Integrated Nested Laplace Approximations for Large-Scale Spatial-Temporal Bayesian Modeling

TL;DR

This paper introduces INLA-DIST, a scalable distributed memory variant of the INLA-SPDE approach, enabling efficient Bayesian spatial-temporal modeling with millions of parameters using CPU and GPU solvers.

Contribution

It develops a high-performance distributed INLA-SPDE method with novel GPU acceleration for large-scale spatial-temporal Bayesian inference.

Findings

Capable of handling models with millions of latent parameters

Achieves high accuracy and performance on climate datasets

Provides scalable CPU and GPU solver options

Abstract

Bayesian inference tasks continue to pose a computational challenge. This especially holds for spatial-temporal modeling where high-dimensional latent parameter spaces are ubiquitous. The methodology of integrated nested Laplace approximations (INLA) provides a framework for performing Bayesian inference applicable to a large subclass of additive Bayesian hierarchical models. In combination with the stochastic partial differential equations (SPDE) approach it gives rise to an efficient method for spatial-temporal modeling. In this work we build on the INLA-SPDE approach, by putting forward a performant distributed memory variant, INLA-DIST, for large-scale applications. To perform the arising computational kernel operations, consisting of Cholesky factorizations, solving linear systems, and selected matrix inversions, we present two numerical solver options, a sparse CPU-based library and a novel blocked GPU-accelerated approach which we propose. We leverage the recurring nonzero block structure in the arising precision (inverse covariance) matrices, which allows us to employ dense subroutines within a sparse setting. Both versions of INLA-DIST are highly scalable, capable of performing inference on models with millions of latent parameters. We demonstrate their accuracy and performance on synthetic as well as real-world climate dataset applications.