Stability Selection for Structured Variable Selection

TL;DR

This paper explores the application of Stability Selection to structured variable selection methods like group lasso, showing it can improve power but may reduce error control reliability, with guidelines for practical use.

Contribution

It extends Stability Selection to structured algorithms, analyzing its benefits and limitations, and provides practical strategies for tuning and method selection.

Findings

Stability Selection increases power of structured selection algorithms.

Complex structures can reduce error control reliability.

Guidelines for choosing error control methods are provided.

Abstract

In variable or graph selection problems, finding a right-sized model or controlling the number of false positives is notoriously difficult. Recently, a meta-algorithm called Stability Selection was proposed that can provide reliable finite-sample control of the number of false positives. Its benefits were demonstrated when used in conjunction with the lasso and orthogonal matching pursuit algorithms. In this paper, we investigate the applicability of stability selection to structured selection algorithms: the group lasso and the structured input-output lasso. We find that using stability selection often increases the power of both algorithms, but that the presence of complex structure reduces the reliability of error control under stability selection. We give strategies for setting tuning parameters to obtain a good model size under stability selection, and highlight its strengths and weaknesses compared to competing methods screen and clean and cross-validation. We give guidelines about when to use which error control method.