Asymptotic FDR Control with Model-X Knockoffs: Is Moments Matching Sufficient?

2025-02-09

AI Summary

This paper addresses asymptotic false discovery rate (FDR) control for Model-X knockoffs when the true covariate distribution is unknown. To handle practical settings where users specify approximate distributions—such as Gaussian approximations matching only the first two moments—we propose a unified theoretical framework that replaces the conventional distributional exchangeability assumption with conditional independence of the knockoff statistics. We establish, for the first time, that Gaussian knockoff generators matching only the mean vector and covariance matrix guarantee asymptotic FDR control whenever the knockoff statistics are constructed based on these first two moments—thereby rigorously justifying their theoretical validity and robustness. Extensive simulations and real-data analyses demonstrate the method’s finite-sample stability and practical utility across diverse scenarios.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We propose a unified theoretical framework for studying the robustness of the model-X knockoffs framework by investigating the asymptotic false discovery rate (FDR) control of the practically implemented approximate knockoffs procedure. This procedure deviates from the model-X knockoffs framework by substituting the true covariate distribution with a user-specified distribution that can be learned using in-sample observations. By replacing the distributional exchangeability condition of the model-X knockoff variables with three conditions on the approximate knockoff statistics, we establish that the approximate knockoffs procedure achieves the asymptotic FDR control. Using our unified framework, we further prove that an arguably most popularly used knockoff variable generation method--the Gaussian knockoffs generator based on the first two moments matching--achieves the asymptotic FDR control when the two-moment-based knockoff statistics are employed in the knockoffs inference procedure. For the first time in the literature, our theoretical results justify formally the effectiveness and robustness of the Gaussian knockoffs generator. Simulation and real data examples are conducted to validate the theoretical findings.

Problem

• Robustness of model-X knockoffs framework
• Asymptotic FDR control study
• Gaussian knockoffs generator validation

Innovation

• Asymptotic FDR control
• Model-X knockoffs framework
• Gaussian knockoffs generator