Sample-and-Forward: Communication-Efficient Control of the False Discovery Rate in Networks

TL;DR

This paper introduces Sample-and-Forward, a communication-efficient method for controlling the false discovery rate in networks that does not require nodes to share individual p-values, maintaining statistical power with minimal communication.

Contribution

It proposes a novel, communication-efficient adaptation of the BH procedure for multihop networks that ensures FDR control without exchanging raw p-values.

Findings

Achieves finite-sample FDR control in network settings.

Maintains competitive detection power with minimal communication.

Provides asymptotic power analysis under a mixture model.

Abstract

This work concerns controlling the false discovery rate (FDR) in networks under communication constraints. We present sample-and-forward, a flexible and communication-efficient version of the Benjamini-Hochberg (BH) procedure for multihop networks with general topologies. Our method evidences that the nodes in a network do not need to communicate p-values to each other to achieve a decent statistical power under the global FDR control constraint. Consider a network with a total of $m$ p-values, our method consists of first sampling the (empirical) CDF of the p-values at each node and then forwarding $\mathcal{O}(\log m)$ bits to its neighbors. Under the same assumptions as for the original BH procedure, our method has both the provable finite-sample FDR control as well as competitive empirical detection power, even with a few samples at each node. We provide an asymptotic analysis of power under a mixture model assumption on the p-values.