Variable Selection via Adaptive False Negative Control in Linear Regression

TL;DR

This paper introduces an adaptive variable selection method in linear regression that directly controls the false negative proportion, aiming to efficiently identify relevant predictors while balancing false positives.

Contribution

It proposes a novel approach to directly estimate and control false negative proportion in variable selection, adapting to user-specified levels and data strength.

Findings

Method effectively controls FNP at desired levels.

Performance improves with stronger effects or larger samples.

Numerical results align with theoretical analysis.

Abstract

Variable selection methods have been developed in linear regression to provide sparse solutions. Recent studies have focused on further interpretations on the sparse solutions in terms of false positive control. In this paper, we consider false negative control for variable selection with the goal to efficiently select a high proportion of relevant predictors. Different from existing studies in power analysis and sure screening, we propose to directly estimate the false negative proportion (FNP) of a decision rule and select the smallest subset of predictors that has the estimated FNP less than a user-specified control level. The proposed method is adaptive to the user-specified control level on FNP by selecting less candidates if a higher level is implemented. On the other hand, when data has stronger effect size or larger sample size, the proposed method controls FNP more efficiently with less false positives. New analytic techniques are developed to cope with the major challenge of FNP control when relevant predictors cannot be consistently separated from irrelevant ones. Our numerical results are in line with the theoretical findings.