  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.
