Path thresholding: Asymptotically tuning-free high-dimensional sparse regression

Divyanshu Vats, Richard G. Baraniuk

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, called path thresholding (PaTh), that transforms any tuning parameter-dependent sparse regression algorithm into an asymptotically tuning-free sparse regression algorithm. More specifically, we prove that, as the problem size becomes large (in the number of variables and in the number of observations), PaTh performs accurate sparse regression, under appropriate conditions, without specifying a tuning parameter. In finite-dimensional settings, we demonstrate that PaTh can alleviate the computational burden of model selection algorithms by significantly reducing the search space of tuning parameters.

Original languageEnglish (US)
Pages (from-to)948-957
Number of pages10
JournalJournal of Machine Learning Research
Volume33
StatePublished - 2014

ASJC Scopus subject areas

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

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