Improving online FDR procedures via online analogs of e-closure and compound e-values

2026-03-25

AI Summary

This work addresses the challenge of controlling the false discovery rate (FDR) under arbitrary dependence structures while enhancing statistical power in online hypothesis testing. The authors propose an online e-closure principle combined with a donation-based composite e-value method, which strictly guarantees FDR control and significantly outperforms existing online multiple testing procedures based on either p-values or e-values. By integrating e-value theory, closure principles, and efficient algorithmic design, the method enables real-time decision-making with a computational complexity of O(log t). Extensive experiments on both synthetic and real-world data demonstrate that the proposed approach achieves superior FDR control accuracy and higher statistical power compared to current state-of-the-art methods.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

In many scientific applications, hypotheses are generated and tested continuously in a stream. We develop a framework for improving online multiple testing procedures with false discovery rate (FDR) control under arbitrary dependence. Our approach is two-fold: we construct methods via the online e-closure principle, as well as a novel formulation of online compound e-values that is defined through donations. This yields strict power improvements over state-of-the-art e-value and p-value procedures while retaining FDR control. We further derive algorithms that compute the decision at time $t$ in $O(\log t)$ time, and we demonstrate improved empirical performance on synthetic and real data.

Problem

• online multiple testing
• false discovery rate
• e-values
• arbitrary dependence
• streaming hypotheses

Innovation

• online FDR control
• e-closure
• compound e-values
• donation-based e-values
• streaming hypothesis testing