DAG-GAN: Causal Structure Learning with Generative Adversarial Nets

Learning Directed Acyclic Graph (DAG) from purely observational data is a critical problem for causal inference. Most existing works tackle this problem by exploring gradient-based learning methods with a smooth characterization of acyclicity. A major shortcoming of current gradient based works is that they independently optimize SEMs with a single sample and neglect the interactions between different samples. In this paper, we consider DAG structure learning from the perspective of distributional optimization and design an adversarial framework named DAG-GAN to detect the DAG structure from data. We theoretically analyze the Nash equilibrium property of DAG-GAN and propose a novel score function to exploit the interactions between different samples. In addition, extensive experiments are conducted to validate the efficiency of DAG-GAN against several state-of-the-art DAG learning methods.