Abstract

Analyzing clinical diagnosis along with high-dimensional imaging data,

while accounting for the piecewise constant nature of the imaging, presents challenges to existing statistical approaches. In this paper, we propose a generalized

tensor regression framework with Internal Variation (IV) regularization to address these challenges. The inclusion of IV regularization allows for the explicit

utilization of the rich spatial structure, particularly the piecewise constant nature

of high-order imaging data, albeit with a more complex algorithm and demanding theoretical investigation. We develop an efficient IV regularized optimization

procedure for estimating unknown scalar and tensor coefficients. We investigate

the theoretical properties of scalar and tensor coefficient estimates, especially

the error bounds of regularized tensor coefficient estimates. Extensive numerical

studies assess the finite sample performance of our method, demonstrating its

superiority over existing approaches. Finally, we apply the proposed method to

a chronic sinusitis computed tomography (CT) imaging dataset and identify the

most activated subregion across the maxillary sinus cavity associated with the

diagnosis.

All authors contributed equally to this paper, and their names are listed in alpha-

Information

Preprint No.SS-2024-0281
Manuscript IDSS-2024-0281
Complete AuthorsYang Bai, Ting Li, Yang Sui
Corresponding AuthorsYang Bai
Emailsstatbyang@mail.shufe.edu.cn

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Acknowledgments

The authors thank the reviewers, associate editor, and co-editor for their

helpful suggestions and comments. In addition, Li’s research is partially

supported by the National Science Foundation of China, Grant 12571304,

the Shanghai Pujiang Programme (No. 24PJC030), and the Program for Innovative Research Team of Shanghai University of Finance and Economics.

Bai’s research is supported by the Program for Innovative Research Team of

Shanghai University of Finance and Economics and the Shanghai Research

Center for Data Science and Decision Technology.

Supplementary Materials

In the supplementary material, we present the complete algorithm for estimating the parameters and provide additional numerical results. In addi-

tion, we give some useful lemmas and proofs of theorems.

9.

Supplementary materials are available for download.