Learning causality from observational data has received increasing interest across various scientific fields. However, most existing methods assume the absence of latent confounders and restrict the underlying causal graph to be acyclic, assumptions that are often violated in many real-world applications. In this paper, we address these challenges by proposing a novel framework for causal discovery that accommodates both cycles and latent confounders. By leveraging the identifiability results from noisy independent component analysis and recent advances in factor analysis, we establish the unique causal identifiability under mild conditions. Building on this foundation, we further develop a fully Bayesian approach for causal structure learning, called BayCausal, and evaluate its identifiability, utility, and superior performance against state-of-the-art alternatives through extensive simulation studies. Application to a dataset from the Women's Interagency HIV Study yields interpretable and clinically meaningful insights. To facilitate broader applications, we have implemented BayCausal in an R package, BayCausal, which is the first publicly available software capable of achieving unique causal identification in the presence of both cycles and latent confounders.

翻译：从观测数据中学习因果关系在多个科学领域受到日益增长的关注。然而，现有方法大多假设不存在潜在混杂因子，且要求基础因果图为无环结构，这些假设在实际应用中常被违背。本文通过提出一种新颖的因果发现框架来解决这些挑战，该框架同时兼容循环结构与潜在混杂因子。基于噪声独立成分分析的可识别性结果与因子分析的最新进展，我们在温和条件下建立了唯一的因果可识别性。在此基础上，我们进一步开发了一种完全贝叶斯的因果结构学习方法，称为BayCausal，并通过大量模拟研究评估了其可识别性、实用性及相对于前沿替代方法的优越性能。应用于女性艾滋病跨机构研究数据集，我们获得了具有可解释性与临床意义的洞见。为促进更广泛的应用，我们已将BayCausal实现为R软件包BayCausal，这是首个能够在存在循环与潜在混杂因子的情况下实现唯一因果识别的公开可用软件。