Regularization with the Smooth-Lasso procedure

Mohamed Hebiri (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We consider the linear regression problem. We propose the S-Lasso procedure to estimate the unknown regression parameters. This estimator enjoys sparsity of the representation while taking into account correlation between successive variables (or predictors). The study covers the case when n << p, i.e. the number of observations is much smaller than the number of variables. Moreover, for fixed p, we establish asymptotic normality and consistency in variable selection results for our procedure. Furthermore, we provide an estimator of the effective degree of freedom of the S-Lasso estimator. A simulation study shows that the S-Lasso performs better than the Lasso as far as variable selection is concerned especially when high correlations between successive variables exist. This procedure also appears to be a good challenger to the Elastic-Net (Zou and Hastie, 2005).

Mots clés: Lasso; LARS; Sparsity; Variable selection; Regularization paths

Domaines: Statistiques [math.ST]

Mohamed Hebiri. Regularization with the Smooth-Lasso procedure. 2008. ⟨hal-00260816v1⟩