Gradient-based causal discovery with latent variables.

Discovering causal graphs from observational data is a challenging problem, which has garnered significant attention due to its crucial role in understanding causal relationships. In recent advancements, this problem is cast as a continuous optimization task with structural constraints, through which the great power of gradient-based methods can be exploited to address the causal discovery problem. Despite their statistical validity, these approaches return causal graphs with spurious edges in the presence of latent variables. In this paper, we generalize the gradient-based method to accommodate the existence of latent confounders and latent intermediate variables. Specifically, we propose a causal discovery method based on latent variable reconstruction. This method primarily consists of two stages. In the first stage, we propose a series of causal models that includes latent variables, which can be applied to different data assumptions. However, due to the influence of latent variables, the causal graph inevitably contains reversed edges. In light of this fact, we propose the method to correct these reversed edges on the second stage via variational autoencoder. Theoretical results show that under some mild conditions, our method can correctly identify the causal relations. Experiments on both synthetic and real datasets demonstrate the superiority of our method to existing gradient-based learning algorithms in the presence of latent variables. [ABSTRACT FROM AUTHOR]