Title: Identification of Causal Relationships in Linear Cyclic Models with Latent Variables
Primary area: causal reasoning
Keywords: Causal Discovery, latent variables, cyclic  model

Abstract: Causal discovery aims to model the intricate mechanisms underlying complex systems. Numerous methods have been proposed to identify causal relationships from observational data, but they often assume that the causal model is acyclic and all variables are observed. Those methods risk yielding misleading or spurious causal relationships when confronted with the challenges posed by cycles and latent variables. To address these challenges, we propose a novel method that leverages higher-order cumulants to recover the causal structure among observed variables, even in the presence of cycles and latent variables. Specifically, we construct two cumulant matrices that incorporate various (joint) cumulants of the observed variables. By utilizing these matrices, we provide identifiability theories that determine the existence of cycles and latent variables based on the rank differences of the constructed cumulant matrix, and determine the causal relationship between two observed variables. This innovative method provides a robust framework for accurate causal discovery in complex systems with inherent cyclic and latent structures. Experimental results in simulated and real-world data demonstrate the effectiveness of our proposed method.