即使存在任意多个隐藏混杂因素，也能准确判断变量间的因果方向。
Identification of Causal Direction under an Arbitrary Number of Latent Confounders
- 利用观测变量的高阶累积量矩阵的秩缺陷特性识别因果方向。
- 在任意数量隐藏混杂下仍能正确识别因果关系，且无需迭代计算。
- 适用于真实世界中多重隐藏混杂场景，理论严谨且实验验证有效。
在存在隐藏变量的情况下恢复因果结构是一项重要但具有挑战性的任务。尽管已有多种方法提出，但多数依赖严格且不可检验的因果结构假设。现实中，观测变量常受多个隐藏变量同时影响，而现有方法难以处理此类情况。本文研究线性非高斯情形，通过特定构造的观测变量联合高阶累积量矩阵，发现令人惊讶的是：即使存在任意数量的隐藏混杂因素，两个观测变量之间的因果不对称性仍可直接从该矩阵的秩缺陷中看出。本文建立了可识别性理论，并提出了不涉及迭代过程的识别方法。实验结果表明所提方法具有有效性与渐近正确性。
原文摘要 · Abstract (English)
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.
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