Multivariate regression with calibration

Han Liu, Lie Wang, Tuo Zhao

Research output: Contribution to journalConference article

14 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)127-135
Number of pages9
JournalAdvances in Neural Information Processing Systems
Volume1
Issue numberJanuary
StatePublished - Jan 1 2014
Event28th Annual Conference on Neural Information Processing Systems 2014, NIPS 2014 - Montreal, Canada
Duration: Dec 8 2014Dec 13 2014

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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    Liu, H., Wang, L., & Zhao, T. (2014). Multivariate regression with calibration. Advances in Neural Information Processing Systems, 1(January), 127-135.