Communication-Efficient Distributed Multiple Testing for Large-Scale Inference

TL;DR

This paper introduces a communication-efficient distributed method for multiple testing that approximates the Benjamini-Hochberg procedure in large-scale networks, reducing communication while maintaining FDR control.

Contribution

It develops a novel distributed algorithm that achieves asymptotic equivalence to the global BH procedure with minimal communication overhead.

Findings

Method is asymptotically equivalent to global BH

Requires only local null proportion estimates and p-value counts

Demonstrates robustness across various settings

Abstract

The Benjamini-Hochberg (BH) procedure is a celebrated method for multiple testing with false discovery rate (FDR) control. In this paper, we consider large-scale distributed networks where each node possesses a large number of p-values and the goal is to achieve the global BH performance in a communication-efficient manner. We propose that every node performs a local test with an adjusted test size according to the (estimated) global proportion of true null hypotheses. With suitable assumptions, our method is asymptotically equivalent to the global BH procedure. Motivated by this, we develop an algorithm for star networks where each node only needs to transmit an estimate of the (local) proportion of nulls and the (local) number of p-values to the center node; the center node then broadcasts a parameter (computed based on the global estimate and test size) to the local nodes. In the experiment section, we utilize existing estimators of the proportion of true nulls and consider various settings to evaluate the performance and robustness of our method.