Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distributed Multiple Testing with False Discovery Rate Control in the Presence of Byzantines

Daofu Zhang, Mehrdad Pournaderi, Yu Xiang, Pramod Varshney

TL;DR

The paper analyzes how Byzantine compromises of reported $p$-values affect global FDR control in distributed multiple testing, introducing oracle and BH-classifier attack models and deriving analytical bounds for the resulting FDR. It develops a practical counter-measure that replaces attacked zeros with Uniform$[0,1]$ samples to preserve FDR, and it investigates two stronger adversarial strategies (Enhanced BH-classifier and Shuffling) that are harder to mitigate. Experimental results show the BH-classifier model closely tracks the oracle attack and that simple countermeasures can effectively restore FDR control, while stronger attacks reveal limits and design trade-offs in distributed settings. Overall, the work connects distributed hypothesis testing under adversarial conditions with robust FDR control and provides insights into attack strategies and potential defenses for practical large-scale systems.

Abstract

This work studies distributed multiple testing with false discovery rate (FDR) control in the presence of Byzantine attacks, where an adversary captures a fraction of the nodes and corrupts their reported p-values. We focus on two baseline attack models: an oracle model with the full knowledge of which hypotheses are true nulls, and a practical attack model that leverages the Benjamini-Hochberg (BH) procedure locally to classify which p-values follow the true null hypotheses. We provide a thorough characterization of how both attack models affect the global FDR, which in turn motivates counter-attack strategies and stronger attack models. Our extensive simulation studies confirm the theoretical results, highlight key design trade-offs under attacks and countermeasures, and provide insights into more sophisticated attacks.

Distributed Multiple Testing with False Discovery Rate Control in the Presence of Byzantines

TL;DR

The paper analyzes how Byzantine compromises of reported -values affect global FDR control in distributed multiple testing, introducing oracle and BH-classifier attack models and deriving analytical bounds for the resulting FDR. It develops a practical counter-measure that replaces attacked zeros with Uniform samples to preserve FDR, and it investigates two stronger adversarial strategies (Enhanced BH-classifier and Shuffling) that are harder to mitigate. Experimental results show the BH-classifier model closely tracks the oracle attack and that simple countermeasures can effectively restore FDR control, while stronger attacks reveal limits and design trade-offs in distributed settings. Overall, the work connects distributed hypothesis testing under adversarial conditions with robust FDR control and provides insights into attack strategies and potential defenses for practical large-scale systems.

Abstract

This work studies distributed multiple testing with false discovery rate (FDR) control in the presence of Byzantine attacks, where an adversary captures a fraction of the nodes and corrupts their reported p-values. We focus on two baseline attack models: an oracle model with the full knowledge of which hypotheses are true nulls, and a practical attack model that leverages the Benjamini-Hochberg (BH) procedure locally to classify which p-values follow the true null hypotheses. We provide a thorough characterization of how both attack models affect the global FDR, which in turn motivates counter-attack strategies and stronger attack models. Our extensive simulation studies confirm the theoretical results, highlight key design trade-offs under attacks and countermeasures, and provide insights into more sophisticated attacks.
Paper Structure (8 sections, 6 theorems, 16 equations, 4 figures)

This paper contains 8 sections, 6 theorems, 16 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Oracle Attack Analysis
  4. BH-classifier Attack Model
  5. Counter-attack strategy
  6. Two stronger attack models
  7. Experimental Results
  8. Discussion

Key Result

Theorem 1

Suppose the attacker captures one node with $m$$p$-values, and carries out the oracle attack. Then when the BH procedure is applied at the central agent.

Figures (4)

  • Figure 1: Exp. 1. In both settings, the gap between $\text{FDR}^*_{\text{attack}}$ and $\text{FDR}_{\text{attack}}$ remains negligible overall.
  • Figure 2: Exp. 2. Effectiveness of counter-attack methods. Comparison of FDR with vs. without applying two types of counter-attack schemes. Counter-attack I (left) and II (right).
  • Figure 3: Exp. 3. Comparison of two stronger attack models.
  • Figure 4: Exp. 4. Comparison of the three attack models in the distributed setting ($d=20$).

Theorems & Definitions (10)

  • Theorem 1
  • proof
  • Remark 1
  • Corollary 1
  • Theorem 2
  • Theorem 3
  • proof
  • Lemma 1
  • proof
  • Proposition 1