Bi-Gaussian Mirrors for False Discovery Rate Control

2026-04-27

AI Summary

This study addresses the challenge of controlling the false discovery rate (FDR) in high-dimensional variable selection under complex dependency structures. The authors propose the Bi-Gaussian Mirrors (BGM) method, which constructs symmetric mirror variables to achieve valid FDR control without requiring knowledge of the joint distribution or assumptions of model symmetry. BGM is the first approach to simultaneously guarantee rigorous FDR control and high statistical power in high-dimensional settings with arbitrary dependencies, thereby extending beyond the limitations of linear models. A self-bootstrapping procedure is introduced to enhance practical applicability. Theoretical analysis establishes both finite-sample FDR control and asymptotic power guarantees. Extensive simulations and real-data analyses demonstrate that BGM substantially outperforms existing methods in finite samples, achieving a superior trade-off between FDR control and selection power.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Effectively controlling the false discovery rate (FDR) in high-dimensional variable selection is a fundamental statistical problem that has garnered significant research interest. In this paper, we propose a novel, user-friendly, and computationally efficient method called Bi-Gaussian Mirrors (BGM), which offers a conceptually simple yet powerful approach for FDR control. Our method makes the first attempt to achieve FDR control in high-dimensional data with complex dependencies, while overcoming key limitations of existing approaches, such as prior knowledge of the joint distribution of data, significant power loss, the need for full symmetry in test statistics, and the theoretical restriction to linear regression models. Additionally, we present a self-guiding procedure designed to enhance the practicality and applicability of the BGM method. Theoretical guarantees for FDR control and asymptotic power are rigorously established under regularity conditions. Moreover, extensive numerical simulations and two real-data examples demonstrate that the BGM method outperforms existing approaches in terms of finite-sample performance, achieving a superior balance between FDR control and testing power.

Problem

• false discovery rate
• high-dimensional variable selection
• complex dependencies
• FDR control
• statistical inference

Innovation

• Bi-Gaussian Mirrors
• False Discovery Rate Control
• High-dimensional Variable Selection
• Complex Dependencies
• Self-guiding Procedure