This work concerns developing communication- and computation-efficient methods for large-scale multiple testing over networks, which is of interest to many practical applications. We take an asymptotic approach and propose two methods, proportion-matching and greedy aggregation, tailored to distributed settings. The proportion-matching method achieves the global BH performance yet only requires a one-shot communication of the (estimated) proportion of true null hypotheses as well as the number of p-values at each node. By focusing on the asymptotic optimal power, we go beyond the BH procedure by providing an explicit characterization of the asymptotic optimal solution. This leads to the greedy aggregation method that effectively approximates the optimal rejection regions at each node, while computation efficiency comes from the greedy-type approach naturally. Moreover, for both methods, we provide the rate of convergence for both the FDR and power. Extensive numerical results over a variety of challenging settings are provided to support our theoretical findings.

翻译：本文关注为网络中的大规模多重检验开发通信高效和计算高效的方法，这在许多实际应用中具有重要意义。我们采用渐近方法，提出了两种针对分布式环境量身定制的算法：比例匹配法和贪婪聚合法。比例匹配法能够实现全局BH（Benjamini-Hochberg）性能，但仅需在每个节点进行一次性的（估计）原假设真比例以及p值数量的通信。通过聚焦于渐近最优功效，我们在BH过程的基础上进一步提供了渐近最优解的显式刻画，由此导出的贪婪聚合法能够在每个节点有效近似最优拒绝区域，而计算效率则通过自然的贪婪策略得以实现。此外，针对两种方法，我们分别给出了FDR（错误发现率）和功效的收敛速率。为支持理论发现，我们在多种具有挑战性的场景下提供了丰富的数值实验结果。