Identification of Causal Structure with Latent Variables Based on Higher Order Cumulants
This addresses a crucial but challenging task in causal inference for researchers, offering a novel method for a specific bottleneck in latent variable identification.
The paper tackles the problem of causal discovery with latent variables, specifically identifying when two observed variables are influenced by a latent variable and may have a causal edge between them, by using higher-order cumulants of non-Gaussian data to estimate causal coefficients and determine causal direction, with experimental results showing effectiveness.
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.