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

动态张量数据，由随时间变化的多维数组表示，在整个社会中变得越来越重要。它被广泛应用于生物学和医学研究、自然科学、工程学、社会科学、经济学和金融学等领域。本研究旨在发展新的统计理论、方法和算法来分析大型动态张量数据。这项工作还包括分析正在开发的方法的计算效率和效用。研究结果将提供最先进的统计工具，以便有效地从这些数据中提取有用的信息，并在广泛的应用中协助实际决策。该项目将把新方法应用于重要的例子，包括运动行为建模和犯罪数据分析。该项目将通过参与前沿研究，促进学生和年轻研究人员之间的合作。软件和其他工具将向公众开放，在实际应用中促进科学进步和数据驱动的决策过程。本研究的目标是发展分析大型动态张量数据的统计理论、方法和算法，并证明其在有趣应用中的可行性、有效性和实用性。动态张量数据是一个有机会从统计学角度进行系统方法和理论处理的领域，它为研究人员带来了新的挑战和机遇。该项目将开发用于连续张量时间序列数据的自回归和动态因子模型，以及用于二进制、计数和其他非高斯数据的广义动态张量模型；为这些模型提供预测、参数估计和统计推断的新工具；并研究了新方法的理论和经验性质。项目研究结果预计将对其他统计领域产生影响，包括离散张量分析、视频分析、高维张量推理和高维动态系统分析。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.