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Journal of Data Science


An Effective Tensor Regression with Latent Sparse Regularization
Volume 20, Issue 2 (2022), pp. 228–252
Pub. online: 9 May 2022      Type: Statistical Data Science      Open accessOpen Access
Received
31 December 2021
Accepted
10 April 2022
Published
9 May 2022

Abstract

As data acquisition technologies advance, longitudinal analysis is facing challenges of exploring complex feature patterns from high-dimensional data and modeling potential temporally lagged effects of features on a response. We propose a tensor-based model to analyze multidimensional data. It simultaneously discovers patterns in features and reveals whether features observed at past time points have impact on current outcomes. The model coefficient, a k-mode tensor, is decomposed into a summation of k tensors of the same dimension. We introduce a so-called latent F-1 norm that can be applied to the coefficient tensor to performed structured selection of features. Specifically, features will be selected along each mode of the tensor. The proposed model takes into account within-subject correlations by employing a tensor-based quadratic inference function. An asymptotic analysis shows that our model can identify true support when the sample size approaches to infinity. To solve the corresponding optimization problem, we develop a linearized block coordinate descent algorithm and prove its convergence for a fixed sample size. Computational results on synthetic datasets and real-life fMRI and EEG datasets demonstrate the superior performance of the proposed approach over existing techniques.

Supplementary material

 Supplementary Material
The code and data can be found: https://doi.org/10.6084/m9.figshare.19166474.v1. For data generation, we provide DataGenerator.py to generate synthetic data including training and test sets; For model fitting, we provide tensorQIF_model_Tensorflow_v2.py to run models and ReportGenerator.py to report on performance. For experiments comparisons, we have Granger_model.py, GEE_model.m, Kruskal_model.m.

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Copyright
2022 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.
Open access article under the CC BY license.

Keywords
longitudinal data quadratic inference function tensors

Funding
This work was partially supported by the National Science Foundation with a grant IIS-1718738 at the U.S., and by the National Institutes of Health with grants R01DA051922, K02DA043063, and R01MH119678 to J Bi.

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