# PENSE R package

This R package implements the Penalized Elastic Net S-Estimator (PENSE) and MM-estimator (PENSEM) for linear regression.

## Overview

The main functions in the package are * `pense()`

… to compute a robust elastic net S-estimator for linear regression * `pensem()`

… 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).

## Installation

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")
```

## References

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.