Time Varying Networks: Reverse Engineering and Analyzing Rewiring Social and Genetic Interactions

A plausible representation of the relational information among entities in dynamic systems such as a social community or a living cell is a stochastic network that is topologically rewiring and semantically evolving over time. While there is a rich literature in modeling static or temporally invariant networks, until recently, little has been done toward modeling the dynamic processes underlying rewiring networks, and on recovering such networks when they are not observable. In this talk, I will present a new formalism for modeling network evolution over time based on temporal exponential random graphs, and several new algorithms for estimating the structure of time evolving probabilistic graphical models underlying nonstationary time-series of nodal attributes. I will show some promising results on recovering the latent sequence of evolving social networks in the US Senate based it voting history, and the gene networks over more than 4000 genes during the life cycle of Drosophila melanogaster from microarray time course, at a time resolution only limited by sample frequency. I will also sketch some theoretical results on the asymptotic sparsistency of the proposed methods, which differ significantly from traditional sparsistency analysis of static structure estimation based on iid samples because of the temporal relatedness of samples. If time permits, I will also report a hierarchical Bayesian model for estimating and visualizing the trajectories of latent mixed-membership nodal states in the recovered evolving networks.