Sparse Reduced-Rank Regression for Simultaneous Rank and Variable Selection via Manifold Optimization
This work addresses a specific issue in statistical modeling for researchers dealing with high-rank regression parameters, representing an incremental improvement over traditional methods.
The paper tackles the problem of constructing a reduced-rank regression model with high true rank by developing an estimation algorithm that combines sparse regularization and manifold optimization for simultaneous rank and variable selection, resulting in accurate parameter estimation as demonstrated through Monte Carlo experiments and real data analysis.
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 real data analysis to illustrate the effectiveness of our proposed method.