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A Splicing Approach to Best Subset of Groups Selection

Author

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  • Yanhang Zhang

    (School of Statistics, Renmin University of China, Beijing 100872, China; Southern China Center for Statistical Science, Department of Statistical Science, School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China)

  • Junxian Zhu

    (Saw Swee Hock School of Public Health, National University of Singapore, 117549 Singapore)

  • Jin Zhu

    (Southern China Center for Statistical Science, Department of Statistical Science, School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China)

  • Xueqin Wang

    (Department of Statistics and Finance/International Institute of Finance, School of Management, University of Science and Technology of China, Hefei 230026, China)

Abstract

Best subset of groups selection (BSGS) is the process of selecting a small part of nonoverlapping groups to achieve the best interpretability on the response variable. It has attracted increasing attention and has far-reaching applications in practice. However, due to the computational intractability of BSGS in high-dimensional settings, developing efficient algorithms for solving BSGS remains a research hotspot. In this paper, we propose a group-splicing algorithm that iteratively detects the relevant groups and excludes the irrelevant ones. Moreover, coupled with a novel group information criterion, we develop an adaptive algorithm to determine the optimal model size. Under certain conditions, it is certifiable that our algorithm can identify the optimal subset of groups in polynomial time with high probability. Finally, we demonstrate the efficiency and accuracy of our methods by comparing them with several state-of-the-art algorithms on both synthetic and real-world data sets.

Suggested Citation

  • Yanhang Zhang & Junxian Zhu & Jin Zhu & Xueqin Wang, 2023. "A Splicing Approach to Best Subset of Groups Selection," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 104-119, January.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:1:p:104-119
    DOI: 10.1287/ijoc.2022.1241
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    References listed on IDEAS

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    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. Daehan Won & Hasan Manzour & Wanpracha Chaovalitwongse, 2020. "Convex Optimization for Group Feature Selection in Networked Data," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 182-198, January.
    3. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    5. Wenliang Pan & Xueqin Wang & Weinan Xiao & Hongtu Zhu, 2019. "A Generic Sure Independence Screening Procedure," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 928-937, April.
    6. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    7. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    8. Wei Pan & Benhuai Xie & Xiaotong Shen, 2010. "Incorporating Predictor Network in Penalized Regression with Application to Microarray Data," Biometrics, The International Biometric Society, vol. 66(2), pages 474-484, June.
    9. Xiaotong Shen & Wei Pan & Yunzhang Zhu & Hui Zhou, 2013. "On constrained and regularized high-dimensional regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 807-832, October.
    10. 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. Wen, Xin & Li, Yang & Zheng, Zemin, 2024. "Scalable efficient reproducible multi-task learning via data splitting," Statistics & Probability Letters, Elsevier, vol. 208(C).

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