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Matrix regression heterogeneity analysis

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Abstract

The development of modern science and technology has facilitated the collection of a large amount of matrix data in fields such as biomedicine. Matrix data modeling has been extensively studied, which advances from the naive approach of flattening the matrix into a vector. However, existing matrix modeling methods mainly focus on homogeneous data, failing to handle the data heterogeneity frequently encountered in the biomedical field, where samples from the same study belong to several underlying subgroups, and different subgroups follow different models. In this paper, we focus on regression-based heterogeneity analysis. We propose a matrix data heterogeneity analysis framework, by combining matrix bilinear sparse decomposition and penalized fusion techniques, which enables data-driven subgroup detection, including determining the number of subgroups and subgrouping membership. A rigorous theoretical analysis is conducted, including asymptotic consistency in terms of subgroup detection, the number of subgroups, and regression coefficients. Numerous numerical studies based on simulated and real data have been constructed, showcasing the superior performance of the proposed method in analyzing matrix heterogeneous data.

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Data and code availability

Data and codes to reproduce the numerical results are posted on the GitHub page, the https://github.com/Zhang-Fengchuan/Matrix-heterogeneity-linear-regression.git, https://github.com/Zhang-Fengchuan/Matrix-heterogeneity-logistic-regression.git.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China No. 12171454, U19B2940, Fundamental Research Funds for the Central Universities, Beijing Natural Science Foundation (JQ20029), National Key R &D Program of China (2022YFC3502502), and National Natural Science Foundation of China, No. 82071000.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China

    Fengchuan Zhang & Sanguo Zhang

  2. Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, China

    Fengchuan Zhang & Sanguo Zhang

  3. Beijing Tongren Eye Center, Beijing Tongren Hospital, Capital Medical University, Beijing Key Laboratory of Ophthalmology and Visual Sciences, Beijing, China

    Shi-Ming Li

  4. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China

    Mingyang Ren

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  1. Fengchuan Zhang
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  2. Sanguo Zhang
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  3. Shi-Ming Li
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Contributions

SZ and MR conceived the study. FZ and MR wrote the main manuscript text and supplementary information, planned and carried out the simulations, and developed the theory. SL provided the real data and guided the real data analysis. All authors reviewed the manuscript and contributed to the final manuscript.

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Correspondence to Shi-Ming Li or Mingyang Ren.

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Zhang, F., Zhang, S., Li, SM. et al. Matrix regression heterogeneity analysis. Stat Comput 34, 95 (2024). https://doi.org/10.1007/s11222-024-10401-z

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