Scalable Spatio-Temporal Smoothing via Hierarchical Sparse Cholesky Decomposition

TL;DR

This paper introduces a scalable method for spatio-temporal smoothing that leverages hierarchical Vecchia approximation to efficiently handle large covariance matrices, enabling applications in high-dimensional Bayesian state-space models.

Contribution

It presents a novel scalable FFBS algorithm for large-scale spatio-temporal data using hierarchical Vecchia approximation, improving computational efficiency over existing low-rank methods.

Findings

Outperforms low-rank FFBS in simulations

Effective on real-world large-scale data

Reduces computational burden significantly

Abstract

We propose an approximation to the forward-filter-backward-sampler (FFBS) algorithm for large-scale spatio-temporal smoothing. FFBS is commonly used in Bayesian statistics when working with linear Gaussian state-space models, but it requires inverting covariance matrices which have the size of the latent state vector. The computational burden associated with this operation effectively prohibits its applications in high-dimensional settings. We propose a scalable spatio-temporal FFBS approach based on the hierarchical Vecchia approximation of Gaussian processes, which has been previously successfully used in spatial statistics. On simulated and real data, our approach outperformed a low-rank FFBS approximation.