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

• Activity Number: 39 - Recent Advances on Causal Inference and Mediation Analysis
• Type: Invited
• Date/Time: Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
• Sponsor: WNAR
• Author(s): Chengchun Shi* and Yunzhe Zhou and Lexin Li
• Companies: LSE and University of California, Berkeley and University of California, Berkeley
• Keywords: Hypothesis testing; Directed acyclic graph; Generative adversarial networks; Multilayer perceptron networks; Brain effective connectivity analysis

Abstract

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 and establish the asymptotic guarantees of the test, by 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 effective connectivity analysis based on functional magnetic resonance imaging data.