Talk:Elastic net regularization

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Elastic Net After Rescaling

In the paper Regularization and variable selection via the elastic net by Hui Zou and Trevor Hastie, they state (in equation 14) the Elastic Net estimates after rescaling are given by:

${\hat {\beta }}=\arg \min \limits _{\beta }\beta ^{T}\left({\frac {\mathbf {X} ^{T}\mathbf {X} +\lambda _{2}\mathbf {I} }{1+\lambda _{2}}}\right)\beta -2\mathbf {y} ^{T}\mathbf {X} \beta +\lambda _{1}|\beta |_{1}$

This alternative form may be useful for some people. It allows one to optimize directly in the already rescaled space. It is also insightful as it provides insight as to why the authors rescaled by the factor $1+\lambda _{2}$ . Mouse7mouse9 05:13, 27 October 2015 (UTC)