Multivariate Regression with Calibration

• Activity Number: 280
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Lie Wang*+ and Han Liu and Tuo Zhao
• Companies: Massachusetts Institute of Technology and Princeton University and Johns Hopkins University
• Keywords: multivariate regression ; Tuning insensitive

Abstract

We propose a new method named calibrated multivariate regression (CMR) for fitting high dimensional multivariate regression models. Compared to existing methods, CMR calibrates the regularization for each regression task with respect to its noise level so that it is simultaneously tuning insensitive and achieves an improved finite sample performance. We prove that CMR achieves the optimal rate of convergence in parameter estimation and we develop an efficient smoothed proximal gradient algorithm to implement it. We apply CMR on a brain activity prediction problem andfind that CMR even outperforms the handcrafted models created by human experts.