# Graphical Gaussian Process Models for Highly Multivariate Spatial Data

arXiv: https://arxiv.org/abs/2009.04837 · HTML: https://mlsanity.com/paper/2009.04837/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2020.

## Built on by (most cited first, 6 of 6)

- [Neural networks for geospatial data](https://mlsanity.com/paper/2304.09157/) (2023)
- [Modeling massive highly-multivariate nonstationary spatial data with the basis graphical lasso](https://mlsanity.com/paper/2101.02404/) (2021)
- [Graphical Dirichlet Process for Clustering Non-Exchangeable Grouped Data](https://mlsanity.com/paper/2302.09111/) (2023)
- [Bayesian Spatial Predictive Synthesis](https://mlsanity.com/paper/2203.05197/) (2022)
- [Dynamic Bayesian Learning for Spatiotemporal Mechanistic Models](https://mlsanity.com/paper/2208.06528/) (2022)
- [Deep autoregressive modeling for land use land cover](https://mlsanity.com/paper/2401.01395/) (2024)

## Abstract (arXiv)

For multivariate spatial Gaussian process (GP) models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence among the variables. This is undesirable, especially for highly multivariate settings, where popular cross-covariance functions such as the multivariate Mat'ern suffer from a "curse of dimensionality" as the number of parameters and floating point operations scale up in quadratic and cubic order, respectively, in the number of variables. We propose a class of multivariate "Graphical Gaussian Processes" using a general construction called "stitching" that crafts cross-covariance functions from graphs and ensures process-level conditional independence among variables. For the Mat'ern family of functions, stitching yields a multivariate GP whose univariate components are Mat'ern GPs, and conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive computational gains and parameter dimension reduction. We demonstrate the utility of the graphical Mat'ern GP to jointly model highly multivariate spatial data using simulation examples and an application to air-pollution modelling.