notably diminishing the frequent likelihood evaluations. Diving into the factor affecting the accuracy of the block Vecchia, the neighbor selection criterion is investigated, where we found that the random ordering markedly enhances the approximated quality as the block count becomes large. To verify the scalability and efficiency of the algorithm, we conduct a series of numerical studies and simulations, demonstrating their practical utility and effectiveness compared to the exact GP. Moreover, we tackle large-scale real datasets using the block Vecchia method, i.e., high-resolution 3D profile wind speed with a million points.