On Joint Estimation of Gaussian Graphical Models for Spatial and Temporal Data

TL;DR

This paper introduces a Bayesian joint estimation method for Gaussian Graphical Models that effectively captures spatial and temporal dependencies, improving network estimation accuracy in complex structured data.

Contribution

It develops a Bayesian approach with MRF models for joint GGM estimation across multiple data groups, including spatial and temporal structures, with an efficient parallel algorithm.

Findings

Outperforms methods ignoring spatial and temporal dependencies in shared-structure scenarios

Achieves comparable performance when no shared structure exists

Demonstrates effectiveness on human brain gene expression data

Abstract

In this paper, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model converges to one. When there are multiple groups of data available, instead of estimating the networks independently for each group, joint estimation of the networks may utilize the shared information among groups and lead to improved estimation for each individual network. Our method is extended to jointly estimate GGMs in multiple groups of data with complex structures, including spatial data, temporal data and data with both spatial and temporal structures. Markov random field (MRF) models are used to efficiently incorporate the complex data structures. We develop and implement an efficient algorithm for statistical inference that enables parallel computing. Simulation studies suggest that our approach achieves better accuracy in network estimation compared with methods not incorporating spatial and temporal dependencies when there are shared structures among the networks, and that it performs comparably well otherwise. Finally, we illustrate our method using the human brain gene expression microarray dataset, where the expression levels of genes are measured in different brain regions across multiple time periods.