Semi-parametric Methods for Estimating Time-varying Graph Structure

Stochastic networks are a plausible representation of the relational information among entities in dynamic systems such as living cells or social communities. While there is a rich literature in estimating a static or temporally invariant network from observation data, little has been done towards estimating time-varying networks from time series of entity attributes. In this paper, we present two new machine learning methods for estimating time-varying networks, which both build on a temporally smoothed l1-regularized logistic regression formalism that can be cast as standard convex-optimization problem and solved efficiently using generic solvers scalable to large networks. We report promising results on recovering simulated time-varying networks. For real datasets, we reverse engineer the latent sequence of temporally rewiring political networks between Senators from the US Senate voting records and the latent evolving regulatory networks underlying 588 genes across the life cycle of Drosophila melanogaster from microarray time course. We provide some theoretical guarantees for the proposed methods. ∗This work was done under supervision of my advisor Eric Xing. A part of this work is going to appear in Annals of Applied Statistics (Kolar, Song, Ahmed, Xing. Estimating Timevarying Networks). I am very grateful for multiple discussions I had with Larry Wasserman and John Lafferty.