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Trace regression model with simultaneously low rank and row(column) sparse parameter

Author

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  • Zhao, Junlong
  • Niu, Lu
  • Zhan, Shushi

Abstract

In this paper, we consider the trace regression model with matrix covariates, where the parameter is a matrix of simultaneously low rank and row(column) sparse. To estimate the parameter, we formulate a convex optimization problem with the nuclear norm and group Lasso penalties, and propose an alternating direction method of multipliers (ADMM) algorithm. The asymptotic properties of the estimator are established. Simulation results confirm the effectiveness of our method.

Suggested Citation

  • Zhao, Junlong & Niu, Lu & Zhan, Shushi, 2017. "Trace regression model with simultaneously low rank and row(column) sparse parameter," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 1-18.
    • Handle: RePEc:eee:csdana:v:116:y:2017:i:c:p:1-18
    DOI: 10.1016/j.csda.2017.06.009
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    References listed on IDEAS

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    1. Jianhui Chen & Jieping Ye, 2014. "Sparse trace norm regularization," Computational Statistics, Springer, vol. 29(3), pages 623-639, June.
    2. Hua Zhou & Lexin Li & Hongtu Zhu, 2013. "Tensor Regression with Applications in Neuroimaging Data Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 540-552, June.
    3. Hua Zhou & Lexin Li, 2014. "Regularized matrix regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 463-483, March.
    4. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    Cited by:

    1. Wang, Lei & Zhang, Jing & Li, Bo & Liu, Xiaohui, 2022. "Quantile trace regression via nuclear norm regularization," Statistics & Probability Letters, Elsevier, vol. 182(C).
    2. Yiting Ma & Pan Shang & Lingchen Kong, 2025. "Tuning parameter selection for the adaptive nuclear norm regularized trace regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(3), pages 491-516, June.
    3. Ling Peng & Xiaohui Liu & Xiangyong Tan & Yiweng Zhou & Shihua Luo, 2024. "The statistical rate for support matrix machines under low rankness and row (column) sparsity," Statistical Papers, Springer, vol. 65(7), pages 4567-4598, September.
    4. Xiumin Liu & Lu Niu & Junlong Zhao, 2023. "Statistical inference on the significance of rows and columns for matrix-valued data in an additive model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(3), pages 785-828, September.
    5. Zhou, Chengyu & Fang, Xiaolei, 2023. "A convex two-dimensional variable selection method for the root-cause diagnostics of product defects," Reliability Engineering and System Safety, Elsevier, vol. 229(C).

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