TESLA is software for estimating time-varying network from time-series of nodal attributes. TELSA stems from the acronym TESLLOR, which stands for TEmporally Smoothed 11-regularized Logistic Regression. It represents a novel extension of the well-known lasso-style sparse structure recovery technique. Building on the highly scalable iterative l1-regularized logistic regression algorithm for estimating single sparse networks, we developed a new regression regularization scheme that connects multiple time-specific network inference functions via a first-order edge smoothness function that encourages edge retention between time-adjacent networks. An important property of TESLA is that it fully integrates all available samples of the entire time series in a single inference procedure that recovers the rewiring patterns between nodes over a time series of arbitrary resolution — from a network for every single time point, to one network for every K time points where K is very small — and makes it possible to uncover interconnections that exist for a short moment in time.

TESLA can be cast as a convex optimization problem for which a globally optimal solution exists and can be efficiently computed for networks with thousands of nodes. Moreover TESLA is a direct formalism that uses the smooth-evolution property as an explicit penalty in the loss function that can be traded-off with data-fitness. Moreover, TESLA does not require that the network be always smoothly evolving and thus can accommodate sharp structural changes in the network topology. Example of sharp structural changes include: sudden rewiring of a gene network in response to a stimulus, a surge of activity in a company’s email network due to economic disaster or bankruptcy, or an influx of links on the blog sphere to propagate an important piece of news.

We successfully used TESLA to reverse engineer the latent sequence of temporally rewiring political voting alliance, shifts in the social network of the machine learning academic community, and the evolving gene networks over more than 4000 genes during the life cycle of Drosophila Melanogaster from a microarray time course at a resolution limited only by sample frequency. See Results page for a visual display.