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Selective factor extraction in high dimensions

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  • Yiyuan She

Abstract

SUMMARY This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset of input features. The proposed estimators enjoy sharp oracle inequalities, and with a predictive information criterion for model selection, they adapt to unknown sparsity by controlling both rank and row support of the coefficient matrix. A class of algorithms is developed that can accommodate various convex and nonconvex sparsity-inducing penalties, and can be used for rank-constrained variable screening in high-dimensional multivariate data. The paper also showcases applications in macroeconomics and computer vision to demonstrate how low-dimensional data structures can be effectively captured by joint variable selection and projection.

Suggested Citation

  • Yiyuan She, 2017. "Selective factor extraction in high dimensions," Biometrika, Biometrika Trust, vol. 104(1), pages 97-110.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:1:p:97-110.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw059
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    References listed on IDEAS

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    1. Shen, Haipeng & Huang, Jianhua Z., 2008. "Sparse principal component analysis via regularized low rank matrix approximation," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1015-1034, July.
    2. Kun Chen & Kung‐Sik Chan & Nils Chr. Stenseth, 2012. "Reduced rank stochastic regression with a sparse singular value decomposition," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 203-221, March.
    3. James H. Stock & Mark W. Watson, 2012. "Generalized Shrinkage Methods for Forecasting Using Many Predictors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 481-493, June.
    4. She, Yiyuan, 2012. "An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2976-2990.
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    Cited by:

    1. Yixuan Qiu & Jing Lei & Kathryn Roeder, 2023. "Gradient-based sparse principal component analysis with extensions to online learning," Biometrika, Biometrika Trust, vol. 110(2), pages 339-360.
    2. Aaron J. Molstad & Rohit K. Patra, 2023. "Dimension reduction for integrative survival analysis," Biometrics, The International Biometric Society, vol. 79(3), pages 1610-1623, September.
    3. Canhong Wen & Zhenduo Li & Ruipeng Dong & Yijin Ni & Wenliang Pan, 2023. "Simultaneous Dimension Reduction and Variable Selection for Multinomial Logistic Regression," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1044-1060, September.
    4. Mishra, Aditya & Müller, Christian L., 2022. "Robust regression with compositional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).

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