Description Usage Arguments Details Value Author(s) References See Also
Object of the penalty
class to handle the L1-Norm based Improved Correlation-Based (LICB) Penalty (Ulbricht, 2010).
1 |
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 L_1-norm based correlation penalty term. Both parameters must be nonnegative. |
... |
further arguments |
The improved correlation-based (LICB) penalty is defined as
P_{λ}^{licb}(\boldsymbol{β}) = λ_1 ∑_{i=1}^p |β_i| + λ_2 ∑_{i=1}^{p-1} ∑_{j > i} ≤ft\{\frac{|β_i - β_j|}{1 - \varrho_{ij}} + \frac{|β_i + β_j|}{1 + \varrho_{ij}}\right\}.
The LICB 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.
An object of the class penalty
. This is a list with elements
penalty |
character: the penalty name. |
lambda |
double: the (nonnegative) regularization parameter. |
first.derivative |
function: This returns the J-dimensional vector of the first derivative of the J penalty terms with respect to |\mathbf{a}^\top_j\boldsymbol{β|}. |
a.coefs |
function: This returns the p-dimensional coefficient vector \mathbf{a}_j of the J penalty terms. |
Jan Ulbricht
Ulbricht, Jan (2010) Variable Selection in Generalized Linear Models. Ph.D. Thesis. LMU Munich.
penalty
, penalreg
, icb
, weighted.fusion
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