Improving the adjusted Benjamini--Hochberg method using e-values in knockoff-assisted variable selection

2026-02-12

AI Summary

This work addresses the limited power of knockoff-based variable selection under weak or sparse signals and low target false discovery rate (FDR) settings. Building upon the e-value-weighted Benjamini–Hochberg (BH) framework, the authors propose three novel approaches: introducing a bounded p-to-e calibrator to enable flexible weight allocation, unifying the Sarkar–Tang method as a special case of e-value-weighted BH, and designing an adaptive procedure that estimates the proportion of true null hypotheses. Both theoretical analysis and empirical experiments demonstrate that the proposed methods rigorously control the FDR in finite samples while substantially improving statistical power in challenging scenarios with low FDR thresholds or weak/sparse signals, outperforming or matching existing state-of-the-art methods.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Considering the knockoff-based multiple testing framework of Barber and Cand\`es [2015], we revisit the method of Sarkar and Tang [2022] and identify it as a specific case of an un-normalized e-value weighted Benjamini-Hochberg procedure. Building on this insight, we extend the method to use bounded p-to-e calibrators that enable more refined and flexible weight assignments. Our approach generalizes the method of Sarkar and Tang [2022], which emerges as a special case corresponding to an extreme calibrator. Within this framework, we propose three procedures: an e-value weighted Benjamini-Hochberg method, its adaptive extension using an estimate of the proportion of true null hypotheses, and an adaptive weighted Benjamini-Hochberg method. We establish control of the false discovery rate (FDR) for the proposed methods. While we do not formally prove that the proposed methods outperform those of Barber and Cand\`es [2015] and Sarkar and Tang [2022], simulation studies and real-data analysis demonstrate large and consistent improvement over the latter in all cases, and better performance than the knockoff method in scenarios with low target FDR, a small number of signals, and weak signal strength. Simulation studies and a real-data application in HIV-1 drug resistance analysis demonstrate strong finite sample FDR control and exhibit improved, or at least competitive, power relative to the aforementioned methods.

Problem

• false discovery rate
• knockoff
• e-values
• multiple testing
• variable selection

Innovation

• e-values
• knockoff
• weighted Benjamini-Hochberg
• false discovery rate
• p-to-e calibration