Causal discovery with latent confounders is an important but challenging task in many scientific areas. Despite the success of some overcomplete independent component analysis (OICA) based methods in certain domains, they are computationally expensive and can easily get stuck into local optima. We notice that interestingly, by making use of higher-order cumulants, there exists a closed-form solution to OICA in specific cases, e.g., when the mixing procedure follows the One-Latent-Component structure. In light of the power of the closed-form solution to OICA corresponding to the One-Latent-Component structure, we formulate a way to estimate the mixing matrix using the higher-order cumulants, and further propose the testable One-Latent-Component condition to identify the latent variables and determine causal orders. By iteratively removing the share identified latent components, we successfully extend the results on the One-Latent-Component structure to the Multi-Latent-Component structure and finally provide a practical and asymptotically correct algorithm to learn the causal structure with latent variables. Experimental results illustrate the asymptotic correctness and effectiveness of the proposed method.

翻译：含隐变量的因果发现是许多科学领域中重要但具有挑战性的任务。尽管某些基于过完全独立成分分析(OICA)的方法在特定领域取得了成功，但它们计算成本高且容易陷入局部最优解。有趣的是，我们发现通过利用高阶累积量，在特定情况下（例如当混合过程遵循单隐变量分量结构时）存在OICA的闭式解。鉴于与单隐变量分量结构对应的OICA闭式解的优势，我们提出了一种利用高阶累积量估计混合矩阵的方法，并进一步提出了可检验的单隐变量分量条件来识别隐变量并确定因果顺序。通过迭代移除已识别的共享隐变量分量，我们成功将单隐变量分量结构的结果推广到多隐变量分量结构，最终提出了一种实用且渐近正确的算法来学习含隐变量的因果结构。实验结果验证了所提方法的渐近正确性和有效性。