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Sparse reduced-rank regression for simultaneous rank and variable selection via manifold optimization

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  • Kohei Yoshikawa

    (The University of Electro-Communications
    NTT DATA Mathematical Systems Inc.)

  • Shuichi Kawano

    (The University of Electro-Communications)

Abstract

We consider the problem of constructing a reduced-rank regression model whose coefficient parameter is represented as a singular value decomposition with sparse singular vectors. The traditional estimation procedure for the coefficient parameter often fails when the true rank of the parameter is high. To overcome this issue, we develop an estimation algorithm with rank and variable selection via sparse regularization and manifold optimization, which enables us to obtain an accurate estimation of the coefficient parameter even if the true rank of the coefficient parameter is high. Using sparse regularization, we can also select an optimal value of the rank. We conduct Monte Carlo experiments and a real data analysis to illustrate the effectiveness of our proposed method.

Suggested Citation

  • Kohei Yoshikawa & Shuichi Kawano, 2023. "Sparse reduced-rank regression for simultaneous rank and variable selection via manifold optimization," Computational Statistics, Springer, vol. 38(1), pages 53-75, March.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01216-5
    DOI: 10.1007/s00180-022-01216-5
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    References listed on IDEAS

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    1. 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.
    2. A. Mukherjee & K. Chen & N. Wang & J. Zhu, 2015. "On the degrees of freedom of reduced-rank estimators in multivariate regression," Biometrika, Biometrika Trust, vol. 102(2), pages 457-477.
    3. Yanming Li & Bin Nan & Ji Zhu, 2015. "Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure," Biometrics, The International Biometric Society, vol. 71(2), pages 354-363, June.
    4. 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.
    5. Ming Yuan & Ali Ekici & Zhaosong Lu & Renato Monteiro, 2007. "Dimension reduction and coefficient estimation in multivariate linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 329-346, June.
    6. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
    7. Kun Chen & Hongbo Dong & Kung-Sik Chan, 2013. "Reduced rank regression via adaptive nuclear norm penalization," Biometrika, Biometrika Trust, vol. 100(4), pages 901-920.
    8. 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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