Variable selection with error control: Another look at Stability Selection

TL;DR

This paper introduces Complementary Pairs Stability Selection (CPSS), a variant of Stability Selection, providing theoretical bounds on error rates without strong assumptions, thereby enhancing variable selection reliability.

Contribution

The paper proposes CPSS, a new stability selection variant, with theoretical error bounds that do not rely on exchangeability assumptions, improving variable selection robustness.

Findings

Bounds on false inclusions and exclusions are derived.

Error control is improved under certain shape restrictions.

Method increases applicability of stability-based variable selection.

Abstract

Stability Selection was recently introduced by Meinshausen and Buhlmann (2010) as a very general technique designed to improve the performance of a variable selection algorithm. It is based on aggregating the results of applying a selection procedure to subsamples of the data. We introduce a variant, called Complementary Pairs Stability Selection (CPSS), and derive bounds both on the expected number of variables included by CPSS that have low selection probability under the original procedure, and on the expected number of high selection probability variables that are excluded. These results require no (e.g. exchangeability) assumptions on the underlying model or on the quality of the original selection procedure. Under reasonable shape restrictions, the bounds can be further tightened, yielding improved error control, and therefore increasing the applicability of the methodology.