English

On the generic uniform uniqueness of the LASSO estimator

Statistics Theory 2016-03-02 v2 Computation Statistics Theory

Abstract

The LASSO is a variable subset selection procedure in statistical linear regression based on 1\ell_1 penalization of the least-squares operator. Uniqueness of the LASSO is an important issue, especially for the study of the LASSO path. The goal of the present paper is to provide a generic sufficient condition on the design matrix for the LASSO minimizer to be unique. Unlike previous works on the question of uniqueness, our condition only depends on the design matrix. Our study is based on a general position condition on the design matrix which holds with probability one for most experimental models.

Keywords

Cite

@article{arxiv.1105.1430,
  title  = {On the generic uniform uniqueness of the LASSO estimator},
  author = {Stephane Chretien and Sebastien Darses},
  journal= {arXiv preprint arXiv:1105.1430},
  year   = {2016}
}