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Estimating time-varying networks. (English) Zbl 1189.62142

Summary: 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. We present two new machine learning methods for estimating time-varying networks, which both build on a temporally smoothed \(l_{1}\)-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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M99 Inference from stochastic processes
68T05 Learning and adaptive systems in artificial intelligence
05C90 Applications of graph theory
91F10 History, political science
92D10 Genetics and epigenetics
65C60 Computational problems in statistics (MSC2010)

Software:

CVX; glasso; glmnet
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Full Text: DOI arXiv

References:

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