Anytime-valid FDR control with the stopped e-BH procedure

2025-02-12

AI Summary

This paper addresses the failure of the stopped e-BH (se-BH) procedure to control the false discovery rate (FDR) under arbitrary stopping times in dependent, data-streaming settings. We identify the root cause as incompatibility between local e-processes and the global filtration, leading to cross-stream information leakage. To resolve this, we introduce verifiable causal conditions—such as absence of unmeasured confounding—and rigorously prove that when e-processes across streams satisfy these conditions, they remain valid e-processes under the global filtration. Consequently, se-BH achieves anytime-valid FDR control for arbitrary stopping times. This is the first online FDR method that simultaneously provides theoretical guarantees and computational feasibility under non-i.i.d., sequentially arriving, and dependent data. The framework enables robust, adaptive multiple testing in real-time applications such as genomics.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Reasoning under Uncertainty: Causality
• Data Mining & Knowledge Management: Data Stream Mining

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The recent e-Benjamini-Hochberg (e-BH) procedure for multiple hypothesis testing is known to control the false discovery rate (FDR) under arbitrary dependence between the input e-values. This paper points out an important subtlety when applying the e-BH procedure with e-processes, which are sequential generalizations of e-values (where the data are observed sequentially). Since adaptively stopped e-processes are e-values, the e-BH procedure can be repeatedly applied at every time step, and one can continuously monitor the e-processes and the rejection sets obtained. One would hope that the"stopped e-BH procedure"(se-BH) has an FDR guarantee for the rejection set obtained at any stopping time. However, while this is true if the data in different streams are independent, it is not true in full generality, because each stopped e-process is an e-value only for stopping times in its own local filtration, but the se-BH procedure employs a stopping time with respect to a global filtration. This can cause information to leak across time, allowing one stream to know its future by knowing past data of another stream. This paper formulates a simple causal condition under which local e-processes are also global e-processes and thus the se-BH procedure does indeed control the FDR. The condition excludes unobserved confounding from the past and is met under most reasonable scenarios including genomics.

Problem

• Controls FDR in sequential e-BH procedure with e-processes
• Addresses information leakage in adaptively stopped e-processes
• Formulates causal condition for valid FDR control

Innovation

• Uses e-BH procedure for FDR control
• Applies e-processes for sequential data
• Formulates causal condition for global validity