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

TL;DR

This paper introduces a novel hypothesis testing method for directed acyclic graphs (DAGs) that accommodates nonlinear associations and time-dependent data using neural networks, with proven asymptotic guarantees and demonstrated effectiveness.

Contribution

It presents a flexible, neural network-based DAG testing approach that relaxes traditional model assumptions and handles dependent, nonlinear data.

Findings

The proposed test performs well in simulations.

It successfully analyzes brain connectivity networks.

The method provides asymptotic guarantees for diverging data dimensions.

Abstract

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.