Title: Lasso-zero: Model selection by thresholding the $\ell_1$-minimal solution
Authors: Pascaline Descloux - University of Geneva (Switzerland) [presenting]
Sylvain Sardy - University of Geneva (Switzerland)
Abstract: The Lasso estimator is widely used in high-dimensional linear regression. However, no matter which criterion (cross-validation, SURE, BIC, ) is used for selecting the regularization parameter $\lambda$, its performance in terms of model selection is limited: the proportion of false discoveries tends to be large and restrictive conditions are required on the design matrix for achieving exact recovery of the set of important variables. Rather than focusing on the first part of the Lasso path where sparsest solutions are obtained, it is suggested to consider the limiting solution as $\lambda$ goes to zero, and to threshold the obtained coefficients. A choice of threshold aiming for low false discovery rate is proposed. The performance of this ``Lasso-Zero'' estimator is investigated and numerical experiments demonstrate that it provides an excellent tradeoff between false discovery and true positive rates and that it can exactly recover the set of important variables in situations where Lasso fails.