# Hierarchical sparse Cholesky decomposition with applications to high-dimensional spatio-temporal filtering

arXiv: https://arxiv.org/abs/2006.16901 · HTML: https://mlsanity.com/paper/2006.16901/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2020.

## Built on by (most cited first, 4 of 4)

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- [Learning non-Gaussian spatial distributions via Bayesian transport maps with parametric shrinkage](https://mlsanity.com/paper/2409.19208/) (2024)
- [Spectral structure learning for clinical time series](https://mlsanity.com/paper/2502.11680/) (2025)

## Abstract (arXiv)

Spatial statistics often involves Cholesky decomposition of covariance matrices. To ensure scalability to high dimensions, several recent approximations have assumed a sparse Cholesky factor of the precision matrix. We propose a hierarchical Vecchia approximation, whose conditional-independence assumptions imply sparsity in the Cholesky factors of both the precision and the covariance matrix. This remarkable property is crucial for applications to high-dimensional spatio-temporal filtering. We present a fast and simple algorithm to compute our hierarchical Vecchia approximation, and we provide extensions to non-linear data assimilation with non-Gaussian data based on the Laplace approximation. In several numerical comparisons, including a filtering analysis of satellite data, our methods strongly outperformed alternative approaches.