Tiny but uniform improvements of adaptive BH procedures via compound e-values

2026-03-22

AI Summary

This work aims to enhance the statistical power of adaptive Benjamini–Hochberg (BH) procedures while maintaining control of the false discovery rate (FDR). By unifying existing adaptive FDR methods under a common framework—interpreting them as weighted BH procedures based on composite e-values (ep-BH)—the study reveals their shared structural foundation and demonstrates for the first time that most estimators of the proportion of true null hypotheses inherently correspond to composite e-values. Building on this insight, the authors propose a novel framework that uniformly improves upon nearly all existing methods without requiring additional assumptions, and they develop a new ep-BH procedure with finite-sample FDR guarantees. In canonical settings such as t-tests, the proposed method achieves consistent and robust power gains while rigorously controlling the FDR.

Technology Category

Machine Learning: Ensemble MethodsCognitive Modeling & Cognitive Systems: Adaptive BehaviorGame Theory and Economic Paradigms: Adversarial Learning

Application Category

Web Mining and Content Analysis: Robustness and generalizability of Web mining methodsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSearch and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

After the seminal Benjamini-Hochberg (BH) procedure for controlling the false discovery rate (FDR) was proposed, dozens of papers have attempted to improve its power by adapting to the unknown proportion of nulls. We observe that most null proportion estimates are simply compound e-values in disguise, and thus most adaptive FDR procedures can be interpreted as instances of the e-weighted BH (ep-BH) procedure of Ignatiadis, Wang, and Ramdas [2024], i.e., the BH procedure weighted by compound e-values. This lens helps us show that most existing procedures are inadmissible, and we provide uniform improvements to them. While the improvements are small in practice, they still come for free (without additional assumptions), and help unify the literature. We also use our "leave-one-out ep-BH method" to design a new method with finite-sample FDR control for the simultaneous t-test setting.

Problem

• adaptive BH procedure
• false discovery rate
• compound e-values
• null proportion estimation
• FDR control

Innovation

• compound e-values
• adaptive BH procedure
• uniform improvement
• false discovery rate
• leave-one-out ep-BH