Boosting e-BH via conditional calibration

TL;DR

This paper introduces a conditional calibration framework to enhance the power of the e-BH multiple testing procedure, maintaining FDR control under arbitrary dependence, with applications across various testing scenarios.

Contribution

It proposes a novel boosting method for e-BH using conditional calibration, applicable to multiple testing problems with improved power and preserved FDR control.

Findings

Significant power improvement over standard e-BH.

Effective across parametric, model-X, and conformal testing.

Validated through extensive simulations and real data application.

Abstract

The e-BH procedure is an e-value-based multiple testing procedure that provably controls the false discovery rate (FDR) under any dependence structure between the e-values. Despite this appealing theoretical FDR control guarantee, the e-BH procedure often suffers from low power in practice. In this paper, we propose a general framework that boosts the power of e-BH without sacrificing its FDR control under arbitrary dependence. This is achieved by the technique of conditional calibration, where we take as input the e-values and calibrate them to be a set of "boosted e-values" that are guaranteed to be no less -- and are often more -- powerful than the original ones. Our general framework is explicitly instantiated in three classes of multiple testing problems: (1) testing under parametric models, (2) conditional independence testing under the model-X setting, and (3) model-free conformalized selection. Extensive numerical experiments show that our proposed method significantly improves the power of e-BH while continuing to control the FDR. We also demonstrate the effectiveness of our method through an application to an observational study dataset for identifying individuals whose counterfactuals satisfy certain properties.