CP Factor Model for Dynamic Tensors

时间:2022-04-26         阅读:

光华讲坛——社会名流与企业家论坛第6098期

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

时间2022年4月29日(周五)上午9:00-10:00

举办地点:腾讯会议:464682153

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

主讲人简介:

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。

内容简介

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.

各种应用中的观测结果经常被表示为多维数组的时间序列,该时间序列被称为张量时间序列,能保留固有的多维结构。本文提出了一种类似于张量CP分解的因子模型方法,用于分析高维动态张量时间序列。由于荷载向量是唯一定义的,但不一定是正交的,因此它与现有的基于Tucker型张量分解的张量因子模型有很大的不同。该模型结构允许一组不相关的一维潜在动态因子过程存在,这使得研究时间序列的潜在动态更加方便。利用Tucker型张量因子模型和一般张量CP分解方法中常用的高阶正交迭代方法的特殊结构和思想,本文提出了一种新的高阶投影估计方法。通过理论研究,本文提供了该方法的统计误差范围,并证明了利用这种特殊模型结构的显著优势。通过仿真研究,本文进一步证明了估计量的有限样本性质。实际数据的应用也能说明该模型及其解释。