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Feature Selection by Canonical Correlation Search in High-Dimensional Multiresponse Models With Complex Group Structures

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  • Shan Luo
  • Zehua Chen

Abstract

High-dimensional multiresponse models with complex group structures in both the response variables and the covariates arise from current researches in important fields such as genetics and medicine. However, no enough research has been done on such models. One of a few researches, if not the only one, is the article by Li, Nan, and Zhu where the sparse group Lasso approach is extended to such models. In this article, we propose a novel approach named the sequential canonical correlation search (SCCS) procedure. In the SCCS procedure, the nonzero group by group blocks of regression coefficients are searched stepwise using a canonical correlation measure. Each step of the procedure consists of a block selection and a sparsity identification. The model selection criterion, EBIC, is used as the stopping rule of the procedure. We establish the selection consistency of the SCCS procedure and conduct simulation studies for the comparison of existing methods. The SCCS procedure has two advantages over the sparse grouped Lasso method: (i) it is more accurate in the identification of nonzero coefficient blocks and their nonzero entries, and (ii) its implementation is not limited by the dimensionality of the models and requires much less computation. A real example in genetic studies is also considered. Supplementary materials for this article are available online.

Suggested Citation

  • Shan Luo & Zehua Chen, 2020. "Feature Selection by Canonical Correlation Search in High-Dimensional Multiresponse Models With Complex Group Structures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1227-1235, July.
  • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:531:p:1227-1235
    DOI: 10.1080/01621459.2019.1609972
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    Cited by:

    1. Jun Lu & Dan Wang & Qinqin Hu, 2022. "Interaction screening via canonical correlation," Computational Statistics, Springer, vol. 37(5), pages 2637-2670, November.
    2. Juan C. Laria & M. Carmen Aguilera-Morillo & Rosa E. Lillo, 2023. "Group linear algorithm with sparse principal decomposition: a variable selection and clustering method for generalized linear models," Statistical Papers, Springer, vol. 64(1), pages 227-253, February.
    3. Ping Wang & Lu Lin, 2023. "Conditional characteristic feature screening for massive imbalanced data," Statistical Papers, Springer, vol. 64(3), pages 807-834, June.
    4. Yuanyuan Shi & Junyu Zhao & Xianchong Song & Zuoyu Qin & Lichao Wu & Huili Wang & Jian Tang, 2021. "Hyperspectral band selection and modeling of soil organic matter content in a forest using the Ranger algorithm," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-15, June.

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