Bayesian estimation of possible causal direction in the presence of latent confounders using a linear non-Gaussian acyclic structural equation model with individual-specific effects

Abstract

We consider learning the possible causal direction of two observed variables in the presence of latent confounding variables. Several existing methods have been shown to consistently estimate causal direction assuming linear or some type of nonlinear relationship and no latent confounders. However, the estimation results could be distorted if either assumption is actually violated. In this paper, we first propose a new linear non-Gaussian acyclic structural equation model with individual-specific effects that allows latent confounders to be considered. We then propose an empirical Bayesian approach for estimating possible causal direction using the new model. We demonstrate the effectiveness of our method using artificial and real-world data.

21 pages, 4 figures. A revised version was accepted at Journal of Machine Learning Research

References in corpus (5)

• Strong Completeness and Faithfulness in Bayesian Networks
• Causal Inference on Discrete Data using Additive Noise Models
• Causal discovery of linear acyclic models with arbitrary distributions
• Bayesian Discovery of Linear Acyclic Causal Models
• Invariant Gaussian Process Latent Variable Models and Application in Causal Discovery