Learning Dynamics of Complex Systems from High-dimensional Data (Sumanta Basu - University of California, Berkeley)

Abstract: The problem of learning interrelationships among the components of large, complex systems from high-dimensional datasets is common in many areas of modern economic and biological sciences. Examples include macroeconomic policy making, financial risk management, gene regulatory network reconstruction and elucidating functional roles of epigenetic regulators driving cellular mechanisms. In addition to their inherent computational challenges, principled statistical analyses of these big data problems often face unique challenges emerging from temporal and cross-sectional dependence in the data and complex dynamics (heterogeneity, nonlinear and high-order interactions) among the system components. In this talk, I will present Network Granger causality - a unified framework for structure learning and forecasting of large dynamic systems using multivariate time series and panel data. The proposed framework relies on regularized estimation of high-dimensional vector autoregressive models (VAR), is flexible enough to incorporate grouping and latent structures, allows parallel implementation for large scale data sets and enjoys strong theoretical guarantees under high-dimensional scaling. I will demonstrate the advantage of the proposed methodology on a motivating application from financial econometrics - system-wide risk monitoring of U.S. financial sector before, during and after the crisis of 2007-2009. I will conclude with some of my ongoing works on learning nonlinear and potentially high-order interactions in high-dimensional, heterogeneous settings.