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321 – Methods and Applications in Biomedical Data and Clinical Trials, Part 1

Generalized Elastic Net Regression

Sponsor: Section on Statistical Learning and Data Mining
Keywords: Elastic Net, Fitted Values, Generalized Lasso, Least Angle Regression, Variable Selection

Geoffroy Mouret

École Polytechnique Montréal

Jean-Jules Brault

École Polytechnique Montréal

Vahid Partovinia

École Polytechnique Montréal

This work presents a variation of the elastic net penalization method. We propose applying a combined l1 and l2 norm penalization on a linear combination of regression parameters. This approach is an alternative to the l1-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 l2 regularization parameter is proposed as an alternative to cross-validation. A simulation study is conducted to check the validity of the new technique.

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