Parallelized integrated nested Laplace approximations for fast Bayesian inference

TL;DR

This paper introduces parallelization strategies for INLA, significantly accelerating Bayesian inference on large-scale models by leveraging multi-core architectures, and is integrated into the R-INLA package.

Contribution

The paper presents novel parallelization techniques for INLA, enabling faster Bayesian inference on high-dimensional models using multi-core systems.

Findings

Achieved speedups of 10x or more on large models

Successfully integrated parallel INLA into R-INLA package

Demonstrated improved performance on real-world applications

Abstract

There is a growing demand for performing larger-scale Bayesian inference tasks, arising from greater data availability and higher-dimensional model parameter spaces. In this work we present parallelization strategies for the methodology of integrated nested Laplace approximations (INLA), a popular framework for performing approximate Bayesian inference on the class of Latent Gaussian models. Our approach makes use of nested OpenMP parallelism, a parallel line search procedure using robust regression in INLA's optimization phase and the state-of-the-art sparse linear solver PARDISO. We leverage mutually independent function evaluations in the algorithm as well as advanced sparse linear algebra techniques. This way we can flexibly utilize the power of today's multi-core architectures. We demonstrate the performance of our new parallelization scheme on a number of different real-world applications. The introduction of parallelism leads to speedups of a factor 10 and more for all larger models. Our work is already integrated in the current version of the open-source R-INLA package, making its improved performance conveniently available to all users.