On Grouping Effect of Sparse Stable Outlier-Robust Regression

Kyohei Suzuki, Masahiro Yukawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

This paper elucidates the grouping effect of the sparse stable outlier-robust regression (S-SORR) estimator which exploits the minimax concave (MC) penalty and the Tikhonov regularization simultaneously together with the MC loss. The main theoretical result is the following: where μ 1 > 0$ is the regularization parameter, and ai and aj are the unit vectors with their associated coefficients hat xi and hat xj. Remarkably, the bound is independent of possible outliers which may be contained in the observation vector y, whereas the bound for the popular elastic net estimator increases in proportion to the norm of y which is largely affected by outliers. Numerical examples show that S-SORR extracts the group structure correctly under huge outliers.

Original languageEnglish
Title of host publication2022 IEEE 32nd International Workshop on Machine Learning for Signal Processing, MLSP 2022
PublisherIEEE Computer Society
ISBN (Electronic)9781665485470
DOIs
Publication statusPublished - 2022
Event32nd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2022 - Xi'an, China
Duration: 2022 Aug 222022 Aug 25

Publication series

NameIEEE International Workshop on Machine Learning for Signal Processing, MLSP
Volume2022-August
ISSN (Print)2161-0363
ISSN (Electronic)2161-0371

Conference

Conference32nd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2022
Country/TerritoryChina
CityXi'an
Period22/8/2222/8/25

Keywords

  • convex optimization
  • grouping effect
  • minimax concave function
  • sparse modeling
  • sparse outlier-robust regression

ASJC Scopus subject areas

  • Human-Computer Interaction
  • Signal Processing

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