张量回归模型及其应用研究综述
A Brief Survey on Tensor Regression Model and Its Application
摘要: 21世纪以来，张量引起了数据科学和统计学领域的极大兴趣，张量技术被广泛应用于数据挖掘、机器学习和统计学等领域，其中，张量回归模型是一类很重要的工具。本文研究了近十年张量回归模型理论及应用的发展和现状，对张量回归模型进行了简单梳理，主要介绍了张量线性回归模型的理论和应用。为了方便读者理解，本文还介绍了张量、张量分解等基本概念。
Abstract: Since the 21st century, tensor has aroused great interest in the field of data science and statistics. Tensor technology has been widely used in data mining, machine learning and statistics, among which tensor regression model is a very important tool. This paper studies the development and current situation of the theory and application of tensor regression model in the past ten years. It simply sorts out the tensor regression model, and mainly introduces the theory and application of tensor linear regression model. In order to facilitate readers to understand, this paper also introduces the basic concepts of tensor and tensor decomposition.
文章引用：罗来辉. 张量回归模型及其应用研究综述[J]. 统计学与应用, 2020, 9(5): 855-861. https://doi.org/10.12677/SA.2020.95089

参考文献

[1] Hitchcock, F.L. (1927) The Expression of a Tensor or a Polyadic as a Sum of Products. Journal of Mathematical Physics, 6, 164-189.
[Google Scholar] [CrossRef] 
[2] Ji, Y., Wang, Q., Li, X. and Liu, J. (2019) A Survey on Tensor Techniques and Applications in Machine Learning. IEEE Access, 7, 162950-162990.
[Google Scholar] [CrossRef] 
[3] Bi, X., Tang, X., Yuan, Y., Zhang, Y. and Qu, A. (2020) Tensors in Statistics. Annual Review of Statistics and Its Application, 8.
[Google Scholar] [CrossRef] 
[4] Kolda, T.G. and Bader, B.W. (2009) Tensor Decompositions and Applications. SIAM Review, 51, 455-500.
[Google Scholar] [CrossRef] 
[5] Guo, W., Kotsia, I. and Patras, I. (2012) Tensor Learning for Regression. IEEE Transactions on Image Processing, 21, 816-827.
[Google Scholar] [CrossRef] 
[6] Zhou, H., Li, L. and Zhu, H. (2013) Tensor Regression with Applications in Neuroimaging Data Analysis. Journal of the American Statistical Association, 108, 229-239.
[Google Scholar] [CrossRef] [PubMed]
[7] 石美丽, 夏志明. 张量线性回归模型中的参数估计与假设检验问题[J]. 陕西师范大学学报(自然科学版), 2020, 48(2): 110-116.
[8] Li, X., Xu, D., Zhou, H. and Li, L. (2018) Tucker Tensor Regression and Neuroimaging Analysis. Statistics in Biosciences, 10, 520-545.
[Google Scholar] [CrossRef] [PubMed]
[9] Guhaniyogi, R., Qamar, S. and Dunson, D.B. (2017) Bayesian Tensor Regression. Journal of Machine Learning Research, 18, 1-31.
[10] Billio, M., Casarin, R., Kaufmann, S. and Iacopini, M. (2018) Bayesian Dynamic Tensor Regression. University Ca’ Foscari of Venice, Dept. of Economics Research Paper Series No. 13/WP/2018.
https://ssrn.com/abstract=3192340
[Google Scholar] [CrossRef] 
[11] Zhao, Q., Caiafa, C.F., Mandic, D.P., Chao, Z.C., Nagasaka, Y., Fujii, N., Zhang, L. and Cichocki, A. (2013) Higher Order Partial Least Squares (HOPLS): A Generalized Multilinear Regression Method. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35, 1660-1673.
[Google Scholar] [CrossRef] 
[12] Miranda, M.F., Zhu, H. and Ibrahim, J.G. (2018) Tprm: Tensor Partition Regression Models with Applications in Imaging Biomarker Detection. Annals of Applied Statistics, 12, 1422-1450.
[Google Scholar] [CrossRef] 
[13] Sun, W.W. and Li, L. (2017) STORE: Sparse Tensor Response Regression and Neuroimaging Analysis. Journal of Machine Learning Research, 18, 4908-4944.
[14] Li, L. and Zhang, X. (2017) Parsimonious Tensor Response Regression. Journal of the American Statistical Association, 112, 1131-1146.
[Google Scholar] [CrossRef] 
[15] Hoff, P.D. (2015) Multilinear Tensor Regression for Longitudinal Relational Data. The Annals of Applied Statistics, 9, 1169-1193.
[Google Scholar] [CrossRef] 
[16] Lock, E.F. (2018) Tensor-on-Tensor Regression. Journal of Computational and Graphical Statistics, 27, 638-647.
[Google Scholar] [CrossRef] [PubMed]
[17] Zhao, Q., Zhou, G., Zhang, L. and Cichocki, A. (2014) Tensor-Variate Gaussian Processes Regression and Its Application to Video Surveillance. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’14), Florence, 4-9 May 2014, 1265-1269.
[Google Scholar] [CrossRef] 
[18] Kossaifi, J., et al. (2020) Tensor Regression Networks. Journal of Machine Learning Research, 21, 1-21.
[19] Hung, H. and Wang, C.-C. (2013) Matrix Variate Logistic Regression Model with Application to EEG Data. Biostatistics, 14, 189-202.
[Google Scholar] [CrossRef] [PubMed]
[20] Hou, M. and Chaib-draa, B. (2015) Hierarchical Tucker Tensor Regression: Application to Brain Imaging Data Analysis. IEEE International Conference on Image Processing (ICIP’15), Quebec City, 27-30 September 2015, 1344-1348.
[Google Scholar] [CrossRef] 
[21] Hou, M. (2017) Tensor-Based Regression Models and Applications. PhD Dissertation, Laval Univ., Quebec City.
[22] Gao, Q., Cheng, J., Xie, D., Zhang, P., Xia, W. and Wang, Q. (2019) Tensor Linear Regression and Its Application to Color Face Recognition. 2019 IEEE/CVF International Conference on Computer Vision Workshop (ICCVW), Seoul, 523-531.
[Google Scholar] [CrossRef] 
[23] Romera-Paredes, B., Aung, H., Bianchi-Berthouze, N. and Pontil, M. (2013) Multilinear Multitask Learning. International Conference on Machine Learning (ICML’13), Atlanta, 16-21 June 2013, 1444-1452.

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