title: Multivariate Regression with Calibration.
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. Computationally, we develop an efficient smoothed proximal gradient algorithm which has a worst-case iteration complexityO(1/ε), whereεis a pre-specified numerical accuracy. Theoretically, we prove that CMR achieves the optimal rate of convergence in parameter estimation. We illustrate the usefulness of CMR by thorough numerical simulations and show that CMR consistently outperforms other high dimensional multivariate regression methods. We also apply CMR on a brain activity prediction problem and find that CMR is as competitive as the handcrafted model created by human experts.
authors.affiliation: Department of Operations Research and Financial Engineering, Princeton University.
authors.forename: Han
authors.initials: H
authors.lastname: Liu
authors.affiliation: Department of Mathematics, Massachusetts Institute of Technology.
authors.forename: Lie
authors.initials: L
authors.lastname: Wang
authors.affiliation: Department of Computer Science, Johns Hopkins University.
authors.forename: Tuo
authors.initials: T
authors.lastname: Zhao