Stability Selection with Error Control

Resampling procedures to assess the stability of selected variables with additional finite sample error control for high-dimensional variable selection procedures such as Lasso or boosting. Both, standard stability selection (Meinshausen & Buhlmann, 2010, ) and complementary pairs stability selection with improved error bounds (Shah & Samworth, 2013, ) are implemented. The package can be combined with arbitrary user specified variable selection approaches.

stabs

stabs implements resampling procedures to assess the stability of selected variables with additional finite sample error control for high-dimensional variable selection procedures such as Lasso or boosting. Both, standard stability selection (Meinshausen & Bühlmann, 2010, doi:10.1111/j.1467-9868.2010.00740.x) and complementarty pairs stability selection with improved error bounds (Shah & Samworth, 2013, doi:10.1111/j.1467-9868.2011.01034.x) are implemented. The package can be combined with arbitrary user specified variable selection approaches.

For an expanded and executable version of this file please see

vignette("Using_stabs", package = "stabs")

Current version (from CRAN):

install.packages("stabs")

Latest development version from GitHub:

library("devtools")
install_github("hofnerb/stabs")

To be able to use the install_github() command, one needs to install devtools first:

install.packages("devtools")

Using stabs

A simple example of how to use stabs with package lars:

library("stabs")
library("lars")
## make data set available
data("bodyfat", package = "TH.data")
## set seed
set.seed(1234)
 
## lasso
(stab.lasso <- stabsel(x = bodyfat[, -2], y = bodyfat[,2],
                       fitfun = lars.lasso, cutoff = 0.75,
                       PFER = 1))
 
## stepwise selection
(stab.stepwise <- stabsel(x = bodyfat[, -2], y = bodyfat[,2],
                          fitfun = lars.stepwise, cutoff = 0.75,
                          PFER = 1))
 
## plot results
par(mfrow = c(2, 1))
plot(stab.lasso, main = "Lasso")
plot(stab.stepwise, main = "Stepwise Selection")

We can see that stepwise selection seems to be quite unstable even in this low dimensional example!

User-specified variable selection approaches

To use stabs with user specified functions, one can specify an own fitfun. These need to take arguments x (the predictors), y (the outcome) and q the number of selected variables as defined for stability selection. Additional arguments to the variable selection method can be handled by .... In the function stabsel() these can then be specified as a named list which is given to args.fitfun.

The fitfun function then needs to return a named list with two elements selected and path:

selected is a vector that indicates which variable was selected.
path is a matrix that indicates which variable was selected in which step. Each row represents one variable, the columns represent the steps. The latter is optional and only needed to draw the complete selection paths.

The following example shows how lars.lasso is implemented:

lars.lasso <- function(x, y, q, ...) {
    if (!requireNamespace("lars"))
        stop("Package ", sQuote("lars"), " needed but not available")
 
    if (is.data.frame(x)) {
        message("Note: ", sQuote("x"),
                " is coerced to a model matrix without intercept")
        x <- model.matrix(~ . - 1, x)
    }
 
    ## fit model
    fit <- lars::lars(x, y, max.steps = q, ...)
 
    ## which coefficients are non-zero?
    selected <- unlist(fit$actions)
    ## check if variables are removed again from the active set
    ## and remove these from selected
    if (any(selected < 0)) {
        idx <- which(selected < 0)
        idx <- c(idx, which(selected %in% abs(selected[idx])))
        selected <- selected[-idx]
    }
 
    ret <- logical(ncol(x))
    ret[selected] <- TRUE
    names(ret) <- colnames(x)
    ## compute selection paths
    cf <- fit$beta
    sequence <- t(cf != 0)
    ## return both
    return(list(selected = ret, path = sequence))
}

To see more examples simply print, e.g., lars.stepwise, glmnet.lasso, or glmnet.lasso_maxCoef. Please contact me if you need help to integrate your method of choice.

Using boosting with stability selection

Instead of specifying a fitting function, one can also use stabsel directly on computed boosting models from mboost.

library("stabs")
library("mboost")
### low-dimensional example
mod <- glmboost(DEXfat ~ ., data = bodyfat)
 
## compute cutoff ahead of running stabsel to see if it is a sensible
## parameter choice.
##   p = ncol(bodyfat) - 1 (= Outcome) + 1 ( = Intercept)
stabsel_parameters(q = 3, PFER = 1, p = ncol(bodyfat) - 1 + 1,
                   sampling.type = "MB")
## the same:
stabsel(mod, q = 3, PFER = 1, sampling.type = "MB", eval = FALSE)
 
## now run stability selection
(sbody <- stabsel(mod, q = 3, PFER = 1, sampling.type = "MB"))
opar <- par(mai = par("mai") * c(1, 1, 1, 2.7))
plot(sbody, type = "paths")
par(opar)
 
plot(sbody, type = "maxsel", ymargin = 6)

Citation

To cite the package in publications please use

citation("stabs")

which will currently give you

To cite package 'stabs' in publications use:
 
  Benjamin Hofner and Torsten Hothorn (2017). stabs: Stability
  Selection with Error Control, R package version R package version
  0.6-3, https://CRAN.R-project.org/package=stabs.
 
  Benjamin Hofner, Luigi Boccuto and Markus Goeker (2015). Controlling
  false discoveries in high-dimensional situations: Boosting with
  stability selection. BMC Bioinformatics, 16:144.
  doi:10.1186/s12859-015-0575-3
  
To cite the stability selection for 'gamboostLSS' models use:
 
  Thomas, J., Mayr, A., Bischl, B., Schmid, M., Smith, A., 
  and Hofner, B. (2017). Gradient boosting for distributional regression -
  faster tuning and improved variable selection via noncyclical updates. 
  Statistics and Computing. Online First. DOI 10.1007/s11222-017-9754-6  
 
Use ‘toBibtex(citation("stabs"))’ to extract BibTeX references.