Elastic Net Regression (Ridge & LASSO)

Elastic Net - Objective Function

• $I_{{\lambda }_1,{\lambda }_2}(\beta )=(y-X\beta {)}^T(y-X\beta )+{\lambda }_1||\beta |{|}_1+{\lambda }_2||\beta |{|}_2$

where:

• ${\lambda }_1||\beta |{|}_1\text{ - is the LASSO part that provides a sparse model}$
• ${\lambda }_2||\beta |{|}_2\text{ - is the Ridge part that stabilizes the regularization, and provides a unique minimum}$