Causal Discovery with Latent Confounders Based on Higher-Order Cumulants
Ruichu Cai Zhiyi Huang Wei Chen Zhifeng Hao Kun Zhang
Causal discovery with latent confounders is an important but challenging task
in many scientific areas. Despite the success of some overcomplete independent
component analysis (OICA) based methods in certain domains, they are
computationally expensive and can easily get stuck into local optima. We notice
that interestingly, by making use of higher-order cumulants, there exists a
closed-form solution to OICA in specific cases, e.g., when the mixing procedure
follows the One-Latent-Component structure. In light of the power of the
closed-form solution to OICA corresponding to the One-Latent-Component
structure, we formulate a way to estimate the mixing matrix using the
higher-order cumulants, and further propose the testable One-Latent-Component
condition to identify the latent variables and determine causal orders. By
iteratively removing the share identified latent components, we successfully
extend the results on the One-Latent-Component structure to the
Multi-Latent-Component structure and finally provide a practical and
asymptotically correct algorithm to learn the causal structure with latent
variables. Experimental results illustrate the asymptotic correctness and
effectiveness of the proposed method.