stabsel.FDboost: Stability Selection

Description

Function for stability selection with functional response. Per default the sampling is done on the level of curves and if the model contains a smooth functional intercept, this intercept is refittedn in each sampling fold.

Usage

# S3 method for FDboost
stabsel(
  x,
  refitSmoothOffset = TRUE,
  cutoff,
  q,
  PFER,
  folds = cvLong(x$id, weights = rep(1, l = length(x$id)), type = "subsampling", B = B),
  B = ifelse(sampling.type == "MB", 100, 50),
  assumption = c("unimodal", "r-concave", "none"),
  sampling.type = c("SS", "MB"),
  papply = mclapply,
  verbose = TRUE,
  eval = TRUE,
  ...
)

Value

An object of class stabsel with a special print method. For the elements of the object, see stabsel

Arguments

x: fitted FDboost-object
refitSmoothOffset: logical, should the offset be refitted in each learning sample? Defaults to TRUE.
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 of stabsel.
folds: a weight matrix with number of rows equal to the number of observations, see {cvLong}. 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.
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 complementary pairs in the former case this leads to 2B subsamples.
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 "none".
sampling.type: use sampling scheme of of Shah & Samworth (2013), i.e., with complementary pairs (sampling.type = "SS"), or the original sampling scheme of Meinshausen & Buehlmann (2010).
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.
eval: logical. Determines whether stability selection is evaluated (eval = TRUE; default) or if only the parameter combination is returned.
...: additional arguments to cvrisk or validateFDboost.

Details

The number of boosting iterations is an important hyper-parameter of the boosting algorithms and can be chosen using the functions cvrisk.FDboost and validateFDboost as they compute honest, i.e. out-of-bag, estimates of the empirical risk for different numbers of boosting iterations. The weights (zero weights correspond to test cases) are defined via the folds matrix, see cvrisk in package mboost. See Hofner et al. (2015) for the combination of stability selection and component-wise boosting.

References

B. Hofner, L. Boccuto and M. Goeker (2015), Controlling false discoveries in high-dimensional situations: boosting with stability selection. BMC Bioinformatics, 16, 1-17.

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.

Examples

Run this code

######## Example for function-on-scalar-regression
data("viscosity", package = "FDboost")
## set time-interval that should be modeled
interval <- "101"

## model time until "interval" and take log() of viscosity
end <- which(viscosity$timeAll == as.numeric(interval))
viscosity$vis <- log(viscosity$visAll[,1:end])
viscosity$time <- viscosity$timeAll[1:end]
# with(viscosity, funplot(time, vis, pch = 16, cex = 0.2))

## fit a model cotaining all main effects 
modAll <- FDboost(vis ~ 1 
          + bolsc(T_C, df=1) %A0% bbs(time, df=5) 
          + bolsc(T_A, df=1) %A0% bbs(time, df=5)
          + bolsc(T_B, df=1) %A0% bbs(time, df=5)
          + bolsc(rspeed, df=1) %A0% bbs(time, df=5)
          + bolsc(mflow, df=1) %A0% bbs(time, df=5), 
       timeformula = ~bbs(time, df=5), 
       numInt = "Riemann", family = QuantReg(), 
       offset = NULL, offset_control = o_control(k_min = 10),
       data = viscosity, 
       control = boost_control(mstop = 100, nu = 0.2))


## create folds for stability selection  
## only 5 folds for a fast example, usually use 50 folds 
set.seed(1911)
folds <- cvLong(modAll$id, weights = rep(1, l = length(modAll$id)), 
                type = "subsampling", B = 5) 
    
# \donttest{        
## stability selection with refit of the smooth intercept 
stabsel_parameters(q = 3, PFER = 1, p = 6, sampling.type = "SS")
sel1 <- stabsel(modAll, q = 3, PFER = 1, folds = folds, grid = 1:200, sampling.type = "SS")
sel1

## stability selection without refit of the smooth intercept 
sel2 <- stabsel(modAll, refitSmoothOffset = FALSE, q = 3, PFER = 1, 
                folds = folds, grid = 1:200, sampling.type = "SS")
sel2
# }

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