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.

翻译：本研究关注在通信受限的网络中控制错误发现率（FDR）。我们提出了样本-转发方法，这是一种适用于通用拓扑多跳网络的Benjamini-Hochberg（BH）过程的灵活且通信高效的版本。该方法表明，在全局FDR控制约束下，网络中的节点无需相互通信p值即可实现可观的统计功效。考虑一个包含总计$m$个p值的网络，我们的方法首先在每个节点处对p值的（经验）累积分布函数进行采样，然后向其邻居转发$\mathcal{O}(\log m)$比特。在与原始BH过程相同的假设下，我们的方法不仅具有可证明的有限样本FDR控制能力，而且即使在每个节点仅使用少量样本的情况下，也具有具有竞争力的经验检测功效。我们基于p值的混合模型假设提供了功效的渐近分析。