# fusedLasso: Auxiliary function which returns the objective, penalty, and... In smoothedLasso: A Framework to Smooth L1 Penalized Regression Operators using Nesterov Smoothing

## Description

Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the fused Lasso.

## Usage

 `1` ```fusedLasso(X, y, E, lambda, gamma) ```

## Arguments

 `X` The design matrix. `y` The response vector. `E` The adjacency matrix which encodes with a one in position (i,j) the presence of an edge between variables i and j. Note that only the upper triangle of E is read. `lambda` The first regularization parameter of the fused Lasso. `gamma` The second regularization parameter of the fused Lasso.

## Value

A list with six functions, precisely the objective u, penalty v, and dependence structure w, as well as their derivatives du, dv, and dw.

## References

Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., and Knight, K. (2005). Sparsity and Smoothness via the Fused Lasso. J Roy Stat Soc B Met, 67(1):91-108.

Arnold, T.B. and Tibshirani, R.J. (2020). genlasso: Path Algorithm for Generalized Lasso Problems. R package version 1.5.

Hahn, G., Lutz, S., Laha, N., and Lange, C. (2020). A framework to efficiently smooth L1 penalties for linear regression. bioRxiv:2020.09.17.301788.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```library(smoothedLasso) n <- 100 p <- 500 betavector <- runif(p) X <- matrix(runif(n*p),nrow=n,ncol=p) y <- X %*% betavector E <- matrix(sample(c(TRUE,FALSE),p*p,replace=TRUE),p) lambda <- 1 gamma <- 0.5 temp <- fusedLasso(X,y,E,lambda,gamma) ```

smoothedLasso documentation built on March 21, 2021, 9:07 a.m.