Identification of Causal Direction under an Arbitrary Number of Latent Confounders

TL;DR

This paper introduces a novel method for identifying causal direction between variables in the presence of multiple latent confounders using higher-order cumulant matrices, without strict assumptions or iterative procedures.

Contribution

It presents a new approach leveraging rank deficiency of cumulant matrices to detect causal asymmetry with arbitrary latent confounders in linear, non-Gaussian models.

Findings

Method accurately identifies causal direction in simulations.

The approach is effective even with multiple latent confounders.

The method is asymptotically correct and computationally efficient.

Abstract

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.