Identification of Causal Structure with Latent Variables Based on Higher
  Order Cumulants
Wei Chen Zhiyi Huang Ruichu Cai Zhifeng Hao Kun Zhang
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.