Identification of Causal Direction under an Arbitrary Number of Latent Confounders
This addresses a challenging issue in causal inference for real-world scenarios where existing methods fail due to strict assumptions, though it is incremental as it builds on linear, non-Gaussian models.
The paper tackles the problem of identifying causal direction between observed variables in the presence of multiple latent confounders, showing that causal asymmetry can be detected using higher-order cumulant matrices without iterative procedures, with experimental results confirming effectiveness and asymptotic correctness.
Recovering causal structure in the presence of latent variables is an important but challenging task. While many methods have been proposed to handle it, most of them require strict and/or untestable assumptions on the causal structure. In real-world scenarios, observed variables may be affected by multiple latent variables simultaneously, which, generally speaking, cannot be handled by these methods. In this paper, we consider the linear, non-Gaussian case, and make use of the joint higher-order cumulant matrix of the observed variables constructed in a specific way. We show that, surprisingly, causal asymmetry between two observed variables can be directly seen from the rank deficiency properties of such higher-order cumulant matrices, even in the presence of an arbitrary number of latent confounders. Identifiability results are established, and the corresponding identification methods do not even involve iterative procedures. Experimental results demonstrate the effectiveness and asymptotic correctness of our proposed method.