Calibrated Multivariate Regression with Application to Neural Semantic Basis Discovery.
We propose a calibrated multivariate regression method named CMR for fitting high dimensional multivariate regression models. Compared with existing methods, CMR calibrates regularization for each regression task with respect to its noise level so that it simultaneously attains improved finite-sample performance and tuning insensitiveness. Theoretically, we provide sufficient conditions under which CMR achieves the optimal rate of convergence in parameter estimation. Computationally, we propose an efficient smoothed proximal gradient algorithm with a worst-case numerical rate of convergenceO(1/ϵ), whereϵis a pre-specified accuracy of the objective function value. We conduct thorough numerical simulations to illustrate that CMR consistently outperforms other high dimensional multivariate regression methods. We also apply CMR to solve a brain activity prediction problem and find that it is as competitive as a handcrafted model created by human experts. The R package camel implementing the proposed method is available on the Comprehensive R Archive Network http://cran.r-project.org/web/packages/camel/.
Department of Operations Research and Financial Engineering, Princeton University, NJ 08544, USA, hanliu@princeton.edu.
Han
H
Liu
Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA 02139, USA, liewang@math.mit.edu.
Lie
L
Wang
Tuo
T
Zhao
brain activity prediction; calibration; high dimension; low Rank; multivariate regression; sparsity