Scaled and square-root elastic net

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

2 Citations (Scopus)

Abstract

In scaled lasso, the unknown regression coefficients and the scale parameter of the error distribution are estimated jointly. In lasso, the optimal penalty parameter is well-known to depend on the error scale, and it is therefore typically chosen using cross-validation. The main benefit of scaled lasso is that the penalty parameter is scale-free and can be predetermined from pure theoretical considerations. Nevertheless, scaled lasso performs poorly when there exist strong correlations between the predictors. As a remedy, we propose two different scaled elastic net (EN) formulations and derive convergent algorithms for their computation. The first formulation uses a conventional EN penalty whereas the second formulation differs from the former in that the ℓ2-loss is not squared. The former approach is referred to as the scaled EN estimator and the latter as the square-root EN estimator. We illustrate via numerical examples and simulations that the proposed methods outperform the scaled lasso, especially in the presence of high mutual coherence in the feature space.

Original languageEnglish
Title of host publication2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PublisherIEEE
Pages4336-4340
Number of pages5
ISBN (Electronic)9781509041176
DOIs
Publication statusPublished - 16 Jun 2017
MoE publication typeA4 Article in a conference publication
EventIEEE International Conference on Acoustics, Speech, and Signal Processing - New Orleans, United States
Duration: 5 Mar 20179 Mar 2017

Publication series

NameProceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing
PublisherIEEE
ISSN (Electronic)2379-190X

Conference

ConferenceIEEE International Conference on Acoustics, Speech, and Signal Processing
Abbreviated titleICASSP
CountryUnited States
CityNew Orleans
Period05/03/201709/03/2017

Keywords

  • elastic net
  • penalized linear regression
  • scale invariance
  • Scaled lasso
  • square-root lasso

Cite this