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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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