No penalty no tears: Least squares in high-dimensional linear models

Published

Conference Paper

© 2016 by the author(s). Ordinary least squares (OI,S) is the default method for fitting linear models, but is not applicable for problems with dimensionality larger than the sample size. For these problems, we advocate the use of a generalized version of OLS motivated by ridge regression, and propose two novel three-step algorithms involving least squares fitting and hard thresholding. The algorithms are methodologically simple to understand intuitively, computationally easy to implement efficiently, and theoretically appealing for choosing models consistently. Numerical exercises comparing our methods with penalization-based approaches in simulations and data analyses illustrate the great potential of the proposed algorithms.

Duke Authors

Cited Authors

  • Wang, X; Dunson, D; Leng, C

Published Date

  • January 1, 2016

Published In

  • 33rd International Conference on Machine Learning, Icml 2016

Volume / Issue

  • 4 /

Start / End Page

  • 2685 - 2706

International Standard Book Number 13 (ISBN-13)

  • 9781510829008

Citation Source

  • Scopus