fused.lasso: Fused Lasso Penalty

In lqa: Penalized Likelihood Inference for GLMs

Description

Object of the penalty to handle the fused lasso penalty (Tibshirani et al., 2005)

Usage

fused.lasso (lambda = NULL, ...)

Arguments

lambda	two-dimensional tuning parameter. The first component corresponds to the regularization parameter λ_1 of the lasso penalty, the second one to the regularization parameter λ_2 of the fusion penalty. Both must be nonnegative.
...	further arguments

Details

The fused lasso penalty is defined as

P_{\tilde{λ}}^{fl} (\boldsymbol{β}) = λ_1 ∑_{i=1}^p |β_i| + λ_2 ∑_{i=2}^p |β_{i} - β_{i-1}|,

where \tilde{λ} = (λ_1, λ_2) contains two regularization parameters. The main idea of the fused lasso penalty is to encourage sparsity in the coefficients by using the L_1-norm lasso penalty, and additionally to force sparsity in the differences of the coefficients by the L_1-norm of their differences as reflected in the second penalty term. As a result, the fused lasso penalty conveys the estimated coefficients to behave in a smooth manner, with only a small number of big jumps. See Tibshirani et al. (2005) for further 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.
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.

Author(s)

Jan Ulbricht

References

Tibshirani, R., M. Saunders, S. Rosset, J. Zhu and K. Knight (2005) Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society B 67, 91–108.

See Also

penalty, lasso, ridge, weighted.fusion

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