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

• URL: http://arxiv.org/abs/2210.02555v2
• Date: Tue, 16 May 2023 03:51:05 GMT
• Title: Sample-and-Forward: Communication-Efficient Control of the False Discovery Rate in Networks
• Authors: Mehrdad Pournaderi and Yu Xiang
• Abstract summary: 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.
• Score: 19.786769414376323
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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