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

TL;DR

This paper introduces new online FDR control methods using e-closure and compound e-values, achieving better power while maintaining FDR control in dependent testing streams.

Contribution

It develops novel online FDR procedures based on e-closure and compound e-values, with algorithms that are computationally efficient and empirically effective.

Findings

Improved power over existing online FDR methods

Algorithms with $O( ext{log } t)$ decision time

Validated on synthetic and real datasets

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.