Identification of Causal Structure with Latent Variables Based on Higher Order Cumulants

TL;DR

This paper introduces a novel method for causal discovery involving latent variables by utilizing higher-order cumulants of non-Gaussian data, providing analytical solutions and an asymmetry criterion for causal direction identification.

Contribution

The paper presents a new approach leveraging higher-order cumulants to identify causal structures with latent variables, including analytical estimation and direction determination.

Findings

Effective identification of causal edges influenced by latent variables.

Successful estimation of causal coefficients using higher-order cumulants.

Method demonstrates strong performance in experimental tests.

Abstract

Causal discovery with latent variables is a crucial but challenging task. Despite the emergence of numerous methods aimed at addressing this challenge, they are not fully identified to the structure that two observed variables are influenced by one latent variable and there might be a directed edge in between. Interestingly, we notice that this structure can be identified through the utilization of higher-order cumulants. By leveraging the higher-order cumulants of non-Gaussian data, we provide an analytical solution for estimating the causal coefficients or their ratios. With the estimated (ratios of) causal coefficients, we propose a novel approach to identify the existence of a causal edge between two observed variables subject to latent variable influence. In case when such a causal edge exits, we introduce an asymmetry criterion to determine the causal direction. The experimental results demonstrate the effectiveness of our proposed method.