Testing Directed Acyclic Graph via Structural, Supervised and Generative Adversarial Learning
This addresses a gap in DAG inference for researchers in fields like neuroscience, though it appears incremental as it builds on existing DAG estimation methods with flexible neural networks.
The authors tackled the problem of hypothesis testing for directed acyclic graphs (DAGs) by proposing a new method that allows nonlinear associations and time-dependent data, establishing asymptotic guarantees and demonstrating efficacy through simulations and a brain connectivity analysis.
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.