Stability Selection

TL;DR

Stability selection is a versatile method combining subsampling with high-dimensional algorithms to improve structure estimation accuracy and control false discoveries, applicable across various statistical models.

Contribution

The paper introduces stability selection, a general approach that enhances variable and structure estimation, providing finite sample error control and proving its consistency for randomized Lasso.

Findings

Improves variable selection and structure estimation accuracy.

Provides finite sample control of false discovery rates.

Proves consistency of stability selection with randomized Lasso.

Abstract

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.