The problem of estimating high-dimensional network structures arises naturally in the analyses of many physical, biological and socio-economic systems. Examples include stock price fluctuations in financial markets and gene regulatory networks representing effects of regulators (transcription factors) on regulated genes in Genetics. In many of these applications, the variables have inherent grouping structures, that when incorporated, can result in improved estimation and prediction. We aim to learn the structure of the network over time employing the framework of Granger causal models, under the assumptions of sparsity of its edges and inherent grouping structure among its nodes. I introduce a truncated penalty variant of group lasso to discover the Granger causal interactions among the nodes of the network. Asymptotic results on the consistency of the new estimation procedure are developed. The performance of the proposed methodology is assessed through an extensive set of simulation studies and comparisons with existing techniques. Finally, various extensions of the framework to more complex Granger causal structures are discussed.
Joint work with Sumanta Basu and George Michailidis (University of Michigan)