Causal Discovery for Linear Non-Gaussian Acyclic Models in the Presence of Latent Gaussian Confounders

LiNGAM has been successfully applied to casual inferences of some real world problems. Nevertheless, basic LiNGAM assumes that there is no latent confounder of the observed variables, which may not hold as the confounding effect is quite common in the real world. Causal discovery for LiNGAM in the presence of latent confounders is a more significant and challenging problem. In this paper, we propose a cumulant-based approach to the pairwise causal discovery for LiNGAM in the presence of latent confounders. The method assumes that the latent confounder is Gaussian distributed and statistically independent of the disturbances. We give a theoretical proof that in the presence of latent Gaussian confounders, the causal direction of the observed variables is identifiable under the mild condition that the disturbances are both super-gaussian or sub-gaussian. Experiments on synthesis data and real world data have been conducted to show the effectiveness of our proposed method.