Collaborative Research: Learning Graphical Models for Nonstationary Time Series

Cornell University, Ithaca NY

Investigators

Abstract

In the biological and social sciences, many central questions require one to understand how interactions within a complex system evolve over time. For example, in neurosciences, monitoring time-varying connections among different brain regions is important for studying the progression of neurodegenerative diseases. As another example, risk management and monitoring in interconnected financial markets often require learning how the linkages among different firms evolve over time. These examples demonstrate the need to develop rigorous and scalable statistical methods that are able to learn the evolution of connectivity from large-scale complex time series data. Such methods can help offer insights into the working of a complex system and guide data-driven policy making. While graphical models (GM) offer a powerful framework for data-driven discovery of network architecture, existing statistical research in this area has focused primarily on modeling time-invariant connections from stationary time series. This project will develop estimation and inference methods for a nonstationary graphical model framework called NonStGM. This framework captures nonstationary dynamics in a multivariate system in the form of a sparse operator in the Fourier domain, whose structure can in turn be estimated from data using regularized regression methods. Key emphasis will be given on two classes of structured nonstationarity which are prevalent in many applications: (a) local stationarity that allows both abrupt changes and smooth evolution of the temporal dynamics, and (b) periodic stationarity. NonStGM structures learned from large-scale time series data will be used to build directed graphs with time-varying vector autoregressive (VAR) models. Algorithms developed in this project will be validated with extensive numerical experiments and real electroencephalogram (EEG) data sets. All products will be made publicly available in the form of open-source software packages. These products are expected to aid clinical researchers, amongst others, in their understanding of connectome abnormalities in the brains of patients suffering from neurological disorders. Research outcomes will be integrated into educational modules of graduate level courses. The project will provide numerous opportunities to train graduate students in a topical research area of large-scale time series modeling and will actively focus on enhancing diversity and inclusion in statistical sciences. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.