| icb {lqa} | R Documentation |
Improved Correlation-based Penalty
Description
Object of the penalty class to handle the Improved Correlation-Based (ICB) Penalty (Ulbricht, 2010).
Usage
icb(lambda = NULL, ...)
Arguments
lambda |
two dimensional tuning parameter parameter. The first component corresponds to the regularization parameter |
... |
further arguments |
Details
The improved correlation-based (ICB) penalty is defined as
P_{\lambda}^{icb}(\boldsymbol{\beta}) = \lambda_1 |\boldsymbol{\beta}|_1 + \frac{1}{2}\lambda_2 \boldsymbol{\beta}^\top \mathbf{M}^{cb} \boldsymbol{\beta},
with tuning parameter \lambda = (\lambda_1, \lambda_2), where \mathbf{M}^{cb} = (m_{ij}) is determined by
m_{ij} = 2\sum_{s\neq i}\frac{1}{1-\varrho_{is}^2} if i = j, and m_{ij} = -2\frac{\varrho_{ij}}{1-\varrho_{ij}^2} otherwise.
The ICB has been introduced to overcome the major drawback of the correlation based-penalized estimator, that is its lack of sparsity.
See Ulbricht (2010) for details.
Value
An object of the class penalty. This is a list with elements
penalty |
character: the penalty name. |
lambda |
double: the (nonnegative) regularization 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.
See Also
penalty, penalreg, licb, weighted.fusion