A note on selection stability: combining stability and prediction

TL;DR

This paper introduces PASS, a new criterion combining stability selection and cross-validation for tuning parameter choice in linear regression, enhancing variable selection consistency and performance.

Contribution

The paper proposes PASS, a novel method that integrates stability and prediction criteria for improved tuning parameter selection in variable selection.

Findings

PASS achieves consistent variable selection under certain conditions.

Simulation studies show PASS performs well even when assumptions are violated.

PASS outperforms traditional methods in small sample scenarios.

Abstract

Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which combines the strength of both stability selection and cross-validation and therefore is referred as the prediction and stability selection (PASS). The selection consistency is established assuming the data generating model is a subset of the full model, and the small sample performance is demonstrated through some simulation studies where the assumption is either held or violated.