Time：2022/06/28 09:00-10:00

Form：Tencent Meeting（ID：504 425 161）

Topic：An Efficient Tensor Regression for High-dimensional Data

Abstract:

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater than four or five. However, for the simplest tensor autoregression in handling time series data, its coefficient tensor already has the order of six. This paper revises a newly proposed tensor train (TT) decomposition and then applies it to tensor regression such that a nice statistical interpretation can be obtained. The new tensor regression can well match the data with hierarchical structures, and it even can lead to a better interpretation for the data with factorial structures, which are supposed to be better fitted by models with Tucker decomposition. More importantly, the new tensor regression can be easily applied to the case with higher order tensors since TT decomposition can compress the coefficient tensors much more efficiently. The methodology is also extended to tensor autoregression for time series data, and nonasymptotic properties are derived for the ordinary least squares estimations of both tensor regression and autoregression. A new algorithm is introduced to search for estimators, and its theoretical justification is also discussed. Theoretical and computational properties of the proposed methodology are verified by simulation studies, and the advantages over existing methods are illustrated by two real examples.

Resume:

Guodong Li joined the Department of Statistics & Actuarial Science, University of Hong Kong, in 2009 as an Assistant Professor, and currently is a Professor. Prior to this, I had worked at the Division of Mathematical Sciences, Nanyang Technological University, Singapore, as an Assistant Professor since I received my PhD degree in statistics from the University of Hong Kong in 2007. I got my Bachelor and Master degrees in Statistics from Peking University.