论文标题
网络上的大规模多次测试：一种渐近方法
On Large-Scale Multiple Testing Over Networks: An Asymptotic Approach
论文作者
论文摘要
这项工作涉及开发网络大规模多重测试的通信和计算有效的方法，这对于许多实际应用来说是有趣的。我们采用一种渐近方法，并提出了针对分布式设置量身定制的两种方法：比例匹配和贪婪的聚合。比例匹配方法实现了全局BH性能，但仅需要对（估计的）真实零假设的（估计）比例进行一次性通信以及每个节点处的p值数量。通过关注渐近最佳功率，我们通过提供渐近表征的最佳最佳解决方案来超越BH程序。这导致了贪婪的聚集方法，该方法有效地近似于每个节点处的最佳排斥区域，而计算效率自然来自贪婪型方法。此外，对于这两种方法，我们都提供了FDR和功率的收敛速度。提供了各种具有挑战性的环境的广泛数值结果，以支持我们的理论发现。
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.
