Graphical model inference with external network data

TL;DR

This paper develops methods to incorporate external network data into Gaussian graphical models, enhancing interpretation and inference in applications like COVID-19 spread and stock market analysis.

Contribution

It introduces spike-and-slab and graphical LASSO frameworks for integrating network data into graphical models, improving detection and explanation of dependence structures.

Findings

Connected counties on Facebook show similar COVID-19 evolution

Stock return dependence relates more to economic indicators than policy

Data integration leads to sparser, more interpretable models

Abstract

We consider two applications where we study how dependence structure between many variables is linked to external network data. We first study the interplay between social media connectedness and the co-evolution of the COVID-19 pandemic across USA counties. We next study study how the dependence between stock market returns across firms relates to similarities in economic and policy indicators from text regulatory filings. Both applications are modelled via Gaussian graphical models where one has external network data. We develop spike-and-slab and graphical LASSO frameworks to integrate the network data, both facilitating the interpretation of the graphical model and improving inference. The goal is to detect when the network data relates to the graphical model and, if so, explain how. We found that counties strongly connected on Facebook are more likely to have similar COVID-19 evolution (positive partial correlations), accounting for various factors driving the mean. We also found that the association in stock market returns depends in a stronger fashion on economic than on policy indicators. The examples show that data integration can improve interpretation, statistical accuracy, and out-of-sample prediction, in some instances using significantly sparser graphical models.