In this article, we propose a new hypothesis testing method for directed acyclic graph (DAG). While there is a rich class of DAG estimation methods, there is a relative paucity of DAG inference solutions. Moreover, the existing methods often impose some specific model structures such as linear models or additive models, and assume independent data observations. Our proposed test instead allows the associations among the random variables to be nonlinear and the data to be time-dependent. We build the test based on some highly flexible neural networks learners. We establish the asymptotic guarantees of the test, while allowing either the number of subjects or the number of time points for each subject to diverge to infinity. We demonstrate the efficacy of the test through simulations and a brain connectivity network analysis.

翻译：本文提出了一种针对有向无环图（DAG）的新型假设检验方法。尽管存在丰富的DAG估计方法，但DAG推断解决方案相对匮乏。此外，现有方法通常施加线性模型或加性模型等特定模型结构，并假设数据观测独立。我们提出的检验方法则允许随机变量之间的关联是非线性的，并且数据可以是时间依赖的。我们基于高度灵活的神经网络学习器构建了这一检验。我们在允许每个受试者的样本数或每个受试者的时间点数趋于无穷大的情况下，建立了该检验的渐近保证。通过模拟实验和脑连接网络分析，我们验证了该检验的有效性。