  Estimation of structure, such as in variable selection, graphical modelling
or cluster analysis is notoriously difficult, especially for high-dimensional
data. We introduce stability selection. It is based on subsampling in
combination with (high-dimensional) selection algorithms. As such, the method
is extremely general and has a very wide range of applicability. Stability
selection provides finite sample control for some error rates of false
discoveries and hence a transparent principle to choose a proper amount of
regularisation for structure estimation. Variable selection and structure
estimation improve markedly for a range of selection methods if stability
selection is applied. We prove for randomised Lasso that stability selection
will be variable selection consistent even if the necessary conditions needed
for consistency of the original Lasso method are violated. We demonstrate
stability selection for variable selection and Gaussian graphical modelling,
using real and simulated data.
