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The Annals of Applied Statistics 2010 Vol 4 No 1 94 123 DOI 10 1214 09 AOAS308 Institute of Mathematical Statistics 2010 ESTIMATING TIME VARYING NETWORKS B Y M LADEN KOLAR L E S ONG1 A MR A HMED AND E RIC P X ING2 Carnegie Mellon University 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 toward 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 a 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 data sets 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 the microarray time course 1 Introduction In many problems arising from natural social and information sciences it is often necessary to analyze a large quantity of random variables interconnected by a complex dependency network such as the expressions of genes in a genome or the activities of individuals in a community Real time analysis of such networks is important for understanding and predicting the organizational processes modeling information diffusion detecting vulnerability and assessing the potential impact of interventions in various natural and built systems It is not unusual for network data to be large dynamic heterogeneous noisy incomplete or even unobservable Each of these characteristics adds a degree of

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