We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a finite number of different causal effects result in the same observational distribution. Most existing algorithms for identifying these causal effects use overcomplete independent component analysis (ICA), which often suffers from convergence to local optima. Furthermore, the number of latent variables must be known a priori. To address these issues, we propose an algorithm that operates recursively rather than using overcomplete ICA. The algorithm first infers a source, estimates the effect of the source and its latent parents on their descendants, and then eliminates their influence from the data. For both source identification and effect size estimation, we use rank conditions on matrices formed from higher-order cumulants. We prove asymptotic correctness under the mild assumption that locally, the number of latent variables never exceeds the number of observed variables. Simulation studies demonstrate that our method achieves comparable performance to overcomplete ICA even though it does not know the number of latents in advance.

本研究针对线性非高斯结构方程模型中存在未观测干扰的情况，提出了一种新的算法，旨在克服现有算法在局部最优解上易陷入的缺陷，同时避免对潜在变量数量的先验要求。该算法通过递归方式推断源并估计其对后代的影响，表现出与传统方法相当的性能，具有重要的实用价值。

具有未观测干扰的线性非高斯因果模型的因果发现