stabsel: Stability Selection

Description

Selection of influential variables or model components with error control.

Usage

## a method to compute stability selection paths for fitted mboostLSS models
# S3 method for mboostLSS
stabsel(x, cutoff, q, PFER, mstop = NULL,
        folds = subsample(model.weights(x), B = B),
        B = ifelse(sampling.type == "MB", 100, 50),
        assumption = c("unimodal", "r-concave", "none"),
        sampling.type = c("SS", "MB"),
        papply = mclapply, verbose = TRUE, FWER, eval = TRUE, ...)
## a method to get the selected parameters
# S3 method for stabsel_mboostLSS
selected(object, parameter = NULL, ...)

Value

An object of class stabsel with a special print method. The object has the following elements:

phat: selection probabilities.
selected: elements with maximal selection probability greater cutoff.
max: maximum of selection probabilities.
cutoff: cutoff used.
q: average number of selected variables used.
PFER: per-family error rate.
sampling.type: the sampling type used for stability selection.
assumption: the assumptions made on the selection probabilities.
call: the call.

Arguments

x: an fitted model of class "mboostLSS" or "nc_mboostLSS".
cutoff: cutoff between 0.5 and 1. Preferably a value between 0.6 and 0.9 should be used.
q: number of (unique) selected variables (or groups of variables depending on the model) that are selected on each subsample.
PFER: upper bound for the per-family error rate. This specifies the amount of falsely selected base-learners, which is tolerated. See details.
mstop: mstop value to use, if no value is supplied the mstop value of the fitted model is used.
folds: a weight matrix with number of rows equal to the number of observations, see cvrisk and subsample. Usually one should not change the default here as subsampling with a fraction of \(1/2\) is needed for the error bounds to hold. One usage scenario where specifying the folds by hand might be the case when one has dependent data (e.g. clusters) and thus wants to draw clusters (i.e., multiple rows together) not individuals.
assumption: Defines the type of assumptions on the distributions of the selection probabilities and simultaneous selection probabilities. Only applicable for sampling.type = "SS". For sampling.type = "MB" we always use code"none".
sampling.type: use sampling scheme of of Shah & Samworth (2013), i.e., with complementarty pairs (sampling.type = "SS"), or the original sampling scheme of Meinshausen & Buehlmann (2010).
B: number of subsampling replicates. Per default, we use 50 complementary pairs for the error bounds of Shah & Samworth (2013) and 100 for the error bound derived in Meinshausen & Buehlmann (2010). As we use \(B\) complementray pairs in the former case this leads to \(2B\) subsamples.
papply: (parallel) apply function, defaults to mclapply. Alternatively, parLapply can be used. In the latter case, usually more setup is needed (see example of cvrisk for some details).
verbose: logical (default: TRUE) that determines wether warnings should be issued.
FWER: deprecated. Only for compatibility with older versions, use PFER instead.
eval: logical. Determines whether stability selection is evaluated (eval = TRUE; default) or if only the parameter combination is returned.
object: a object of class "stabsel_mboostLSS".
parameter: select one or multiple effects.
...: additional arguments to parallel apply methods such as mclapply and to cvrisk.

Details

Stability selection is to be preferably used with non-cyclic gamboostLSS models, as proposed by Thomas et al. (2018). In this publication, the combination of package gamboostLSS with stability selection was devoloped and is investigated in depth.

For details on stability selection see stabsel in package stabs and Hofner et al. (2014).

References

B. Hofner, L. Boccuto and M. Goeker (2015), Controlling false discoveries in high-dimensional situations: Boosting with stability selection. BMC Bioinformatics, 16:144.

N. Meinshausen and P. Buehlmann (2010), Stability selection. Journal of the Royal Statistical Society, Series B, 72, 417--473.

R.D. Shah and R.J. Samworth (2013), Variable selection with error control: another look at stability selection. Journal of the Royal Statistical Society, Series B, 75, 55--80.

Thomas, J., Mayr, A., Bischl, B., Schmid, M., Smith, A., and Hofner, B. (2018), Gradient boosting for distributional regression - faster tuning and improved variable selection via noncyclical updates. Statistics and Computing. 28: 673-687. tools:::Rd_expr_doi("10.1007/s11222-017-9754-6")
(Preliminary version: https://arxiv.org/abs/1611.10171).

Examples

Run this code


### Data generating process:
set.seed(1907)
x1 <- rnorm(500)
x2 <- rnorm(500)
x3 <- rnorm(500)
x4 <- rnorm(500)
x5 <- rnorm(500)
x6 <- rnorm(500)
mu    <- exp(1.5 +1 * x1 +0.5 * x2 -0.5 * x3 -1 * x4)
sigma <- exp(-0.4 * x3 -0.2 * x4 +0.2 * x5 +0.4 * x6)
y <- numeric(500)
for( i in 1:500)
    y[i] <- rnbinom(1, size = sigma[i], mu = mu[i])
dat <- data.frame(x1, x2, x3, x4, x5, x6, y)

### linear model with y ~ . for both components: 400 boosting iterations
model <- glmboostLSS(y ~ ., families = NBinomialLSS(), data = dat,
                     control = boost_control(mstop = 400),
                     center = TRUE, method = "noncyclic")

### Do not test the following code per default on CRAN as it takes some time to run:

#run stability selection 
(s <- stabsel(model, q = 5, PFER = 1))
#get selected effects
selected(s)

#visualize selection frequencies 
plot(s)

### END (don't test automatically)

Run the code above in your browser using DataLab