Controlling False Discovery Rate Using Gaussian Mirrors

Abstract

Simultaneously finding multiple influential variables and controlling the false discovery rate (FDR) for linear regression models is a fundamental problem. We here propose the Gaussian Mirror (GM) method, which creates for each predictor variable a pair of mirror variables by adding and subtracting a randomly generated Gaussian perturbation, and proceeds with a certain regression method, such as the ordinary least-square or the Lasso (the mirror variables can also be created after selection). The mirror variables naturally lead to test statistics effective for controlling the FDR. Under a mild assumption on the dependence among the covariates, we show that the FDR can be controlled at any designated level asymptotically. We also demonstrate through extensive numerical studies that the GM method is more powerful than many existing methods for selecting relevant variables subject to FDR control, especially for cases when the covariates are highly correlated and the influential variables are not overly sparse.

References in corpus (4)

• Valid post-selection inference
• Optimal Inference After Model Selection
• Veridical Data Science
• Neural Gaussian Mirror for Controlled Feature Selection in Neural Networks

Cited by in corpus (5)

• False Discovery Rate Control via Data Splitting
• A Scale-free Approach for False Discovery Rate Control in Generalized Linear Models
• Neural Gaussian Mirror for Controlled Feature Selection in Neural Networks
• False Discovery Rate Control for Confounder Selection Using Mirror Statistics
• StarTrek: Combinatorial Variable Selection with False Discovery Rate Control