Reduced Rank Ridge Regression and Its Kernel Extension

• Activity Number: 63
• Type: Topic Contributed
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Ashin Mukherjee*+ and Ji Zhu
• Companies: University of Michigan and University of Michigan
• Keywords: statistical learning ; Reduced Rank Regression ; RKHS

Abstract

In multivariate linear regression, it is often assumed that the response matrix is intrinsically of lower rank. This could be due to 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.