We propose a novel methodology for discovering the presence of relationships realized as binary time series between variables in high dimension. To make it visually intuitive, we regard the existence of a relationship as an edge connection, and call a collection of such edges a network. Our objective is thus rephrased as uncovering the network by selecting relevant edges, referred to as the network exploration. Our methodology is based on multiple testing for the presence or absence of each edge, designed to ensure statistical reproducibility via controlling the false discovery rate (FDR). In particular, we carefully construct $p$-variables, and apply the Benjamini-Hochberg (BH) procedure. We show that the BH with our $p$-variables controls the FDR under arbitrary dependence structure with any sample size and dimension, and has asymptotic power one under mild conditions. The validity is also confirmed by simulations and a real data example.

翻译：我们提出了一种新颖的方法论，用于发现高维变量间以二元时间序列形式实现的关系存在性。为使其直观可视，我们将关系的存在视为边连接，并将此类边的集合称为网络。因此，我们的目标被重新表述为通过选择相关边来揭示网络，这一过程称为网络探索。我们的方法论基于对每条边存在与否的多重检验，旨在通过控制错误发现率（FDR）确保统计可复现性。具体而言，我们精心构建$p$变量，并应用Benjamini-Hochberg（BH）程序。我们证明，使用我们构建的$p$变量的BH方法能在任意依赖结构、任意样本量与维度下控制FDR，并在温和条件下具有渐近功效一。其有效性亦通过仿真实验与真实数据案例得到验证。