# Controlling False Discovery Rate Using Gaussian Mirrors

arXiv: https://arxiv.org/abs/1911.09761 · HTML: https://mlsanity.com/paper/1911.09761/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2019.

## Built on by (most cited first, 10 of 10)

- [Data fission: splitting a single data point](https://mlsanity.com/paper/2112.11079/) (2021)
- [Near-optimal multiple testing in Bayesian linear models with finite-sample FDR control](https://mlsanity.com/paper/2211.02778/) (2022)
- [Stability of a Generalized Debiased Lasso with Applications to Resampling-Based Variable Selection](https://mlsanity.com/paper/2405.03063/) (2024)
- [Provable FDR Control for Deep Feature Selection: Deep MLPs and Beyond](https://mlsanity.com/paper/2512.04696/) (2025)
- [CatNet: Controlling the False Discovery Rate in LSTM with SHAP Feature Importance and Gaussian Mirrors](https://mlsanity.com/paper/2411.16666/) (2024)
- [Knockoff-Guided Compressive Sensing: A Statistical Machine Learning Framework for Support-Assured Signal Recovery](https://mlsanity.com/paper/2505.24727/) (2025)
- [False Discovery Rate Control via Bayesian Mirror Statistic](https://mlsanity.com/paper/2510.00875/) (2025)
- [Virtual Dummies: Enabling Scalable FDR-Controlled Variable Selection via Sequential Sampling of Null Features](https://mlsanity.com/paper/2604.07464/) (2026)
- [Model-Agnostic FDR Control via Group Gaussian Mirror and Permutation SHAP](https://mlsanity.com/paper/2608.00989/) (2026)
- [Mitigating Object Hallucination in Large Vision-Language Models via False Discovery Controlled Visual Data Splitting](https://mlsanity.com/paper/2609.38979/) (2026)

## Abstract (arXiv)

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.