Reduced Rank Ridge Regression and Its Kernel Extensions.

Research paper by Ashin A Mukherjee, Ji J Zhu

Indexed on: 21 Sep '12Published on: 21 Sep '12Published in: Statistical Analysis and Data Mining: The ASA Data Science Journal


In multivariate linear regression, it is often assumed that the response matrix is intrinsically of lower rank. This could be because of the correlation structure among the prediction variables or the coefficient matrix being lower rank. To accommodate both, we propose a reduced rank ridge regression for multivariate linear regression. Specifically, we combine the ridge penalty with the reduced rank constraint on the coefficient matrix to come up with a computationally straightforward algorithm. Numerical studies indicate that the proposed method consistently outperforms relevant competitors. A novel extension of the proposed method to the reproducing kernel Hilbert space (RKHS) set-up is also developed.