High-dimensional variable selection

TL;DR

This paper investigates statistical guarantees for variable selection in high-dimensional models, analyzing error rates and power of multi-stage regression methods including screening and cleaning stages.

Contribution

It introduces a framework for consistent variable selection using a combination of screening methods and hypothesis testing in high-dimensional settings.

Findings

Lasso, marginal regression, and forward stepwise regression are effective screening methods.

The proposed multi-stage approach achieves consistent variable selection under certain conditions.

The method balances error control and power in high-dimensional variable selection.

Abstract

This paper explores the following question: what kind of statistical guarantees can be given when doing variable selection in high-dimensional models? In particular, we look at the error rates and power of some multi-stage regression methods. In the first stage we fit a set of candidate models. In the second stage we select one model by cross-validation. In the third stage we use hypothesis testing to eliminate some variables. We refer to the first two stages as "screening" and the last stage as "cleaning." We consider three screening methods: the lasso, marginal regression, and forward stepwise regression. Our method gives consistent variable selection under certain conditions.