Testing Directed Acyclic Graph via Structural, Supervised and Generative Adversarial Learning

AbstractAbstractIn 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. Supplementary materials for this article are available online.KEYWORDS: Brain connectivity networksDirected acyclic graphGenerative adversarial networksHypothesis testingMultilayer perceptron neural networks AcknowledgmentsThe authors wish to thank the Editor, the AE, and the reviewers for their constructive comments, which have led to a significant improvement of the earlier version of this article.Supplementary MaterialsSection A of the supplementary article discusses several extensions of the proposed test. Section B presents additional theoretical and numerical results. Section C gives the detailed proofs.Disclosure StatementThe authors report there are no competing interests to declare.Additional informationFundingLi’s research was partially supported by NSF grant CIF-2102227, and NIH grants R01AG061303, and R01AG062542. Shi’s research was partially supported by EPSRC grant EP/W014971/1.