Identification of Causal Direction under an Arbitrary Number of Latent Confounders

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.

Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants

Federated causal discovery aims to uncover the causal relationships between entities while protecting data privacy, which has significant importance and numerous applications in real-world scenarios. Existing federated causal structure learning methods primarily focus on horizontal federated settings. However, in practical situations, different clients may not necessarily contain data on the same variables. In a single client, the incomplete set of variables can easily lead to spurious causal relationships, thereby affecting the information transmitted to other clients. To address this issue, we comprehensively consider causal structure learning methods under both horizontal and vertical federated settings. We provide the identification theories and methods for learning causal structure in the horizontal and vertical federal setting via higher-order cumulants. Specifically, we first aggregate higher-order cumulant information from all participating clients to construct global cumulant estimates. These global estimates are then used for recursive source identification, ultimately yielding a global causal strength matrix. Our approach not only enables the reconstruction of causal graphs but also facilitates the estimation of causal strength coefficients. Our algorithm demonstrates superior performance in experiments conducted on both synthetic data and real-world data.