CP Factor Model for Dynamic Tensors

时间:2022-04-26         阅读:


主题CP Factor Model for Dynamic Tensors

主讲人罗格斯大学 陈嵘教授

主持人统计学院 常晋源教授



主办单位:数据科学与商业智能联合实验室 统计学院 科研处


Dr. Chen is Distinguished Professor of Statistics, and Chair of Department of Statistics at Rutgers University. His teaching and research interests include analysis of complex time series and dynamic systems, Monte Carlo methods and statistical applications in bioinformatics, business and economics, and engineering. He is an elected Fellow of the American Statistical Association and the Institute of Mathematical Statistics. Dr. Chen served as a co-editor of Journal of Business and Economic Statistics and is currently serving as co-editor ofStatisticaSinica. He is former Treasurer of the Institute of Mathematical Statistics and former program director in the Division of Mathematical Sciences of National Science Foundation. Dr. Chen received both his Ph.D. and M.S. in Statistics from Carnegie Mellon University and his B.S. in mathematics from Peking University in China.

陈嵘教授是罗格斯大学统计学杰出教授和统计系主任。他的教学和研究兴趣包括复杂时间序列和动态系统分析、蒙特卡罗方法以及生物信息学、商业、经济以及工程中的统计应用。他是美国统计协会和国际数理统计学会的当选研究员。陈嵘教授曾担任《Journal of Business and Economic Statistics》的联合主编,目前担任《StatisticaSinica》的联合主编。他是国际数理统计学会的former Treasurer和国家科学基金会数学科学部的前项目主任。陈嵘教授在卡内基梅隆大学获得统计学博士和硕士学位,在北京大学获得数学学士学位。


Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CP decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations.