Multi-Subject Multi-Dimensional Time Series: Tackling Challenges of Heterogeneity and Scale

With widespread technological developments, it has become commonplace to collect high-dimensional time-series data, that is, intensive repeated measurement data on many variables and subjects simultaneously during daily life. This includes sensor-based physiological measurements (e.g., heart rate, skin conductance) and health and movement data (e.g., calorie tracking, Fitbit, GPS) across people, various macro-level indicators recorded over time for different economies, as well as data from many other noisy and complex systems evolving over time across subjects. Although technological advances including machine learning have decreased the burden associated with collecting such high-dimensional time-series data, these developments have also brought a newfound appreciation of the rich heterogeneity inherent to many biological, behavioral and other systems. For example, in neuroscience, extensive between-person heterogeneity is observed in the anatomical organization of brain regions and dynamic network activation profiles. The heterogeneity of firms, countries and other subjects has been well recognized and studied in economics and finance. As such, how best to model processes that exhibit meaningful heterogeneity across subjects is a critical open question in many disciplines, including precision medicine, computational psychiatry and economics, machine learning, and artificial intelligence. This project aims to develop the theoretical foundation, methodological approaches and computational tools needed to model time-dependent systems characterized by unknown heterogeneity. Broader impacts activities will also involve education and training of undergraduate and graduate students. The project advances a unified statistical and machine learning framework for the analysis of complex multivariate time series arising from multiple heterogeneous subjects. It brings together two directions in modern time series methodology: high-dimensional multivariate modeling and joint inference across subjects exhibiting potentially distinct dynamic behavior. A central challenge motivating the project is that heterogeneity may occur not only in the magnitude of model parameters, but also in the underlying structural form of the dynamics themselves, while the degree and nature of similarity across subjects are typically unknown a priori. The work focuses primarily on multi-VAR and multi-FAC frameworks for modeling high-dimensional time series across multiple subjects. Within these settings, the project seeks to establish rigorous theoretical guarantees, including consistency and related asymptotic properties for multi-VAR models, as well as conditions for recovering shared latent structures and dependence patterns in multi-FAC models. The project will further extend these frameworks to a range of applications relevant to empirical research, including: (a) time-varying parameter models, especially in intervention settings; (b) identification of subgroups and cluster-level dynamics when subjects share common dynamic features; and (c) non-Gaussian methods for count-valued and other discrete time series frequently encountered in behavioral research. In addition, the project will develop computational tools, optimization algorithms, and software packages to support the methodological and data-analytic components of the research. 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. NSF Award ID: 2610655 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Vladas Pipiras | Institution: University of North Carolina at Chapel Hill, CHAPEL HILL, NC | Award Amount: $250,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2610655 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2610655.html