FRG: Collaborative Research: Dynamic Tensors: Statistical Methods, Theory, and Applications

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Dynamic tensor data, represented by multidimensional arrays that vary in time, has become increasingly important to society at large. It is collected in a wide range of applications, from biology and medical research, natural sciences, and engineering to social sciences, economics, and finance. This research aims to develop novel statistical theory, methods, and algorithms for analyzing large dynamic tensor data. The work also includes analysis of the computational efficiency and utility of the methods under development. The results will provide state-of-art statistical tools for effectively extracting useful information from such data and aiding practical decision making in a wide spectrum of applications. The project will apply the new methods to important examples, including motion behavior modeling and crime data analysis. The project will foster collaborations among students and young researchers through involvement in cutting-edge research. Software and other tools will be made publicly available, enhancing scientific progress and data driven decision-making processes in practical applications.The objectives of the research are to develop statistical theory, methods, and algorithms for analyzing large dynamic tensor data and to demonstrate their feasibility, effectiveness, and utility in interesting applications. Dynamic tensor data, an area with opportunities for systematic methodological and theoretical treatment from a statistical point of view, is creating new challenges and opportunities for researchers. The project will develop autoregressive and dynamic factor models for continuous tensor time series data, and generalized dynamic tensor models for binary, count, and other non-Gaussian data; produce new tools for forecasting, parameter estimation, and statistical inferences for such models; and study the theoretical and empirical properties of the new methods. The project findings are expected to have impact in other fields of statistics, including discrete tensor analysis, video analysis, inference of high-dimensional tensors, and analysis of high dimensional dynamic systems.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.