Groupe d’études et de recherche en analyse des décisions

# Generalized Elastic Net Regression

## Geoffroy Mouret, Jean-Jules Brault et Vahid Partovi Nia

This work presents a variation of the elastic net penalization method. We propose applying a combined $$l$$1 and $$l$$2 norm penalization on a linear combination of regression parameters. This approach is an alternative to the $$l$$1-penalization for variable selection, but takes care of the correlation between the linear combination of parameters. We devise a path algorithm fitting method similar to the one proposed for the least angle regression. Furthermore, a one-shot estimation technique of $$l$$2 regularization parameter is proposed as an alternative to cross-validation. A simulation study is conducted to check the validity of the new technique.

, 10 pages