Calibrated multivariate regression with application to neural semantic basis discovery

Han Liu, Lie Wang, Tuo Zhao

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

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 convergence O(1/ε), where e is 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/.

Original languageEnglish (US)
Pages (from-to)1579-1606
Number of pages28
JournalJournal of Machine Learning Research
Volume16
StatePublished - Aug 1 2015

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

Keywords

  • Brain activity prediction
  • Calibration
  • High dimension
  • Low rank
  • Multivariate regression
  • Sparsity

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