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

TL;DR

This paper introduces a Bayesian method for determining causal direction between two variables in the presence of latent confounders, using a new linear non-Gaussian structural equation model with individual-specific effects.

Contribution

It proposes a novel linear non-Gaussian acyclic model with individual effects and an empirical Bayesian approach to estimate causal direction considering latent confounders.

Findings

Effective on artificial data

Demonstrates applicability on real-world data

Addresses limitations of existing methods

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.