robustsubsets

Overview

An R implementation of robust subset selection.

Robust subset selection is a robust adaption of the classic best subset selection estimator, and is defined by the constrained least squares problem:

Robust subsets seeks out the best subset of predictors and observations and performs a least squares fit on this subset. The number of predictors used in the fit is controlled by the parameter k and the observations by the parameter h.

Installation

You should install Gurobi and the associated R package gurobi before installing robustsubsets. Gurobi is available for free under academic license at https://www.gurobi.com/.

To install robustsubsets from GitHub, run the following code:

devtools::install_github('ryan-thompson/robustsubsets')

Usage

The rss() function fits a robust subset regression model for a grid of k and h. The cv.rss() function provides a convenient way to automatically cross-validate these parameters.

library(robustsubsets)

# Generate training data with contaminated predictor matrix
set.seed(0)
n <- 100 # Number of observations
p <- 10 # Number of predictors
p0 <- 5 # Number of relevant predictors
ncontam <- 10 # Number of contaminated observations
beta <- c(rep(1, p0), rep(0, p - p0))
x <- matrix(rnorm(n * p), n, p)
e <- rnorm(n, c(rep(10, ncontam), rep(0, n - ncontam)))
y <- x %*% beta + e

# Fit using robust subset selection
fit <- rss(x, y)
coef(fit, k = p0, h = n - ncontam)

##  [1] -0.1424147  0.7800366  1.0083840  1.0259560  1.0409005  0.9616482
##  [7]  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000

# Cross-validate using robust subset selection
cl <- parallel::makeCluster(2)
fit <- cv.rss(x, y, cluster = cl)
parallel::stopCluster(cl)
coef(fit)

##  [1] -0.1424147  0.7800366  1.0083840  1.0259560  1.0409005  0.9616482
##  [7]  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000

Documentation

See the package reference manual.