Robust penalized elastic net S and MM estimator for linear regression. The method is described in detail in Cohen Freue, G. V., Kepplinger, D., Salibian-Barrera, M., and Smucler, E. (2017) < https://gcohenfr.github.io/pdfs/PENSE_manuscript.pdf>.
This R package implements the Penalized Elastic Net S-Estimator (PENSE) and MM-estimator (PENSEM) for linear regression.
The main functions in the package are
pense() … to compute a robust elastic net S-estimator for linear regressionpensem() … to compute a robust elastic net MM-estimator either directly from the data matrix or
from an S-estimator previously computed with pense().Both of these functions perform k-fold cross-validation to choose the optimal penalty level
lambda, but the optimal balance between the L1 and the L2 penalties (the alpha parameter) needs
to be pre-specified by the user.
The default breakdown point is set to 25%. If the user needs an estimator with a higher breakdown
point, the delta argument in the pense_options() and initest_options() can be set to the
desired breakdown point (.e.g, delta = 0.5).
The package also exports an efficient classical elastic net algorithm available via the functions
elnet() and elnet_cv() which chooses an optimal penalty parameter based on cross-validation.
The elastic net solution is computed either by the augmented LARS algorithm
(en_options_aug_lars()) or via the Dual Augmented Lagrangian algorithm (Tomioka, et al. 2011)
selected with en_options_dal() which is much faster in case of a large number of predictors
(> 500) and a small number of observations (< 200).
To install the latest release from CRAN, run the following R code in the R console:
install.packages("pense")The most recent stable version as well as the developing version might not yet be available on CRAN. These can be directly installed from github using the devtools package:
# Install the most recent stable version:install_github("dakep/pense-rpkg")# Install the (unstable) develop version:install_github("dakep/pense-rpkg", ref = "develop")Tomioka, R., Suzuki, T., and Sugiyama, M. (2011). Super-linear convergence of dual augmented lagrangian algorithm for sparsity regularized estimation. The Journal of Machine Learning Research, 12:1537–1586.
STRICT_R_HEADERS)pense and pensem.
Note: The lambda values in this release are not the same as in previous releases!predict() function for pensem objects if computed from a fitted pense object.delta and cc specified in pense_options() for the initial estimator. Remove delta and cc arguments from initest_options() and instead add them to enpy().resid_size) to obj$cv_lambda_grid, where obj is of class pense or pensem.