Sparse trace norm regularization

Jianhui Chen, Jieping Ye

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We study the problem of estimating multiple predictive functions from a dictionary of basis functions in the nonparametric regression setting. Our estimation scheme assumes that each predictive function can be estimated in the form of a linear combination of the basis functions. By assuming that the coefficient matrix admits a sparse low-rank structure, we formulate the function estimation problem as a convex program regularized by the trace norm and the ℓ1-norm simultaneously. We propose to solve the convex program using the accelerated gradient (AG) method; we also develop efficient algorithms to solve the key components in AG. In addition, we conduct theoretical analysis on the proposed function estimation scheme: we derive a key property of the optimal solution to the convex program; based on an assumption on the basis functions, we establish a performance bound of the proposed function estimation scheme (via the composite regularization). Simulation studies demonstrate the effectiveness and efficiency of the proposed algorithms.

Original languageEnglish (US)
Pages (from-to)623-639
Number of pages17
JournalComputational Statistics
Volume29
Issue number3-4
DOIs
StatePublished - Jun 2014

    Fingerprint

Keywords

  • Gradient method
  • Low Rank
  • Performance bound
  • Regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Mathematics

Cite this