# Modeling massive highly-multivariate nonstationary spatial data with the basis graphical lasso

arXiv: https://arxiv.org/abs/2101.02404 · HTML: https://mlsanity.com/paper/2101.02404/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 72 references that are in the map.
- First posted on arXiv 7 Jan 2021.

## Builds on (most cited first, 13 of 13)

- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [Scalable Exact Inference in Multi-Output Gaussian Processes](https://mlsanity.com/paper/1911.06287/) (2019)
- [Cross-Covariance Functions for Multivariate Geostatistics](https://mlsanity.com/paper/1507.08017/) (2015)
- [Nonstationary Multivariate Gaussian Processes for Electronic Health Records](https://mlsanity.com/paper/1910.05851/) (2019)
- [Graphical Gaussian Process Models for Highly Multivariate Spatial Data](https://mlsanity.com/paper/2009.04837/) (2020)
- [Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes](https://mlsanity.com/paper/1910.03134/) (2019)
- [Modeling Nonstationary and Asymmetric Multivariate Spatial Covariances via Deformations](https://mlsanity.com/paper/2004.08724/) (2020)
- [Spatial Factor Modeling: A Bayesian Matrix-Normal Approach for Misaligned Data](https://mlsanity.com/paper/2006.00595/) (2020)
- [Multivariate spatio-temporal models for high-dimensional areal data with application to Longitudinal Employer-Household Dynamics](https://mlsanity.com/paper/1503.00982/) (2015)
- [Semiparametric Estimation of Cross-covariance Functions for Multivariate Random Fields](https://mlsanity.com/paper/1911.02258/) (2019)
- [High-dimensional Multivariate Geostatistics: A Bayesian Matrix-Normal Approach](https://mlsanity.com/paper/2003.10051/) (2020)
- [Multivariate Spatial Covariance Models: A Conditional Approach](https://mlsanity.com/paper/1504.01865/) (2015)
- [Nonparametric Spectral Methods for Multivariate Spatial and Spatial-Temporal Data](https://mlsanity.com/paper/1811.01280/) (2018)

## Built on by (most cited first, 2 of 2)

- [Adaptive LASSO estimation for functional hidden dynamic geostatistical model](https://mlsanity.com/paper/2208.05528/) (2022)
- [Dynamic Bayesian Learning for Spatiotemporal Mechanistic Models](https://mlsanity.com/paper/2208.06528/) (2022)

## Abstract (arXiv)

We propose a new modeling framework for highly-multivariate spatial processes that synthesizes ideas from recent multiscale and spectral approaches with graphical models. The basis graphical lasso writes a univariate Gaussian process as a linear combination of basis functions weighted with entries of a Gaussian graphical vector whose graph is estimated from optimizing an ℓ1 penalized likelihood. This paper extends the setting to a multivariate Gaussian process where the basis functions are weighted with Gaussian graphical vectors. We motivate a model where the basis functions represent different levels of resolution and the graphical vectors for each level are assumed to be independent. Using an orthogonal basis grants linear complexity and memory usage in the number of spatial locations, the number of basis functions, and the number of realizations. An additional fusion penalty encourages a parsimonious conditional independence structure in the multilevel graphical model. We illustrate our method on a large climate ensemble from the National Center for Atmospheric Research's Community Atmosphere Model that involves 40 spatial processes.