We introduce extensions of stability selection, a method to stabilise
variable selection methods introduced by Meinshausen and B\"uhlmann (J R Stat
Soc 72:417-473, 2010). We propose to apply a base selection method repeatedly
to random observation subsamples and covariate subsets under scrutiny, and to
select covariates based on their selection frequency. We analyse the effects
and benefits of these extensions. Our analysis generalizes the theoretical
results of Meinshausen and B\"uhlmann (J R Stat Soc 72:417-473, 2010) from the
case of half-samples to subsamples of arbitrary size. We study, in a
theoretical manner, the effect of taking random covariate subsets using a
simplified score model. Finally we validate these extensions on numerical
experiments on both synthetic and real datasets, and compare the obtained
results in detail to the original stability selection method.Comment: accepted for publication in Statistics and Computin