icb: Improved Correlation-based Penalty

Description Usage Arguments Details Value Author(s) References See Also

View source: R/icb.R

Description

Object of the penalty class to handle the Improved Correlation-Based (ICB) Penalty (Ulbricht, 2010).

Usage

1
icb(lambda = NULL, ...)

Arguments

lambda

two dimensional tuning parameter parameter. The first component corresponds to the regularization parameter λ_1 for the lasso penalty term, the second one λ_2 for the correlation-based penalty. Both parameters must be nonnegative.

...

further arguments

Details

The improved correlation-based (ICB) penalty is defined as

P_{λ}^{icb}(\boldsymbol{β}) = λ_1 |\boldsymbol{β}|_1 + \frac{1}{2}λ_2 \boldsymbol{β}^\top \mathbf{M}^{cb} \boldsymbol{β},

with tuning parameter λ = (λ_1, λ_2), where \mathbf{M}^{cb} = (m_{ij}) is determined by m_{ij} = 2∑_{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


lqa documentation built on May 30, 2017, 3:41 a.m.

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