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.
* Changed the internal scaling of the regularization parameter for `pense` and `pensem`.
**Note**: The _lambda_ values in this release are not the same as in previous releases!
* Fixed a bug when standardizing predictor variables with a MAD of 0 (thanks @hadjipantelis for reporting).
* The maximum value for the regularization parameter lambda is now chosen exactly.
* Fixed a bug when computing "exact" principal sensitivity components.
* Fix error with robustbase-0.92-8 as reported by Martin Maechler.
* Fix undefined behaviour in C++ code resulting in build error on Solaris (x86).
* Fix `predict()` function for `pensem` objects if computed from a fitted `pense` object.
* Always use `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()`.
* Add further measure of the prediction performance (`resid_size`) to `obj$cv_lambda_grid`, where `obj` is of class `pense` or `pensem`.
* Initial stable release of the package.