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We consider the problem of constructing a reduced-rank regression model whosecoefficient parameter is represented as a singular value decomposition withsparse singular vectors. The traditional estimation procedure for thecoefficient parameter often fails when the true rank of the parameter is high.To overcome this issue, we develop an estimation algorithm with rank andvariable selection via sparse regularization and manifold optimization, whichenables us to obtain an accurate estimation of the coefficient parameter evenif the true rank of the coefficient parameter is high. Using sparseregularization, we can also select an optimal value of the rank. We conductMonte Carlo experiments and real data analysis to illustrate the effectivenessof our proposed method.

Sparse Reduced-Rank Regression for Simultaneous Rank and Variable Selection via Manifold Optimization