Learn R Programming

smoothedLasso (version 1.6)

A Framework to Smooth L1 Penalized Regression Operators using Nesterov Smoothing

Description

We provide full functionality to smooth L1 penalized regression operators and to compute regression estimates thereof. For this, the objective function of a user-specified regression operator is first smoothed using Nesterov smoothing (see Y. Nesterov (2005) ), resulting in a modified objective function with explicit gradients everywhere. The smoothed objective function and its gradient are minimized via BFGS, and the obtained minimizer is returned. Using Nesterov smoothing, the smoothed objective function can be made arbitrarily close to the original (unsmoothed) one. In particular, the Nesterov approach has the advantage that it comes with explicit accuracy bounds, both on the L1/L2 difference of the unsmoothed to the smoothed objective functions as well as on their respective minimizers (see G. Hahn, S.M. Lutz, N. Laha, C. Lange (2020) ). A progressive smoothing approach is provided which iteratively smoothes the objective function, resulting in more stable regression estimates. A function to perform cross validation for selection of the regularization parameter is provided.

Copy Link

Version

Install

install.packages('smoothedLasso')

Monthly Downloads

211

Version

1.6

License

GPL (>= 2)

Maintainer

Georg Hahn

Last Published

March 21st, 2021

Functions in smoothedLasso (1.6)

elasticNet

Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the elastic net.
objFunctionSmooth

Auxiliary function to define the objective function of the smoothed L1 penalized regression operator.
objFunctionSmoothGradient

Auxiliary function which computes the gradient of the smoothed L1 penalized regression operator.
minimizeSmoothedSequence

Minimize the objective function of a smoothed regression operator with respect to \(betavector\) using the progressive smoothing algorithm.
minimizeFunction

Minimize the objective function of an unsmoothed or smoothed regression operator with respect to \(betavector\) using BFGS.
fusedLasso

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

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

Auxiliary function to define the objective function of an L1 penalized regression operator.
standardLasso

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

Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the Lasso for polygenic risk scores (prs).
objFunctionGradient

Auxiliary function which computes the (non-smooth) gradient of an L1 penalized regression operator.
crossvalidation

Perform cross validation to select the regularization parameter.