| genet {lqa} | R Documentation |
Generalized Elastic Net Penalty
Description
Object of the penalty to handle the Generalized Elastic Net (GENET) penalty (Ulbricht, 2010).
Usage
genet (lambda = NULL, ...)
Arguments
lambda |
three-dimensional tuning parameter. The first component corresponds to the regularization parameter |
... |
further arguments. |
Details
The GENET penalty can be defined as
P_{\bar{\lambda}}^{genet}(\boldsymbol{\beta}) = \lambda \left\{\alpha \sum_{i=1}^p |\beta_i| + (1-\alpha)
\sum_{i=1}^p |\beta_i|^\gamma \right\}, \quad 0 \leq \alpha \leq
1, \: \gamma > 1
with tuning parameter vector \bar{\lambda} = (\lambda, \alpha, \gamma).
The regularization parameter \lambda determines the overall relevance of the GENET penalty. The balance between L_1-norm penalization,
and hence variable selection, and
bridge penalization for incorporating the grouping effect is managed by an overall tuning parameter \alpha.
For motivation and further details on the GENET penalty see Ulbricht (2010).
Value
An object of the class penalty. This is a list with elements
penalty |
character: the penalty name. |
lambda |
double: the (nonnegative) tuning parameter. |
getpenmat |
function: computes the diagonal penalty matrix. |
Author(s)
Jan Ulbricht
References
Ulbricht, Jan (2010) Variable Selection in Generalized Linear Models. Ph.D. Thesis. LMU Munich.