Multivariate Regression with Calibration.
Name
nihms650162.pdf
Description
Accepted version
Size
953.06 KB
Format
Adobe PDF
Checksum (MD5)
1a4b15aef112d942434a5fd8f184003a
Author(s)
Liu, Han
Wang, Lie
Zhao, Tuo
Date Issued
December 2014
Journal
Adv Neural Inf Process Syst
Citation
Liu, H., L. Wang, and T. Zhao. "Multivariate Regression with Calibration." Adv Neural Inf Process Syst 27 (2014): 5630.
Version
Author's final manuscript
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 complexity O(1/ε), where ε is 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://papers.nips.cc/paper/5630-multivariate-regression-with-calibration
