The Coefficient Estimation of Tensor Autoregression Based on TR Decomposition

doi:10.1007/s42967-024-00424-8

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (5): 1940-1958.doi: 10.1007/s42967-024-00424-8

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The Coefficient Estimation of Tensor Autoregression Based on TR Decomposition

Yu-Hang Li, Ju-Li Zhang

School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, 201620, China

收稿日期:2023-11-30 修回日期:2024-04-26 接受日期:2024-04-27 出版日期:2024-09-12 发布日期:2024-09-12
通讯作者: Ju-Li Zhang,E-mail:xzhzhangjuli@163.com E-mail:xzhzhangjuli@163.com
基金资助:
The authors are grateful to the handling editor and anonymous referees for useful comments and suggestions which contribute to improving the quality of the manuscript. This work is supported by the crossing research project of Shanghai University of Engineering Science (No. SL-001).

The Coefficient Estimation of Tensor Autoregression Based on TR Decomposition

Yu-Hang Li, Ju-Li Zhang

School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, 201620, China

Received:2023-11-30 Revised:2024-04-26 Accepted:2024-04-27 Online:2024-09-12 Published:2024-09-12
Contact: Ju-Li Zhang,E-mail:xzhzhangjuli@163.com E-mail:xzhzhangjuli@163.com
Supported by:
The authors are grateful to the handling editor and anonymous referees for useful comments and suggestions which contribute to improving the quality of the manuscript. This work is supported by the crossing research project of Shanghai University of Engineering Science (No. SL-001).

摘要/Abstract

摘要： With the advent of tensor-valued time series data, tensor autoregression appears in many fields, in which the coefficient estimation is confronted with the problem of dimensional disaster. Based on the tensor ring (TR) decomposition, an autoregression model with one order for tensor-valued responses is proposed in this paper. A randomized method, TensorSketch, is applied to the TR autoregression model for estimating the coefficient tensor. Convergence and some properties of the proposed methods are given. Finally, some numerical experiment results on synthetic data and real data are given to illustrate the effectiveness of the proposed method.

关键词: Tensor autoregression, Tensor ring (TR) decomposition, TensorSketch, Alternating least squares method, Randomized algorithm

Abstract: With the advent of tensor-valued time series data, tensor autoregression appears in many fields, in which the coefficient estimation is confronted with the problem of dimensional disaster. Based on the tensor ring (TR) decomposition, an autoregression model with one order for tensor-valued responses is proposed in this paper. A randomized method, TensorSketch, is applied to the TR autoregression model for estimating the coefficient tensor. Convergence and some properties of the proposed methods are given. Finally, some numerical experiment results on synthetic data and real data are given to illustrate the effectiveness of the proposed method.

Key words: Tensor autoregression, Tensor ring (TR) decomposition, TensorSketch, Alternating least squares method, Randomized algorithm

Yu-Hang Li, Ju-Li Zhang. The Coefficient Estimation of Tensor Autoregression Based on TR Decomposition[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 1940-1958.

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The Coefficient Estimation of Tensor Autoregression Based on TR Decomposition

The Coefficient Estimation of Tensor Autoregression Based on TR Decomposition

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