Scalable Spatio-Temporal Smoothing via Hierarchical Sparse Cholesky Decomposition
Methodology
2022-07-20 v1 Computation
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.
Cite
@article{arxiv.2207.09384,
title = {Scalable Spatio-Temporal Smoothing via Hierarchical Sparse Cholesky Decomposition},
author = {Marcin Jurek and Matthias Katzfuss},
journal= {arXiv preprint arXiv:2207.09384},
year = {2022}
}