Spatio-Temporal Graphical Model Selection

TL;DR

This paper introduces a method for estimating the topology of spatio-temporal interactions in networks, using an $$-penalized likelihood approach, demonstrated on infectious spread simulations.

Contribution

It proposes a novel structure learning method for spatio-temporal graphical models, specifically addressing the topology estimation in discrete state, discrete time settings.

Findings

Topology estimates outperform standard spatial Markov random field methods

Method effectively recovers network interactions in simulated infectious spread

Approach applicable to models like SIR for interaction events

Abstract

We consider the problem of estimating the topology of spatial interactions in a discrete state, discrete time spatio-temporal graphical model where the interactions affect the temporal evolution of each agent in a network. Among other models, the susceptible, infected, recovered ($SIR$) model for interaction events fall into this framework. We pose the problem as a structure learning problem and solve it using an $\ell_1$-penalized likelihood convex program. We evaluate the solution on a simulated spread of infectious over a complex network. Our topology estimates outperform those of a standard spatial Markov random field graphical model selection using $\ell_1$-regularized logistic regression.