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.
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')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
See the package reference manual.